11088 - End up with more teams/11088 11088 - End up with more teams/11088.2 11088 - End up with more teams/11088.2.cpp 11088 - End up with more teams/11088.3 11088 - End up with more teams/11088.3.cpp 11088 - End up with more teams/11088.cpp 11088 - End up with more teams/in.txt 11282 - Mixing invitations/11282 11282 - Mixing invitations/11282.cpp 11481 - Arrange the Numbers/11481 11481 - Arrange the Numbers/11481.cpp 11481 - Arrange the Numbers/in.txt 11484 - Document Object Model/document 11488 - Hyper prefix sets/11488 11488 - Hyper prefix sets/11488.cpp 11488 - Hyper prefix sets/in.txt Documentation/gridpaper.pdf Mi manual de algoritmos/version_maraton_interuniversitaria_2008-2/manual.out Mi manual de algoritmos/version_maraton_interuniversitaria_2008-2/src/combinatoria/highlight.sh Mi manual de algoritmos/version_maraton_interuniversitaria_2008-2/src/combinatoria/pascal_triangle.cpp Mi manual de algoritmos/version_maraton_interuniversitaria_2008-2/src/combinatoria/pascal_triangle.tex Mi manual de algoritmos/version_maraton_interuniversitaria_2008-2/src/dp/highlight.sh Mi manual de algoritmos/version_maraton_interuniversitaria_2008-2/src/dp/particion_troncos.cpp Mi manual de algoritmos/version_maraton_interuniversitaria_2008-2/src/dp/particion_troncos.tex Mi manual de algoritmos/version_maraton_interuniversitaria_2008-2/src/geometria/highlight.sh Mi manual de algoritmos/version_maraton_interuniversitaria_2008-2/src/geometria/is_convex_polygon.cpp Mi manual de algoritmos/version_maraton_interuniversitaria_2008-2/src/geometria/is_convex_polygon.tex Mi manual de algoritmos/version_maraton_interuniversitaria_2008-2/src/geometria/is_inside_concave_polygon.cpp Mi manual de algoritmos/version_maraton_interuniversitaria_2008-2/src/geometria/is_inside_concave_polygon.tex Mi manual de algoritmos/version_maraton_interuniversitaria_2008-2/src/geometria/is_inside_convex_polygon.cpp Mi manual de algoritmos/version_maraton_interuniversitaria_2008-2/src/geometria/is_inside_convex_polygon.tex Mi manual de algoritmos/version_maraton_interuniversitaria_2008-2/src/geometria/polygon_area.cpp Mi manual de algoritmos/version_maraton_interuniversitaria_2008-2/src/geometria/polygon_area.tex Mi manual de algoritmos/version_maraton_interuniversitaria_2008-2/src/grafos/bellman.cpp Mi manual de algoritmos/version_maraton_interuniversitaria_2008-2/src/grafos/bellman.tex Mi manual de algoritmos/version_maraton_interuniversitaria_2008-2/src/highlight.sh Mi manual de algoritmos/version_maraton_interuniversitaria_2008-2/src/java/highlight.sh Mi manual de algoritmos/version_maraton_interuniversitaria_2008-2/src/java/maps_sets.java Mi manual de algoritmos/version_maraton_interuniversitaria_2008-2/src/java/maps_sets.tex Mi manual de algoritmos/version_maraton_interuniversitaria_2008-2/src/java/priority_queue.java Mi manual de algoritmos/version_maraton_interuniversitaria_2008-2/src/java/priority_queue.tex Mi manual de algoritmos/version_maraton_interuniversitaria_2008-2/src/misc/highlight.sh Mi manual de algoritmos/version_maraton_interuniversitaria_2008-2/src/misc/parser_recursivo_desc.cpp Mi manual de algoritmos/version_maraton_interuniversitaria_2008-2/src/misc/parser_recursivo_desc.tex Mi manual de algoritmos/version_maraton_interuniversitaria_2008-2/src/number_theory/highlight.sh Mi manual de algoritmos/version_maraton_nacional_2008/manual.aux Mi manual de algoritmos/version_maraton_nacional_2008/manual.dvi Mi manual de algoritmos/version_maraton_nacional_2008/manual.log Mi manual de algoritmos/version_maraton_nacional_2008/manual.lol Mi manual de algoritmos/version_maraton_nacional_2008/manual.out Mi manual de algoritmos/version_maraton_nacional_2008/manual.pdf Mi manual de algoritmos/version_maraton_nacional_2008/manual.ps Mi manual de algoritmos/version_maraton_nacional_2008/manual.tex Mi manual de algoritmos/version_maraton_nacional_2008/manual.toc Mi manual de algoritmos/version_maraton_nacional_2008/src/c++/fgetws.cpp Mi manual de algoritmos/version_maraton_nacional_2008/src/c++/fgetws.tex Mi manual de algoritmos/version_maraton_nacional_2008/src/c++/io_file.cpp Mi manual de algoritmos/version_maraton_nacional_2008/src/c++/io_file.tex Mi manual de algoritmos/version_maraton_nacional_2008/src/c++/unicode.cpp Mi manual de algoritmos/version_maraton_nacional_2008/src/c++/unicode.tex Mi manual de algoritmos/version_maraton_nacional_2008/src/combinatoria/highlight.sh Mi manual de algoritmos/version_maraton_nacional_2008/src/combinatoria/pascal_triangle.cpp Mi manual de algoritmos/version_maraton_nacional_2008/src/combinatoria/pascal_triangle.tex Mi manual de algoritmos/version_maraton_nacional_2008/src/dp/highlight.sh Mi manual de algoritmos/version_maraton_nacional_2008/src/dp/lcs.cpp Mi manual de algoritmos/version_maraton_nacional_2008/src/dp/lcs.tex Mi manual de algoritmos/version_maraton_nacional_2008/src/dp/particion_troncos.cpp Mi manual de algoritmos/version_maraton_nacional_2008/src/dp/particion_troncos.tex Mi manual de algoritmos/version_maraton_nacional_2008/src/geometria/distance_point_to_line.cpp Mi manual de algoritmos/version_maraton_nacional_2008/src/geometria/distance_point_to_line.tex Mi manual de algoritmos/version_maraton_nacional_2008/src/geometria/distance_point_to_segment.cpp Mi manual de algoritmos/version_maraton_nacional_2008/src/geometria/distance_point_to_segment.tex Mi manual de algoritmos/version_maraton_nacional_2008/src/geometria/grahamscan.cpp Mi manual de algoritmos/version_maraton_nacional_2008/src/geometria/grahamscan.tex Mi manual de algoritmos/version_maraton_nacional_2008/src/geometria/highlight.sh Mi manual de algoritmos/version_maraton_nacional_2008/src/geometria/is_convex_polygon.cpp Mi manual de algoritmos/version_maraton_nacional_2008/src/geometria/is_convex_polygon.tex Mi manual de algoritmos/version_maraton_nacional_2008/src/geometria/is_inside_concave_polygon.cpp Mi manual de algoritmos/version_maraton_nacional_2008/src/geometria/is_inside_concave_polygon.tex Mi manual de algoritmos/version_maraton_nacional_2008/src/geometria/is_inside_convex_polygon.cpp Mi manual de algoritmos/version_maraton_nacional_2008/src/geometria/is_inside_convex_polygon.tex Mi manual de algoritmos/version_maraton_nacional_2008/src/geometria/monotonechain.cpp Mi manual de algoritmos/version_maraton_nacional_2008/src/geometria/monotonechain.tex Mi manual de algoritmos/version_maraton_nacional_2008/src/geometria/polygon_area.cpp Mi manual de algoritmos/version_maraton_nacional_2008/src/geometria/polygon_area.tex Mi manual de algoritmos/version_maraton_nacional_2008/src/grafos/bellman.cpp Mi manual de algoritmos/version_maraton_nacional_2008/src/grafos/bellman.tex Mi manual de algoritmos/version_maraton_nacional_2008/src/grafos/dijkstra.cpp Mi manual de algoritmos/version_maraton_nacional_2008/src/grafos/dijkstra.tex Mi manual de algoritmos/version_maraton_nacional_2008/src/grafos/floyd.cpp Mi manual de algoritmos/version_maraton_nacional_2008/src/grafos/floyd.tex Mi manual de algoritmos/version_maraton_nacional_2008/src/grafos/ford_fulkerson.cpp Mi manual de algoritmos/version_maraton_nacional_2008/src/grafos/ford_fulkerson.tex Mi manual de algoritmos/version_maraton_nacional_2008/src/grafos/highlight.sh Mi manual de algoritmos/version_maraton_nacional_2008/src/grafos/kruskal.cpp Mi manual de algoritmos/version_maraton_nacional_2008/src/grafos/kruskal.tex Mi manual de algoritmos/version_maraton_nacional_2008/src/grafos/prim.cpp Mi manual de algoritmos/version_maraton_nacional_2008/src/grafos/prim.tex Mi manual de algoritmos/version_maraton_nacional_2008/src/grafos/puntos_articulacion.cpp Mi manual de algoritmos/version_maraton_nacional_2008/src/grafos/puntos_articulacion.tex Mi manual de algoritmos/version_maraton_nacional_2008/src/highlight.sh Mi manual de algoritmos/version_maraton_nacional_2008/src/java/.tex Mi manual de algoritmos/version_maraton_nacional_2008/src/java/highlight.sh Mi manual de algoritmos/version_maraton_nacional_2008/src/java/io_estandar.java Mi manual de algoritmos/version_maraton_nacional_2008/src/java/io_estandar.tex Mi manual de algoritmos/version_maraton_nacional_2008/src/java/io_estandar_easy.java Mi manual de algoritmos/version_maraton_nacional_2008/src/java/io_estandar_easy.tex Mi manual de algoritmos/version_maraton_nacional_2008/src/java/io_file.java Mi manual de algoritmos/version_maraton_nacional_2008/src/java/io_file.tex Mi manual de algoritmos/version_maraton_nacional_2008/src/java/maps_sets.java Mi manual de algoritmos/version_maraton_nacional_2008/src/java/maps_sets.tex Mi manual de algoritmos/version_maraton_nacional_2008/src/java/priority_queue.java Mi manual de algoritmos/version_maraton_nacional_2008/src/java/priority_queue.tex Mi manual de algoritmos/version_maraton_nacional_2008/src/misc/highlight.sh Mi manual de algoritmos/version_maraton_nacional_2008/src/misc/parser_recursivo_desc.cpp Mi manual de algoritmos/version_maraton_nacional_2008/src/misc/parser_recursivo_desc.tex Mi manual de algoritmos/version_maraton_nacional_2008/src/number_theory/bigmod.cpp Mi manual de algoritmos/version_maraton_nacional_2008/src/number_theory/bigmod.tex Mi manual de algoritmos/version_maraton_nacional_2008/src/number_theory/criba.cpp Mi manual de algoritmos/version_maraton_nacional_2008/src/number_theory/criba.tex Mi manual de algoritmos/version_maraton_nacional_2008/src/number_theory/divisores.cpp Mi manual de algoritmos/version_maraton_nacional_2008/src/number_theory/divisores.tex Mi manual de algoritmos/version_maraton_nacional_2008/src/number_theory/highlight.sh @@ -22,7 +22,8 @@ ostream& operator<< (ostream& out, const point& c) //P es un polígono ordenado anticlockwise. //Si es clockwise, retorna el area negativa. -//Si no esta ordenado retorna pura mierda +//Si no esta ordenado retorna pura mierda. +//P[0] != P[n-1] double area(const vector<point> &p){ double r = 0.0; for (int i=0; i<p.size(); ++i){ 10065 - Useless tile packers/10065.2.cpp @@ -1,80 +1,80 @@ -#include <iostream> -#include <vector> -#include <stack> -#include <string> -#include <cassert> -using namespace std; - -#define D(x) cout << #x " es " << x << endl - -int main(){ - int n, C=1; - while (cin >> n && n){ - string line; - getline(cin, line); - int m = n/2; - string content[m]; - int parent[m]; - parent[0] = -10000; - vector<int> childs[m]; - stack<int> stk; - for (int x = 0, i = 0; x < n; ++x){ - getline(cin, line); - if (line == "</n>"){ - stk.pop(); - }else{ - string s = ""; - int j = line.find_first_of("'"); - char delimiter = line[j]; - while (assert(j < line.size()), line[++j] != delimiter){ - s += line[j]; - } - content[i] = s; - if (stk.size() > 0){ - childs[stk.top()].push_back(i); - parent[i] = stk.top(); - //D(parent[i]), D(content[i]); - } - stk.push(i); - ++i; - } - } - - int p = 0, q = 0; //p = nodo en donde estoy, q = id de p en la lista de sus hermanos - int I; - cout << "Case " << C++ << ":" << endl; - cin >> I; - while (I--){ - string s; - cin >> s; - int x, y; - //D(s), D(p), D(q); - bool valid = true; - if (s == "first_child"){ - if (childs[p].size() <= 0) valid = false; - else{ - x = childs[p][0]; - y = 0; - } - }else if (s == "next_sibling"){ - y = q+1; - if (parent[p] < 0 || y >= childs[parent[p]].size()) valid = false; - else x = childs[parent[p]][y]; - }else if (s == "previous_sibling"){ - y = q-1; - if (parent[p] < 0 || y < 0 || y >= childs[parent[p]].size()) valid = false; - else x = childs[parent[p]][y]; - }else if (s == "parent"){ - x = parent[p], y = 0; - if (x < 0) valid = false; - } - //D(valid); - if (valid){ - cout << content[x] << endl; - p = x, q = y; - } - else cout << content[p] << endl; - } - } - return 0; -} +#include <iostream> +#include <vector> +#include <stack> +#include <string> +#include <cassert> +using namespace std; + +#define D(x) cout << #x " es " << x << endl + +int main(){ + int n, C=1; + while (cin >> n && n){ + string line; + getline(cin, line); + int m = n/2; + string content[m]; + int parent[m]; + parent[0] = -10000; + vector<int> childs[m]; + stack<int> stk; + for (int x = 0, i = 0; x < n; ++x){ + getline(cin, line); + if (line == "</n>"){ + stk.pop(); + }else{ + string s = ""; + int j = line.find_first_of("'"); + char delimiter = line[j]; + while (assert(j < line.size()), line[++j] != delimiter){ + s += line[j]; + } + content[i] = s; + if (stk.size() > 0){ + childs[stk.top()].push_back(i); + parent[i] = stk.top(); + //D(parent[i]), D(content[i]); + } + stk.push(i); + ++i; + } + } + + int p = 0, q = 0; //p = nodo en donde estoy, q = id de p en la lista de sus hermanos + int I; + cout << "Case " << C++ << ":" << endl; + cin >> I; + while (I--){ + string s; + cin >> s; + int x, y; + //D(s), D(p), D(q); + bool valid = true; + if (s == "first_child"){ + if (childs[p].size() <= 0) valid = false; + else{ + x = childs[p][0]; + y = 0; + } + }else if (s == "next_sibling"){ + y = q+1; + if (parent[p] < 0 || y >= childs[parent[p]].size()) valid = false; + else x = childs[parent[p]][y]; + }else if (s == "previous_sibling"){ + y = q-1; + if (parent[p] < 0 || y < 0 || y >= childs[parent[p]].size()) valid = false; + else x = childs[parent[p]][y]; + }else if (s == "parent"){ + x = parent[p], y = 0; + if (x < 0) valid = false; + } + //D(valid); + if (valid){ + cout << content[x] << endl; + p = x, q = y; + } + else cout << content[p] << endl; + } + } + return 0; +} 11484 - Document Object Model/document.cpp @@ -1,51 +1,78 @@ -6 -<n value='parent'> -<n value='child'> -</n> -<n value='me'> -</n> -</n> -0 - -10 -<n value='a'> -<n value='b'> -</n> -<n value='c'> -</n> -<n value='d'> -</n> -<n value='e'> -</n> -</n> -19 -next_sibling -previous_sibling -first_child -parent -parent -first_child -next_sibling -next_sibling -next_sibling -next_sibling -next_sibling -next_sibling -next_sibling -next_sibling -next_sibling -next_sibling -first_child -previous_sibling -parent - - -4 -<n value='parent'> -<n value='child'> -</n> -</n> -2 -next_sibling -first_child -0 \ No newline at end of file +6 +<n value='parent'> +<n value='child'> +</n> +<n value='me'> +</n> +</n> +8 +parent +parent +first_child +next_sibling +previous_sibling +previous_sibling +next_sibling +first_child + +12 +<n value='a'> +<n value='b'> +</n> +<n value='c'> +</n> +<n value='d'> +</n> +<n value='e'> +<n value='f'> +</n> +</n> +</n> +32 +next_sibling +previous_sibling +first_child +parent +parent +first_child +next_sibling +next_sibling +next_sibling +next_sibling +next_sibling +next_sibling +next_sibling +next_sibling +next_sibling +next_sibling +first_child +previous_sibling +parent +parent +first_child +next_sibling +next_sibling +next_sibling +next_sibling +next_sibling +previous_sibling +next_sibling +first_child +previous_sibling +parent +parent + +4 +<n value='parent'> +<n value='child'> +</n> +</n> +6 +next_sibling +first_child +first_child +parent +parent +parent + +0 11484 - Document Object Model/in.txt @@ -5,33 +5,60 @@ \catcode`<\active \catcode`>\active \es@quoting +\ifx\hyper@anchor\@undefined +\global \let \oldcontentsline\contentsline +\gdef \contentsline#1#2#3#4{\oldcontentsline{#1}{#2}{#3}} +\global \let \oldnewlabel\newlabel +\gdef \newlabel#1#2{\newlabelxx{#1}#2} +\gdef \newlabelxx#1#2#3#4#5#6{\oldnewlabel{#1}{{#2}{#3}}} +\AtEndDocument{\let \contentsline\oldcontentsline +\let \newlabel\oldnewlabel} +\else +\global \let \hyper@last\relax +\fi + \select@language{spanish} \@writefile{toc}{\select@language{spanish}} \@writefile{lof}{\select@language{spanish}} \@writefile{lot}{\select@language{spanish}} -\@writefile{toc}{\contentsline {section}{\numberline {1}Teor\IeC {\'\i }a de n\IeC {\'u}meros}{1}} -\@writefile{toc}{\contentsline {subsection}{\numberline {1.1}Big mod}{1}} -\@writefile{toc}{\contentsline {subsection}{\numberline {1.2}Criba de Erat\IeC {\'o}stenes}{2}} -\@writefile{toc}{\contentsline {subsection}{\numberline {1.3}Divisores de un n\IeC {\'u}mero}{2}} -\@writefile{toc}{\contentsline {section}{\numberline {2}Grafos}{2}} -\@writefile{toc}{\contentsline {subsection}{\numberline {2.1}Algoritmo de Dijkstra}{2}} -\@writefile{toc}{\contentsline {subsection}{\numberline {2.2}Minimum spanning tree: Algoritmo de Prim}{3}} -\@writefile{toc}{\contentsline {subsection}{\numberline {2.3}Minimum spanning tree: Algoritmo de Kruskal + Union-Find}{5}} -\@writefile{toc}{\contentsline {subsection}{\numberline {2.4}Algoritmo de Floyd}{6}} -\@writefile{toc}{\contentsline {subsection}{\numberline {2.5}Puntos de articulaci\IeC {\'o}n}{7}} -\@writefile{toc}{\contentsline {subsection}{\numberline {2.6}M\IeC {\'a}ximo flujo: M\IeC {\'e}todo de Ford-Fulkerson, algoritmo de Edmonds-Karp}{8}} -\@writefile{toc}{\contentsline {section}{\numberline {3}Programaci\IeC {\'o}n din\IeC {\'a}mica}{9}} -\@writefile{toc}{\contentsline {subsection}{\numberline {3.1}Longest common subsequence}{9}} -\@writefile{toc}{\contentsline {section}{\numberline {4}Geometr\IeC {\'\i }a}{9}} -\@writefile{toc}{\contentsline {subsection}{\numberline {4.1}\IeC {\'A}rea de un pol\IeC {\'\i }gono}{9}} -\@writefile{toc}{\contentsline {subsection}{\numberline {4.2}Centro de masa de un pol\IeC {\'\i }gono}{10}} -\@writefile{toc}{\contentsline {subsection}{\numberline {4.3}Convex hull: Graham Scan}{10}} -\@writefile{toc}{\contentsline {subsection}{\numberline {4.4}Convex hull: Andrew's monotone chain}{12}} -\@writefile{toc}{\contentsline {subsection}{\numberline {4.5}M\IeC {\'\i }nima distancia entre un punto y un segmento}{13}} -\@writefile{toc}{\contentsline {subsection}{\numberline {4.6}M\IeC {\'\i }nima distancia entre un punto y una recta}{13}} -\@writefile{toc}{\contentsline {section}{\numberline {5}Java}{14}} -\@writefile{toc}{\contentsline {subsection}{\numberline {5.1}Entrada desde entrada est\IeC {\'a}ndar}{14}} -\@writefile{toc}{\contentsline {subsection}{\numberline {5.2}Entrada desde archivo}{15}} -\@writefile{toc}{\contentsline {section}{\numberline {6}C++}{15}} -\@writefile{toc}{\contentsline {subsection}{\numberline {6.1}Entrada desde archivo}{15}} -\@writefile{toc}{\contentsline {subsection}{\numberline {6.2}Strings con caract\IeC {\'e}res especiales}{16}} +\@writefile{toc}{\contentsline {section}{\numberline {1}Teor\IeC {\'\i }a de n\IeC {\'u}meros}{2}{section.1}} +\@writefile{toc}{\contentsline {subsection}{\numberline {1.1}Big mod}{2}{subsection.1.1}} +\@writefile{toc}{\contentsline {subsection}{\numberline {1.2}Criba de Erat\IeC {\'o}stenes}{2}{subsection.1.2}} +\@writefile{toc}{\contentsline {subsection}{\numberline {1.3}Divisores de un n\IeC {\'u}mero}{3}{subsection.1.3}} +\@writefile{toc}{\contentsline {section}{\numberline {2}Combinatoria}{3}{section.2}} +\@writefile{toc}{\contentsline {subsection}{\numberline {2.1}Cuadro resumen}{3}{subsection.2.1}} +\@writefile{toc}{\contentsline {subsection}{\numberline {2.2}Combinaciones, coeficientes binomiales, tri\IeC {\'a}ngulo de Pascal}{3}{subsection.2.2}} +\@writefile{toc}{\contentsline {subsection}{\numberline {2.3}Permutaciones con elementos indistinguibles}{4}{subsection.2.3}} +\@writefile{toc}{\contentsline {subsection}{\numberline {2.4}Desordenes, desarreglos o permutaciones completas}{4}{subsection.2.4}} +\@writefile{toc}{\contentsline {section}{\numberline {3}Grafos}{4}{section.3}} +\@writefile{toc}{\contentsline {subsection}{\numberline {3.1}Algoritmo de Dijkstra}{4}{subsection.3.1}} +\@writefile{toc}{\contentsline {subsection}{\numberline {3.2}Minimum spanning tree: Algoritmo de Prim}{5}{subsection.3.2}} +\@writefile{toc}{\contentsline {subsection}{\numberline {3.3}Minimum spanning tree: Algoritmo de Kruskal + Union-Find}{6}{subsection.3.3}} +\@writefile{toc}{\contentsline {subsection}{\numberline {3.4}Algoritmo de Floyd-Warshall}{7}{subsection.3.4}} +\@writefile{toc}{\contentsline {subsection}{\numberline {3.5}Algoritmo de Bellman-Ford}{8}{subsection.3.5}} +\@writefile{toc}{\contentsline {subsection}{\numberline {3.6}Puntos de articulaci\IeC {\'o}n}{9}{subsection.3.6}} +\@writefile{toc}{\contentsline {subsection}{\numberline {3.7}M\IeC {\'a}ximo flujo: M\IeC {\'e}todo de Ford-Fulkerson, algoritmo de Edmonds-Karp}{10}{subsection.3.7}} +\@writefile{toc}{\contentsline {section}{\numberline {4}Programaci\IeC {\'o}n din\IeC {\'a}mica}{11}{section.4}} +\@writefile{toc}{\contentsline {subsection}{\numberline {4.1}Longest common subsequence}{11}{subsection.4.1}} +\@writefile{toc}{\contentsline {subsection}{\numberline {4.2}Partici\IeC {\'o}n de troncos}{12}{subsection.4.2}} +\@writefile{toc}{\contentsline {section}{\numberline {5}Geometr\IeC {\'\i }a}{13}{section.5}} +\@writefile{toc}{\contentsline {subsection}{\numberline {5.1}\IeC {\'A}rea de un pol\IeC {\'\i }gono}{13}{subsection.5.1}} +\@writefile{toc}{\contentsline {subsection}{\numberline {5.2}Centro de masa de un pol\IeC {\'\i }gono}{14}{subsection.5.2}} +\@writefile{toc}{\contentsline {subsection}{\numberline {5.3}Convex hull: Graham Scan}{14}{subsection.5.3}} +\@writefile{toc}{\contentsline {subsection}{\numberline {5.4}Convex hull: Andrew's monotone chain}{16}{subsection.5.4}} +\@writefile{toc}{\contentsline {subsection}{\numberline {5.5}M\IeC {\'\i }nima distancia entre un punto y un segmento}{17}{subsection.5.5}} +\@writefile{toc}{\contentsline {subsection}{\numberline {5.6}M\IeC {\'\i }nima distancia entre un punto y una recta}{17}{subsection.5.6}} +\@writefile{toc}{\contentsline {subsection}{\numberline {5.7}Determinar si un pol\IeC {\'\i }gono es convexo}{17}{subsection.5.7}} +\@writefile{toc}{\contentsline {subsection}{\numberline {5.8}Determinar si un punto est\IeC {\'a} dentro de un pol\IeC {\'\i }gono convexo}{18}{subsection.5.8}} +\@writefile{toc}{\contentsline {subsection}{\numberline {5.9}Determinar si un punto est\IeC {\'a} dentro de un pol\IeC {\'\i }gono cualquiera}{18}{subsection.5.9}} +\@writefile{toc}{\contentsline {section}{\numberline {6}Miscel\IeC {\'a}neo}{20}{section.6}} +\@writefile{toc}{\contentsline {subsection}{\numberline {6.1}El \textit {parser} m\IeC {\'a}s r\IeC {\'a}pido del mundo}{20}{subsection.6.1}} +\@writefile{toc}{\contentsline {section}{\numberline {7}Java}{21}{section.7}} +\@writefile{toc}{\contentsline {subsection}{\numberline {7.1}Entrada desde entrada est\IeC {\'a}ndar}{21}{subsection.7.1}} +\@writefile{toc}{\contentsline {subsection}{\numberline {7.2}Entrada desde archivo}{22}{subsection.7.2}} +\@writefile{toc}{\contentsline {subsection}{\numberline {7.3}Mapas y sets}{23}{subsection.7.3}} +\@writefile{toc}{\contentsline {subsection}{\numberline {7.4}Colas de prioridad}{24}{subsection.7.4}} +\newlabel{colas_de_prioridad_java}{{7.4}{24}{Colas de prioridad\relax }{subsection.7.4}{}} +\@writefile{toc}{\contentsline {section}{\numberline {8}C++}{25}{section.8}} +\@writefile{toc}{\contentsline {subsection}{\numberline {8.1}Entrada desde archivo}{25}{subsection.8.1}} +\@writefile{toc}{\contentsline {subsection}{\numberline {8.2}Strings con caract\IeC {\'e}res especiales}{26}{subsection.8.2}} Mi manual de algoritmos/version_maraton_interuniversitaria_2008-2/manual.aux Mi manual de algoritmos/version_maraton_interuniversitaria_2008-2/manual.dvi @@ -1,4 +1,4 @@ -This is pdfTeXk, Version 3.141592-1.40.3 (Web2C 7.5.6) (format=pdflatex 2008.2.17) 14 SEP 2008 20:50 +This is pdfTeXk, Version 3.141592-1.40.3 (Web2C 7.5.6) (format=pdflatex 2008.2.17) 20 SEP 2008 00:15 entering extended mode %&-line parsing enabled. **manual.tex @@ -363,25 +363,101 @@ LaTeX Font Info: Redeclaring font encoding OMS on input line 568. \mathdisplay@stack=\toks23 LaTeX Info: Redefining \[ on input line 2666. LaTeX Info: Redefining \] on input line 2667. +) +(/usr/share/texmf-texlive/tex/latex/tools/verbatim.sty +Package: verbatim 2003/08/22 v1.5q LaTeX2e package for verbatim enhancements +\every@verbatim=\toks24 +\verbatim@line=\toks25 +\verbatim@in@stream=\read1 +) +(/usr/share/texmf-texlive/tex/latex/hyperref/hyperref.sty +Package: hyperref 2007/02/07 v6.75r Hypertext links for LaTeX +\@linkdim=\dimen117 +\Hy@linkcounter=\count111 +\Hy@pagecounter=\count112 + +(/usr/share/texmf-texlive/tex/latex/hyperref/pd1enc.def +File: pd1enc.def 2007/02/07 v6.75r Hyperref: PDFDocEncoding definition (HO) +Now handling font encoding PD1 ... +... no UTF-8 mapping file for font encoding PD1 +) +(/etc/texmf/tex/latex/config/hyperref.cfg +File: hyperref.cfg 2002/06/06 v1.2 hyperref configuration of TeXLive +) +(/usr/share/texmf-texlive/tex/latex/oberdiek/kvoptions.sty +Package: kvoptions 2006/08/22 v2.4 Connects package keyval with LaTeX options ( +HO) +) +Package hyperref Info: Hyper figures OFF on input line 2288. +Package hyperref Info: Link nesting OFF on input line 2293. +Package hyperref Info: Hyper index ON on input line 2296. +Package hyperref Info: Plain pages OFF on input line 2303. +Package hyperref Info: Backreferencing OFF on input line 2308. + +Implicit mode ON; LaTeX internals redefined +Package hyperref Info: Bookmarks ON on input line 2444. +(/usr/share/texmf-texlive/tex/latex/ltxmisc/url.sty +\Urlmuskip=\muskip11 +Package: url 2005/06/27 ver 3.2 Verb mode for urls, etc. +) +LaTeX Info: Redefining \url on input line 2599. +\Fld@menulength=\count113 +\Field@Width=\dimen118 +\Fld@charsize=\dimen119 +\Choice@toks=\toks26 +\Field@toks=\toks27 +Package hyperref Info: Hyper figures OFF on input line 3102. +Package hyperref Info: Link nesting OFF on input line 3107. +Package hyperref Info: Hyper index ON on input line 3110. +Package hyperref Info: backreferencing OFF on input line 3117. +Package hyperref Info: Link coloring OFF on input line 3122. +\Hy@abspage=\count114 +\c@Item=\count115 +\c@Hfootnote=\count116 +) +*hyperref using default driver hpdftex* +(/usr/share/texmf-texlive/tex/latex/hyperref/hpdftex.def +File: hpdftex.def 2007/02/07 v6.75r Hyperref driver for pdfTeX +\Fld@listcount=\count117 ) (./manual.aux) \openout1 = `manual.aux'. -LaTeX Font Info: Checking defaults for OML/cmm/m/it on input line 18. -LaTeX Font Info: ... okay on input line 18. -LaTeX Font Info: Checking defaults for T1/cmr/m/n on input line 18. -LaTeX Font Info: ... okay on input line 18. -LaTeX Font Info: Checking defaults for OT1/cmr/m/n on input line 18. -LaTeX Font Info: ... okay on input line 18. -LaTeX Font Info: Checking defaults for OMS/cmsy/m/n on input line 18. -LaTeX Font Info: ... okay on input line 18. -LaTeX Font Info: Checking defaults for OMX/cmex/m/n on input line 18. -LaTeX Font Info: ... okay on input line 18. -LaTeX Font Info: Checking defaults for U/cmr/m/n on input line 18. -LaTeX Font Info: ... okay on input line 18. - -(./manual.toc) -\tf@toc=\write3 -\openout3 = `manual.toc'. +LaTeX Font Info: Checking defaults for OML/cmm/m/it on input line 20. +LaTeX Font Info: ... okay on input line 20. +LaTeX Font Info: Checking defaults for T1/cmr/m/n on input line 20. +LaTeX Font Info: ... okay on input line 20. +LaTeX Font Info: Checking defaults for OT1/cmr/m/n on input line 20. +LaTeX Font Info: ... okay on input line 20. +LaTeX Font Info: Checking defaults for OMS/cmsy/m/n on input line 20. +LaTeX Font Info: ... okay on input line 20. +LaTeX Font Info: Checking defaults for OMX/cmex/m/n on input line 20. +LaTeX Font Info: ... okay on input line 20. +LaTeX Font Info: Checking defaults for U/cmr/m/n on input line 20. +LaTeX Font Info: ... okay on input line 20. +LaTeX Font Info: Checking defaults for PD1/pdf/m/n on input line 20. +LaTeX Font Info: ... okay on input line 20. +Package hyperref Info: Link coloring OFF on input line 20. + +(/usr/share/texmf-texlive/tex/latex/hyperref/nameref.sty +Package: nameref 2006/12/27 v2.28 Cross-referencing by name of section + +(/usr/share/texmf-texlive/tex/latex/oberdiek/refcount.sty +Package: refcount 2006/02/20 v3.0 Data extraction from references (HO) +) +\c@section@level=\count118 +) +LaTeX Info: Redefining \ref on input line 20. +LaTeX Info: Redefining \pageref on input line 20. + (./manual.out) +(./manual.out) +\@outlinefile=\write3 +\openout3 = `manual.out'. + + (./manual.toc [1 + +{/var/lib/texmf/fonts/map/pdftex/updmap/pdftex.map}]) +\tf@toc=\write4 +\openout4 = `manual.toc'. (/usr/share/texmf-texlive/tex/latex/listings/lstlang1.sty File: lstlang1.sty 2004/09/05 1.3 listings language file @@ -397,36 +473,72 @@ LaTeX Font Warning: Font shape `OMS/cmtt/m/n' undefined (Font) using `OMS/cmsy/m/n' instead (Font) for symbol `textbraceleft' on input line 8. -) [1 +) (./src/number_theory/criba.tex [2]) (./src/number_theory/divisores.tex) -{/var/lib/texmf/fonts/map/pdftex/updmap/pdftex.map}] -(./src/number_theory/criba.tex) (./src/number_theory/divisores.tex) -(./src/grafos/dijkstra.tex [2] +Package amsmath Warning: Foreign command \atopwithdelims; +(amsmath) \frac or \genfrac should be used instead +(amsmath) on input line 101. + +(./src/combinatoria/pascal_triangle.tex) [3] (./src/grafos/dijkstra.tex LaTeX Font Info: Font shape `OT1/cmtt/bx/n' in size <7> not available (Font) Font shape `OT1/cmtt/m/n' tried instead on input line 30. LaTeX Font Info: Font shape `OT1/cmtt/bx/n' in size <5> not available (Font) Font shape `OT1/cmtt/m/n' tried instead on input line 30. -) (./src/grafos/prim.tex [3] [4]) -(./src/grafos/kruskal.tex [5] + +[4]) (./src/grafos/prim.tex [5]) (./src/grafos/kruskal.tex [6] LaTeX Font Warning: Font shape `OMS/cmtt/m/it' undefined (Font) using `OMS/cmtt/m/n' instead -(Font) for symbol `textbackslash' on input line 55. +(Font) for symbol `textbackslash' on input line 54. + +) (./src/grafos/floyd.tex [7]) (./src/grafos/bellman.tex [8]) +(./src/grafos/puntos_articulacion.tex [9]) (./src/grafos/ford_fulkerson.tex +[10]) (./src/dp/lcs.tex) [11] (./src/dp/particion_troncos.tex [12]) +(./src/geometria/polygon_area.tex [13]) (./src/geometria/grahamscan.tex +[14] [15]) (./src/geometria/monotonechain.tex [16]) +(./src/geometria/distance_point_to_segment.tex) +(./src/geometria/distance_point_to_line.tex) +(./src/geometria/is_convex_polygon.tex [17]) +(./src/geometria/is_inside_convex_polygon.tex) +(./src/geometria/is_inside_concave_polygon.tex [18] +LaTeX Font Info: Font shape `OT1/cmtt/bx/n' in size <12> not available +(Font) Font shape `OT1/cmtt/m/n' tried instead on input line 12. + [19]) +(./src/misc/parser_recursivo_desc.tex [20]) (./src/java/io_estandar_easy.tex) +(./src/java/io_estandar.tex [21]) (./src/java/io_file.tex [22]) +(./src/java/maps_sets.tex [23]) +Underfull \hbox (badness 10000) in paragraph at lines 316--316 + + [] + + +Underfull \hbox (badness 10000) in paragraph at lines 316--316 + + [] + +(./src/java/priority_queue.tex [24]) +Underfull \hbox (badness 10000) in paragraph at lines 341--341 + + [] -) (./src/grafos/floyd.tex [6]) (./src/grafos/puntos_articulacion.tex [7]) -(./src/grafos/ford_fulkerson.tex [8]) (./src/dp/lcs.tex) [9] -(./src/geometria/grahamscan.tex [10] [11]) (./src/geometria/monotonechain.tex -[12]) (./src/geometria/distance_point_to_segment.tex) -(./src/geometria/distance_point_to_line.tex [13]) -(./src/java/io_estandar_easy.tex) (./src/java/io_estandar.tex [14]) -(./src/java/io_file.tex) (./src/c++/io_file.tex [15]) (./src/c++/unicode.tex) -(./src/c++/fgetws.tex [16]) [17] (./manual.aux) +(./src/c++/io_file.tex [25]) (./src/c++/unicode.tex) (./src/c++/fgetws.tex +[26]) [27] (./manual.aux) LaTeX Font Warning: Some font shapes were not available, defaults substituted. ) -(\end occurred inside a group at level 20) +(\end occurred inside a group at level 30) +### simple group (level 30) entered at line 3 ({) +### simple group (level 29) entered at line 3 ({) +### simple group (level 28) entered at line 3 ({) +### simple group (level 27) entered at line 3 ({) +### simple group (level 26) entered at line 3 ({) +### simple group (level 25) entered at line 3 ({) +### simple group (level 24) entered at line 3 ({) +### simple group (level 23) entered at line 3 ({) +### simple group (level 22) entered at line 3 ({) +### simple group (level 21) entered at line 3 ({) ### simple group (level 20) entered at line 3 ({) ### simple group (level 19) entered at line 3 ({) ### simple group (level 18) entered at line 3 ({) @@ -449,26 +561,32 @@ LaTeX Font Warning: Some font shapes were not available, defaults substituted. ### simple group (level 1) entered at line 3 ({) ### bottom level Here is how much of TeX's memory you used: - 3460 strings out of 95001 - 44570 string characters out of 1181560 - 106384 words of memory out of 1500000 - 6570 multiletter control sequences out of 10000+50000 - 6630 words of font info for 26 fonts, out of 1200000 for 2000 + 5496 strings out of 95001 + 74605 string characters out of 1181560 + 141213 words of memory out of 1500000 + 8457 multiletter control sequences out of 10000+50000 + 11689 words of font info for 44 fonts, out of 1200000 for 2000 80 hyphenation exceptions out of 8191 - 27i,6n,32p,933b,1339s stack positions out of 5000i,500n,6000p,200000b,5000s + 27i,8n,36p,933b,2422s stack positions out of 5000i,500n,6000p,200000b,5000s </usr/share/texmf-texlive/fonts/type1/bluesky/cm/cmbx10.pfb></u sr/share/texmf-texlive/fonts/type1/bluesky/cm/cmbx12.pfb></usr/share/texmf-texl -ive/fonts/type1/bluesky/cm/cmex10.pfb></usr/share/texmf-texlive/fonts/type1/blu -esky/cm/cmitt10.pfb></usr/share/texmf-texlive/fonts/type1/bluesky/cm/cmmi10.pfb -></usr/share/texmf-texlive/fonts/type1/bluesky/cm/cmmi7.pfb></usr/share/texmf-t -exlive/fonts/type1/bluesky/cm/cmr10.pfb></usr/share/texmf-texlive/fonts/type1/b -luesky/cm/cmr7.pfb></usr/share/texmf-texlive/fonts/type1/bluesky/cm/cmsy10.pfb> -</usr/share/texmf-texlive/fonts/type1/bluesky/cm/cmsy7.pfb></usr/share/texmf-te -xlive/fonts/type1/bluesky/cm/cmti10.pfb></usr/share/texmf-texlive/fonts/type1/b -luesky/cm/cmtt10.pfb> -Output written on manual.pdf (17 pages, 125809 bytes). +ive/fonts/type1/bluesky/cm/cmbx9.pfb></usr/share/texmf-texlive/fonts/type1/blue +sky/cm/cmbxti10.pfb></usr/share/texmf-texlive/fonts/type1/bluesky/cm/cmex10.pfb +></usr/share/texmf-texlive/fonts/type1/bluesky/cm/cmitt10.pfb></usr/share/texmf +-texlive/fonts/type1/bluesky/cm/cmmi10.pfb></usr/share/texmf-texlive/fonts/type +1/bluesky/cm/cmmi12.pfb></usr/share/texmf-texlive/fonts/type1/bluesky/cm/cmmi7. +pfb></usr/share/texmf-texlive/fonts/type1/bluesky/cm/cmr10.pfb></usr/share/texm +f-texlive/fonts/type1/bluesky/cm/cmr12.pfb></usr/share/texmf-texlive/fonts/type +1/bluesky/cm/cmr17.pfb></usr/share/texmf-texlive/fonts/type1/bluesky/cm/cmr7.pf +b></usr/share/texmf-texlive/fonts/type1/bluesky/cm/cmr9.pfb></usr/share/texmf-t +exlive/fonts/type1/bluesky/cm/cmsy10.pfb></usr/share/texmf-texlive/fonts/type1/ +bluesky/cm/cmsy7.pfb></usr/share/texmf-texlive/fonts/type1/bluesky/cm/cmti10.pf +b></usr/share/texmf-texlive/fonts/type1/bluesky/cm/cmti9.pfb></usr/share/texmf- +texlive/fonts/type1/bluesky/cm/cmtt10.pfb></usr/share/texmf-texlive/fonts/type1 +/bluesky/cm/cmtt12.pfb> +Output written on manual.pdf (27 pages, 231829 bytes). PDF statistics: - 105 PDF objects out of 1000 (max. 8388607) - 0 named destinations out of 1000 (max. 131072) - 1 words of extra memory for PDF output out of 10000 (max. 10000000) + 421 PDF objects out of 1000 (max. 8388607) + 69 named destinations out of 1000 (max. 131072) + 337 words of extra memory for PDF output out of 10000 (max. 10000000) Mi manual de algoritmos/version_maraton_interuniversitaria_2008-2/manual.log Mi manual de algoritmos/version_maraton_interuniversitaria_2008-2/manual.pdf @@ -6,6 +6,8 @@ \usepackage{listings} \usepackage[usenames,dvipsnames]{color} \usepackage{amsmath} +\usepackage{verbatim} +\usepackage{hyperref} %\usepackage{color} %--------------------------------------------------------------- @@ -21,7 +23,7 @@ \title{Resumen de algoritmos para torneos de programación} \author{Andrés Mejía} \date{\today} -%\maketitle +\maketitle %--------------------------------------------------------------- %--------------------------------------------------------------- @@ -33,20 +35,27 @@ \section{Teoría de números} %--------------------------------------------------------------- \subsection{Big mod} - \input{./src/number_theory/bigmod}%.tex \subsection{Criba de Eratóstenes} +\small +\textbf{Field-testing:} +\begin{itemize} +\item \emph{SPOJ} - 2912 - Super Primes +\item \emph{Live Archive} - 3639 - Prime Path +\end{itemize} + +\normalsize Marca los números primos en un arreglo. Algunos tiempos de ejecución: \begin{center} \begin{tabular}{c c} \hline\hline SIZE & Tiempo (s) \\ [0.5ex] \hline -100000 & 0.004 \\ -1000000 & 0.078 \\ -10000000 & 1.550 \\ -100000000 & 14.319 \\ [1ex] +100000 & 0.003 \\ +1000000 & 0.060 \\ +10000000 & 0.620 \\ +100000000 & 7.650 \\ [1ex] \hline \end{tabular} \end{center} @@ -63,6 +72,74 @@ responder muy lento. \input{./src/number_theory/divisores}%.tex +\section{Combinatoria} +\subsection{Cuadro resumen} +Fórmulas para combinaciones y permutaciones: +\begin{center} +\renewcommand{\arraystretch}{2} %Multiplica la altura de cada fila de la tabla por 2 +%Si quiero aumentar el tamaño de una fila en particular insertar \rule{0cm}{1cm} en esa fila. +\begin{tabular}{| c | c | c |} +\hline +\textit{Tipo} & \textit{¿Se permite la repetición?} & \textit{Fórmula} \\ [1.5ex] +\hline\hline + +$r$-permutaciones & No & $ \displaystyle\frac{n!}{(n-r)!} $ \\ [1.5ex] +\hline +$r$-combinaciones & No & $ \displaystyle\frac{n!}{r!(n-r)!} $ \\ [1.5ex] +\hline +$r$-permutaciones & Sí & $ \displaystyle n^{r} $ \\ +\hline +$r$-combinaciones & Sí & $ \displaystyle\frac{(n+r-1)!}{r!(n-1)!} $ \\ [1.5ex] +\hline +\end{tabular} +\renewcommand{\arraystretch}{1} +\end{center} +Tomado de \textit{Matemática discreta y sus aplicaciones}, Kenneth Rosen, 5${}^{\hbox{ta}}$ edición, McGraw-Hill, página 315. + +\subsection{Combinaciones, coeficientes binomiales, triángulo de Pascal} +\emph{Complejidad:} $ O(n^2) $ \\ +$$ {n \choose k} = \left\{ +\begin{array}{c l} + 1 & k = 0\\ + 1 & n = k\\ + \displaystyle {n - 1 \choose k - 1} + {n - 1 \choose k} & \mbox{en otro caso}\\ +\end{array} +\right. +$$ + +\input{./src/combinatoria/pascal_triangle}%.tex + +\bigskip +\textbf{Nota:} $ \displaystyle {n \choose k } $ está indefinido en el código anterior si $ n > k$. ¡La tabla puede estar llena con cualquier basura del compilador! + +\subsection{Permutaciones con elementos indistinguibles} +El número de permutaciones \underline{diferentes} de $n$ objetos, donde hay $n_{1}$ objetos indistinguibles de tipo 1, +$n_{2}$ objetos indistinguibles de tipo 2, ..., y $n_{k}$ objetos indistinguibles de tipo $k$, es +$$ +\frac{n!}{n_{1}!n_{2}! \cdots n_{k}!} +$$ +\textbf{Ejemplo:} Con las letras de la palabra \texttt{PROGRAMAR} se pueden formar $ \displaystyle \frac{9!}{2! \cdot 3!} = +30240 $ permutaciones \underline{diferentes}. +\subsection{Desordenes, desarreglos o permutaciones completas} + +Un desarreglo es una permutación donde ningún elemento $i$ está en la +posición $i$-ésima. Por ejemplo, \textit{4213} es un desarreglo de 4 elementos pero +\textit{3241} no lo es porque el 2 aparece en la posición 2. + +Sea $D_{n}$ el número de desarreglos de $n$ elementos, entonces: +$$ {D_{n}} = \left\{ +\begin{array}{c l} + 1 & n = 0\\ + 0 & n = 1\\ + (n-1)(D_{n-1} + D_{n-2}) & n \geq 2\\ +\end{array} +\right. +$$ +Usando el principio de inclusión-exclusión, también se puede encontrar la fórmula +$$ +D_{n} = n!\left [ 1 - \frac{1}{1!} + \frac{1}{2!} - \frac{1}{3!} + \cdots + (-1)^{n}\frac{1}{n!} \right ] += n! \sum_{i=0}^{n} \frac{(-1)^{i}}{i!} +$$ \section{Grafos} \subsection{Algoritmo de Dijkstra} @@ -77,9 +154,17 @@ El peso de todas las aristas debe ser no negativo. \subsection{Minimum spanning tree: Algoritmo de Kruskal + Union-Find} \input{./src/grafos/kruskal}%.tex -\subsection{Algoritmo de Floyd} +\subsection{Algoritmo de Floyd-Warshall} +\emph{Complejidad:} $ O(n^3) $ \\ +Se asume que no hay ciclos de costo negativo. \input{./src/grafos/floyd}%.tex +\subsection{Algoritmo de Bellman-Ford} +Si no hay ciclos de coste negativo, encuentra la distancia más corta entre un nodo +y todos los demás. Si sí hay, permite saberlo. \\ +El coste de las aristas \underline{sí} puede ser negativo. +\input{./src/grafos/bellman}%.tex + \subsection{Puntos de articulación} \input{./src/grafos/puntos_articulacion}%.tex @@ -93,11 +178,37 @@ es utilizar BFS que lo hace más eficiente en algunos grafos. \subsection{Longest common subsequence} \input{./src/dp/lcs}%.tex +\subsection{Partición de troncos} +Este problema es similar al problema de \textit{Matrix Chain Multiplication}. Se tiene +un tronco de longitud $n$, y $m$ puntos de corte en el tronco. Se puede hacer un corte a la vez, +cuyo costo es igual a la longitud del tronco. ¿Cuál es el mínimo costo para partir todo el tronco +en pedacitos individuales? +\\ +\medskip +\textbf{Ejemplo:} Se tiene un tronco de longitud 10. Los puntos de corte son 2, 4, y 7. El mínimo +costo para partirlo es 20, y se obtiene así: +\begin{itemize} +\item Partir el tronco (0, 10) por 4. Vale 10 y quedan los troncos (0, 4) y (4, 10). +\item Partir el tronco (0, 4) por 2. Vale 4 y quedan los troncos (0, 2), (2, 4) y (4, 10). +\item No hay que partir el tronco (0, 2). +\item No hay que partir el tronco (2, 4). +\item Partir el tronco (4, 10) por 7. Vale 6 y quedan los troncos (4, 7) y (7, 10). +\item No hay que partir el tronco (4, 7). +\item No hay que partir el tronco (7, 10). +\item El costo total es $10+4+6 = 20$. +\end{itemize} + +\medskip +El algoritmo es $O(n^3)$, pero optimizable a $O(n^2)$ con una tabla adicional: +\input{./src/dp/particion_troncos}%.tex + \section{Geometría} \subsection{Área de un polígono} Si P es un polígono simple (no se intersecta a sí mismo) su área está dada por: \\ $ A(P) = \frac{1}{2} \displaystyle\sum_{i=0}^{n-1} (x_{i} \cdot y_{i+1} - x_{i+1} \cdot y_{i}) $ \\ +\bigskip +\input{./src/geometria/polygon_area}%.tex \subsection{Centro de masa de un polígono} Si P es un polígono simple (no se intersecta a sí mismo) su centro de masa está dado por: \\ @@ -134,7 +245,40 @@ $ \displaystyle\bar{C}_{y} = \frac{1}{6A} \sum_{i=0}^{n-1} (y_{i} + y_{i+1}) (x_ \subsection{Mínima distancia entre un punto y una recta} \input{./src/geometria/distance_point_to_line}%.tex + +\subsection{Determinar si un polígono es convexo} +\input{./src/geometria/is_convex_polygon}%.tex + +\subsection{Determinar si un punto está dentro de un polígono convexo} +\input{./src/geometria/is_inside_convex_polygon}%.tex + +\subsection{Determinar si un punto está dentro de un polígono cualquiera} +\large{\textbf{ADVERTENCIA:}} Código no probado. +\input{./src/geometria/is_inside_concave_polygon}%.tex + %--------------------------------------------------------------- +\section{Misceláneo} +\subsection{El \textit{parser} más rápido del mundo} +\begin{itemize} +\item Cada no-terminal: un método +\item Cada lado derecho: invocar los métodos de los no-terminales o +\item Cada terminal: invocar proceso \textit{match} +\item Alternativas en una producción: se hace un \textit{if} +\end{itemize} +\medskip +No funciona con gramáticas recursivas por izquierda ó en las que en algún momento haya +varias posibles escogencias que empiezan por el mismo caracter (En ambos casos la gramática se puede factorizar). + +\medskip +\textbf{Ejemplo:} Para la gramática: +$$ +A \longrightarrow (A)A +$$ $$ +A \longrightarrow \epsilon +$$ + +\input{./src/misc/parser_recursivo_desc}%.tex + \section{Java} \subsection{Entrada desde entrada estándar} @@ -148,6 +292,59 @@ Este segundo es más rápido: \\ \subsection{Entrada desde archivo} \input{./src/java/io_file}%.tex +\subsection{Mapas y sets} +Programa de ejemplo: +\input{./src/java/maps_sets}%.tex +\bigskip +La salida de este programa es: \\ + +\ttfamily +\fbox{\parbox{2.0in}{ +Maps\\ +m.size() = 1\\ +465\\ +null\\ +\\ +Sets\\ +54 presente.\\ +s.size() = 3\\ +54\\ +3576\\ +1000000007\\ +s.size() = 0\\ +} +} +\\ \normalfont\normalsize +\bigskip +Si quiere usarse una clase propia como llave del mapa o como elemento del set, la clase debe implementar +algunos métodos especiales: Si va a usarse un TreeMap ó TreeSet hay que implementar los métodos \texttt{compareTo} y +\texttt{equals} de la interfaz \texttt{Comparable} como en la sección \ref{colas_de_prioridad_java}. Si va a usarse +un HashMap ó HashSet hay más complicaciones.\\ +\smallskip +\textbf{Sugerencia:} Inventar una manera de codificar y decodificar la clase en una String o un Integer y meter esa representación en el mapa o set: esas clases ya tienen los métodos implementados. + +\subsection{Colas de prioridad} +\label{colas_de_prioridad_java} +Hay que implementar unos métodos. Veamos un ejemplo: \\ +\input{./src/java/priority_queue}%.tex +\bigskip +La salida de este programa es: \\ + +\ttfamily +\fbox{\parbox{2.0in}{ +peso = 0, destino = 12\\ +peso = 0, destino = 8\\ +peso = 0, destino = 13\\ +peso = 3, destino = 7\\ +peso = 1876, destino = 4\\ +} +} +\\ \normalfont\normalsize +\medskip +Vemos que la función de comparación que definimos no tiene en cuenta \texttt{destino}, +por eso no desempata cuando dos \texttt{Items} tienen el mismo \texttt{peso} si no que escoge +cualquiera de manera arbitraria. + \section{C++} \subsection{Entrada desde archivo} \input{./src/c++/io_file}%.tex Mi manual de algoritmos/version_maraton_interuniversitaria_2008-2/manual.tex @@ -1,27 +1,41 @@ \select@language {spanish} -\contentsline {section}{\numberline {1}Teor\IeC {\'\i }a de n\IeC {\'u}meros}{1} -\contentsline {subsection}{\numberline {1.1}Big mod}{1} -\contentsline {subsection}{\numberline {1.2}Criba de Erat\IeC {\'o}stenes}{2} -\contentsline {subsection}{\numberline {1.3}Divisores de un n\IeC {\'u}mero}{2} -\contentsline {section}{\numberline {2}Grafos}{2} -\contentsline {subsection}{\numberline {2.1}Algoritmo de Dijkstra}{2} -\contentsline {subsection}{\numberline {2.2}Minimum spanning tree: Algoritmo de Prim}{3} -\contentsline {subsection}{\numberline {2.3}Minimum spanning tree: Algoritmo de Kruskal + Union-Find}{5} -\contentsline {subsection}{\numberline {2.4}Algoritmo de Floyd}{6} -\contentsline {subsection}{\numberline {2.5}Puntos de articulaci\IeC {\'o}n}{7} -\contentsline {subsection}{\numberline {2.6}M\IeC {\'a}ximo flujo: M\IeC {\'e}todo de Ford-Fulkerson, algoritmo de Edmonds-Karp}{8} -\contentsline {section}{\numberline {3}Programaci\IeC {\'o}n din\IeC {\'a}mica}{9} -\contentsline {subsection}{\numberline {3.1}Longest common subsequence}{9} -\contentsline {section}{\numberline {4}Geometr\IeC {\'\i }a}{9} -\contentsline {subsection}{\numberline {4.1}\IeC {\'A}rea de un pol\IeC {\'\i }gono}{9} -\contentsline {subsection}{\numberline {4.2}Centro de masa de un pol\IeC {\'\i }gono}{10} -\contentsline {subsection}{\numberline {4.3}Convex hull: Graham Scan}{10} -\contentsline {subsection}{\numberline {4.4}Convex hull: Andrew's monotone chain}{12} -\contentsline {subsection}{\numberline {4.5}M\IeC {\'\i }nima distancia entre un punto y un segmento}{13} -\contentsline {subsection}{\numberline {4.6}M\IeC {\'\i }nima distancia entre un punto y una recta}{13} -\contentsline {section}{\numberline {5}Java}{14} -\contentsline {subsection}{\numberline {5.1}Entrada desde entrada est\IeC {\'a}ndar}{14} -\contentsline {subsection}{\numberline {5.2}Entrada desde archivo}{15} -\contentsline {section}{\numberline {6}C++}{15} -\contentsline {subsection}{\numberline {6.1}Entrada desde archivo}{15} -\contentsline {subsection}{\numberline {6.2}Strings con caract\IeC {\'e}res especiales}{16} +\contentsline {section}{\numberline {1}Teor\IeC {\'\i }a de n\IeC {\'u}meros}{2}{section.1} +\contentsline {subsection}{\numberline {1.1}Big mod}{2}{subsection.1.1} +\contentsline {subsection}{\numberline {1.2}Criba de Erat\IeC {\'o}stenes}{2}{subsection.1.2} +\contentsline {subsection}{\numberline {1.3}Divisores de un n\IeC {\'u}mero}{3}{subsection.1.3} +\contentsline {section}{\numberline {2}Combinatoria}{3}{section.2} +\contentsline {subsection}{\numberline {2.1}Cuadro resumen}{3}{subsection.2.1} +\contentsline {subsection}{\numberline {2.2}Combinaciones, coeficientes binomiales, tri\IeC {\'a}ngulo de Pascal}{3}{subsection.2.2} +\contentsline {subsection}{\numberline {2.3}Permutaciones con elementos indistinguibles}{4}{subsection.2.3} +\contentsline {subsection}{\numberline {2.4}Desordenes, desarreglos o permutaciones completas}{4}{subsection.2.4} +\contentsline {section}{\numberline {3}Grafos}{4}{section.3} +\contentsline {subsection}{\numberline {3.1}Algoritmo de Dijkstra}{4}{subsection.3.1} +\contentsline {subsection}{\numberline {3.2}Minimum spanning tree: Algoritmo de Prim}{5}{subsection.3.2} +\contentsline {subsection}{\numberline {3.3}Minimum spanning tree: Algoritmo de Kruskal + Union-Find}{6}{subsection.3.3} +\contentsline {subsection}{\numberline {3.4}Algoritmo de Floyd-Warshall}{7}{subsection.3.4} +\contentsline {subsection}{\numberline {3.5}Algoritmo de Bellman-Ford}{8}{subsection.3.5} +\contentsline {subsection}{\numberline {3.6}Puntos de articulaci\IeC {\'o}n}{9}{subsection.3.6} +\contentsline {subsection}{\numberline {3.7}M\IeC {\'a}ximo flujo: M\IeC {\'e}todo de Ford-Fulkerson, algoritmo de Edmonds-Karp}{10}{subsection.3.7} +\contentsline {section}{\numberline {4}Programaci\IeC {\'o}n din\IeC {\'a}mica}{11}{section.4} +\contentsline {subsection}{\numberline {4.1}Longest common subsequence}{11}{subsection.4.1} +\contentsline {subsection}{\numberline {4.2}Partici\IeC {\'o}n de troncos}{12}{subsection.4.2} +\contentsline {section}{\numberline {5}Geometr\IeC {\'\i }a}{13}{section.5} +\contentsline {subsection}{\numberline {5.1}\IeC {\'A}rea de un pol\IeC {\'\i }gono}{13}{subsection.5.1} +\contentsline {subsection}{\numberline {5.2}Centro de masa de un pol\IeC {\'\i }gono}{14}{subsection.5.2} +\contentsline {subsection}{\numberline {5.3}Convex hull: Graham Scan}{14}{subsection.5.3} +\contentsline {subsection}{\numberline {5.4}Convex hull: Andrew's monotone chain}{16}{subsection.5.4} +\contentsline {subsection}{\numberline {5.5}M\IeC {\'\i }nima distancia entre un punto y un segmento}{17}{subsection.5.5} +\contentsline {subsection}{\numberline {5.6}M\IeC {\'\i }nima distancia entre un punto y una recta}{17}{subsection.5.6} +\contentsline {subsection}{\numberline {5.7}Determinar si un pol\IeC {\'\i }gono es convexo}{17}{subsection.5.7} +\contentsline {subsection}{\numberline {5.8}Determinar si un punto est\IeC {\'a} dentro de un pol\IeC {\'\i }gono convexo}{18}{subsection.5.8} +\contentsline {subsection}{\numberline {5.9}Determinar si un punto est\IeC {\'a} dentro de un pol\IeC {\'\i }gono cualquiera}{18}{subsection.5.9} +\contentsline {section}{\numberline {6}Miscel\IeC {\'a}neo}{20}{section.6} +\contentsline {subsection}{\numberline {6.1}El \textit {parser} m\IeC {\'a}s r\IeC {\'a}pido del mundo}{20}{subsection.6.1} +\contentsline {section}{\numberline {7}Java}{21}{section.7} +\contentsline {subsection}{\numberline {7.1}Entrada desde entrada est\IeC {\'a}ndar}{21}{subsection.7.1} +\contentsline {subsection}{\numberline {7.2}Entrada desde archivo}{22}{subsection.7.2} +\contentsline {subsection}{\numberline {7.3}Mapas y sets}{23}{subsection.7.3} +\contentsline {subsection}{\numberline {7.4}Colas de prioridad}{24}{subsection.7.4} +\contentsline {section}{\numberline {8}C++}{25}{section.8} +\contentsline {subsection}{\numberline {8.1}Entrada desde archivo}{25}{subsection.8.1} +\contentsline {subsection}{\numberline {8.2}Strings con caract\IeC {\'e}res especiales}{26}{subsection.8.2} Mi manual de algoritmos/version_maraton_interuniversitaria_2008-2/manual.toc @@ -1,11 +1,17 @@ +/* + Graham Scan. + */ #include <iostream> #include <vector> #include <algorithm> #include <iterator> -#include <cmath> +#include <math.h> +#include <stdio.h> using namespace std; +const double pi = 2*acos(0); + struct point{ int x,y; point() {} @@ -20,88 +26,56 @@ ostream& operator<< (ostream& out, const point& c) return out; } -//P es un polígono ordenado anticlockwise. -//Si es clockwise, retorna el area negativa. -//Si no esta ordenado retorna pura mierda -double area(const vector<point> &p){ - double r = 0.0; - for (int i=0; i<p.size(); ++i){ - int j = (i+1) % p.size(); - r += p[i].x*p[j].y - p[j].x*p[i].y; - } - return r/2.0; +inline int distsqr(const point &a, const point &b){ + return (a.x - b.x)*(a.x - b.x) + (a.y - b.y)*(a.y - b.y); +} + +inline double dist(const point &a, const point &b){ + return sqrt(distsqr(a, b)); } -//retorna si c esta a la izquierda de el segmento AB +//retorna > 0 si c esta a la izquierda del segmento AB +//retorna < 0 si c esta a la derecha del segmento AB +//retorna == 0 si c es colineal con el segmento AB inline int cross(const point &a, const point &b, const point &c){ return (b.x-a.x)*(c.y-a.y) - (c.x-a.x)*(b.y-a.y); } //Self < that si esta a la derecha del segmento Pivot-That bool angleCmp(const point &self, const point &that){ - return( cross(pivot, that, self) < 0 ); -} - -inline int distsqr(const point &a, const point &b){ - return (a.x - b.x)*(a.x - b.x) + (a.y - b.y)*(a.y - b.y); + int t = cross(pivot, that, self); + if (t < 0) return true; + if (t == 0){ + //Self < that si está más cerquita + return (distsqr(pivot, self) < distsqr(pivot, that)); + } + return false; } -//vector p tiene los puntos ordenados anticlockwise vector<point> graham(vector<point> p){ + //Metemos el más abajo más a la izquierda en la posición 0 + for (int i=1; i<p.size(); ++i){ + if (p[i].y < p[0].y || (p[i].y == p[0].y && p[i].x < p[0].x )) + swap(p[0], p[i]); + } + pivot = p[0]; sort(p.begin(), p.end(), angleCmp); + //Ordenar por ángulo y eliminar repetidos. - //Si varios puntos tienen el mismo angulo se borran todos excepto el que esté más lejos - for (int i=1; i<p.size()-1; ++i){ - if (cross(p[0], p[i], p[i+1]) == 0){ //Si son colineales... - if (distsqr(p[0], p[i]) < distsqr(p[0], p[i+1])){ //Borrar el mas cercano - p.erase(p.begin() + i); - }else{ - p.erase(p.begin() + i + 1); - } - i--; - } - } - + //Si varios puntos tienen el mismo angulo el más lejano queda después en la lista vector<point> chull(p.begin(), p.begin()+3); //Ahora sí!!! for (int i=3; i<p.size(); ++i){ - while ( chull.size() >= 2 && cross(chull[chull.size()-2], chull[chull.size()-1], p[i]) < 0){ + while ( chull.size() >= 2 && cross(chull[chull.size()-2], chull[chull.size()-1], p[i]) <= 0){ chull.erase(chull.end() - 1); } chull.push_back(p[i]); } - + //chull contiene los puntos del convex hull ordenados anti-clockwise. + //No contiene ningún punto repetido. + //El primer punto no es el mismo que el último, i.e, la última arista + //va de chull[chull.size()-1] a chull[0] return chull; } - -int main(){ - int n; - int tileNo = 1; - while (cin >> n && n){ - vector<point> p; - point min(10000, 10000); - int minPos; - for (int i=0; i<n; ++i){ - int x, y; - cin >> x >> y; - p.push_back(point(x,y)); - if (y < min.y || (y == min.y && x < min.x )){ - min = point(x,y); - minPos = i; - } - } - double tileArea = fabs(area(p)); - - //Destruye el orden cw|ccw poligono, pero hay que hacerlo por que Graham necesita el pivote en p[0] - swap(p[0], p[minPos]); - pivot = p[0]; - double chullArea = fabs(area(graham(p))); - - printf("Tile #%d\n", tileNo++); - printf("Wasted Space = %.2f \%\n\n", (chullArea - tileArea) * 100.0 / chullArea); - - } - return 0; -} Mi manual de algoritmos/version_maraton_interuniversitaria_2008-2/src/geometria/grahamscan.cpp @@ -2,14 +2,20 @@ {\ttfamily \raggedright { \noindent +\mbox{}\textit{\textcolor{Brown}{/*}} \\ +\mbox{}\textit{\textcolor{Brown}{\ \ Graham\ Scan.}} \\ +\mbox{}\textit{\textcolor{Brown}{\ */}} \\ \mbox{}\textbf{\textcolor{RoyalBlue}{\#include}}\ \texttt{\textcolor{Red}{$<$iostream$>$}} \\ \mbox{}\textbf{\textcolor{RoyalBlue}{\#include}}\ \texttt{\textcolor{Red}{$<$vector$>$}} \\ \mbox{}\textbf{\textcolor{RoyalBlue}{\#include}}\ \texttt{\textcolor{Red}{$<$algorithm$>$}} \\ \mbox{}\textbf{\textcolor{RoyalBlue}{\#include}}\ \texttt{\textcolor{Red}{$<$iterator$>$}} \\ -\mbox{}\textbf{\textcolor{RoyalBlue}{\#include}}\ \texttt{\textcolor{Red}{$<$cmath$>$}} \\ +\mbox{}\textbf{\textcolor{RoyalBlue}{\#include}}\ \texttt{\textcolor{Red}{$<$math.h$>$}} \\ +\mbox{}\textbf{\textcolor{RoyalBlue}{\#include}}\ \texttt{\textcolor{Red}{$<$stdio.h$>$}} \\ \mbox{} \\ \mbox{}\textbf{\textcolor{Blue}{using}}\ \textbf{\textcolor{Blue}{namespace}}\ std\textcolor{BrickRed}{;} \\ \mbox{} \\ +\mbox{}\textbf{\textcolor{Blue}{const}}\ \textcolor{ForestGreen}{double}\ pi\ \textcolor{BrickRed}{=}\ \textcolor{Purple}{2}\textcolor{BrickRed}{*}\textbf{\textcolor{Black}{acos}}\textcolor{BrickRed}{(}\textcolor{Purple}{0}\textcolor{BrickRed}{);} \\ +\mbox{} \\ \mbox{}\textbf{\textcolor{Blue}{struct}}\ point\textcolor{Red}{\{} \\ \mbox{}\ \ \textcolor{ForestGreen}{int}\ x\textcolor{BrickRed}{,}y\textcolor{BrickRed}{;} \\ \mbox{}\ \ \textbf{\textcolor{Black}{point}}\textcolor{BrickRed}{()}\ \textcolor{Red}{\{\}} \\ @@ -24,90 +30,58 @@ \mbox{}\ \ \textbf{\textcolor{Blue}{return}}\ out\textcolor{BrickRed}{;} \\ \mbox{}\textcolor{Red}{\}} \\ \mbox{} \\ -\mbox{}\textit{\textcolor{Brown}{//P\ es\ un\ polígono\ ordenado\ anticlockwise.}} \\ -\mbox{}\textit{\textcolor{Brown}{//Si\ es\ clockwise,\ retorna\ el\ area\ negativa.}} \\ -\mbox{}\textit{\textcolor{Brown}{//Si\ no\ esta\ ordenado\ retorna\ pura\ mierda}} \\ -\mbox{}\textcolor{ForestGreen}{double}\ \textbf{\textcolor{Black}{area}}\textcolor{BrickRed}{(}\textbf{\textcolor{Blue}{const}}\ vector\textcolor{BrickRed}{$<$}point\textcolor{BrickRed}{$>$}\ \textcolor{BrickRed}{\&}p\textcolor{BrickRed}{)}\textcolor{Red}{\{} \\ -\mbox{}\ \ \textcolor{ForestGreen}{double}\ r\ \textcolor{BrickRed}{=}\ \textcolor{Purple}{0.0}\textcolor{BrickRed}{;} \\ -\mbox{}\ \ \textbf{\textcolor{Blue}{for}}\ \textcolor{BrickRed}{(}\textcolor{ForestGreen}{int}\ i\textcolor{BrickRed}{=}\textcolor{Purple}{0}\textcolor{BrickRed}{;}\ i\textcolor{BrickRed}{$<$}p\textcolor{BrickRed}{.}\textbf{\textcolor{Black}{size}}\textcolor{BrickRed}{();}\ \textcolor{BrickRed}{++}i\textcolor{BrickRed}{)}\textcolor{Red}{\{} \\ -\mbox{}\ \ \ \ \textcolor{ForestGreen}{int}\ j\ \textcolor{BrickRed}{=}\ \textcolor{BrickRed}{(}i\textcolor{BrickRed}{+}\textcolor{Purple}{1}\textcolor{BrickRed}{)}\ \textcolor{BrickRed}{\%}\ p\textcolor{BrickRed}{.}\textbf{\textcolor{Black}{size}}\textcolor{BrickRed}{();} \\ -\mbox{}\ \ \ \ r\ \textcolor{BrickRed}{+=}\ p\textcolor{BrickRed}{[}i\textcolor{BrickRed}{].}x\textcolor{BrickRed}{*}p\textcolor{BrickRed}{[}j\textcolor{BrickRed}{].}y\ \textcolor{BrickRed}{-}\ p\textcolor{BrickRed}{[}j\textcolor{BrickRed}{].}x\textcolor{BrickRed}{*}p\textcolor{BrickRed}{[}i\textcolor{BrickRed}{].}y\textcolor{BrickRed}{;} \\ -\mbox{}\ \ \textcolor{Red}{\}} \\ -\mbox{}\ \ \textbf{\textcolor{Blue}{return}}\ r\textcolor{BrickRed}{/}\textcolor{Purple}{2.0}\textcolor{BrickRed}{;} \\ +\mbox{}\textbf{\textcolor{Blue}{inline}}\ \textcolor{ForestGreen}{int}\ \textbf{\textcolor{Black}{distsqr}}\textcolor{BrickRed}{(}\textbf{\textcolor{Blue}{const}}\ point\ \textcolor{BrickRed}{\&}a\textcolor{BrickRed}{,}\ \textbf{\textcolor{Blue}{const}}\ point\ \textcolor{BrickRed}{\&}b\textcolor{BrickRed}{)}\textcolor{Red}{\{} \\ +\mbox{}\ \ \textbf{\textcolor{Blue}{return}}\ \textcolor{BrickRed}{(}a\textcolor{BrickRed}{.}x\ \textcolor{BrickRed}{-}\ b\textcolor{BrickRed}{.}x\textcolor{BrickRed}{)*(}a\textcolor{BrickRed}{.}x\ \textcolor{BrickRed}{-}\ b\textcolor{BrickRed}{.}x\textcolor{BrickRed}{)}\ \textcolor{BrickRed}{+}\ \textcolor{BrickRed}{(}a\textcolor{BrickRed}{.}y\ \textcolor{BrickRed}{-}\ b\textcolor{BrickRed}{.}y\textcolor{BrickRed}{)*(}a\textcolor{BrickRed}{.}y\ \textcolor{BrickRed}{-}\ b\textcolor{BrickRed}{.}y\textcolor{BrickRed}{);} \\ +\mbox{}\textcolor{Red}{\}} \\ +\mbox{} \\ +\mbox{}\textbf{\textcolor{Blue}{inline}}\ \textcolor{ForestGreen}{double}\ \textbf{\textcolor{Black}{dist}}\textcolor{BrickRed}{(}\textbf{\textcolor{Blue}{const}}\ point\ \textcolor{BrickRed}{\&}a\textcolor{BrickRed}{,}\ \textbf{\textcolor{Blue}{const}}\ point\ \textcolor{BrickRed}{\&}b\textcolor{BrickRed}{)}\textcolor{Red}{\{} \\ +\mbox{}\ \ \textbf{\textcolor{Blue}{return}}\ \textbf{\textcolor{Black}{sqrt}}\textcolor{BrickRed}{(}\textbf{\textcolor{Black}{distsqr}}\textcolor{BrickRed}{(}a\textcolor{BrickRed}{,}\ b\textcolor{BrickRed}{));} \\ \mbox{}\textcolor{Red}{\}} \\ \mbox{} \\ -\mbox{}\textit{\textcolor{Brown}{//retorna\ si\ c\ esta\ a\ la\ izquierda\ de\ el\ segmento\ AB}} \\ +\mbox{}\textit{\textcolor{Brown}{//retorna\ $>$\ 0\ si\ c\ esta\ a\ la\ izquierda\ del\ segmento\ AB}} \\ +\mbox{}\textit{\textcolor{Brown}{//retorna\ $<$\ 0\ si\ c\ esta\ a\ la\ derecha\ del\ segmento\ AB}} \\ +\mbox{}\textit{\textcolor{Brown}{//retorna\ ==\ 0\ si\ c\ es\ colineal\ con\ el\ segmento\ AB}} \\ \mbox{}\textbf{\textcolor{Blue}{inline}}\ \textcolor{ForestGreen}{int}\ \textbf{\textcolor{Black}{cross}}\textcolor{BrickRed}{(}\textbf{\textcolor{Blue}{const}}\ point\ \textcolor{BrickRed}{\&}a\textcolor{BrickRed}{,}\ \textbf{\textcolor{Blue}{const}}\ point\ \textcolor{BrickRed}{\&}b\textcolor{BrickRed}{,}\ \textbf{\textcolor{Blue}{const}}\ point\ \textcolor{BrickRed}{\&}c\textcolor{BrickRed}{)}\textcolor{Red}{\{} \\ \mbox{}\ \ \textbf{\textcolor{Blue}{return}}\ \textcolor{BrickRed}{(}b\textcolor{BrickRed}{.}x\textcolor{BrickRed}{-}a\textcolor{BrickRed}{.}x\textcolor{BrickRed}{)*(}c\textcolor{BrickRed}{.}y\textcolor{BrickRed}{-}a\textcolor{BrickRed}{.}y\textcolor{BrickRed}{)}\ \textcolor{BrickRed}{-}\ \textcolor{BrickRed}{(}c\textcolor{BrickRed}{.}x\textcolor{BrickRed}{-}a\textcolor{BrickRed}{.}x\textcolor{BrickRed}{)*(}b\textcolor{BrickRed}{.}y\textcolor{BrickRed}{-}a\textcolor{BrickRed}{.}y\textcolor{BrickRed}{);} \\ \mbox{}\textcolor{Red}{\}} \\ \mbox{} \\ \mbox{}\textit{\textcolor{Brown}{//Self\ $<$\ that\ si\ esta\ a\ la\ derecha\ del\ segmento\ Pivot-That}} \\ \mbox{}\textcolor{ForestGreen}{bool}\ \textbf{\textcolor{Black}{angleCmp}}\textcolor{BrickRed}{(}\textbf{\textcolor{Blue}{const}}\ point\ \textcolor{BrickRed}{\&}self\textcolor{BrickRed}{,}\ \textbf{\textcolor{Blue}{const}}\ point\ \textcolor{BrickRed}{\&}that\textcolor{BrickRed}{)}\textcolor{Red}{\{} \\ -\mbox{}\ \ \textbf{\textcolor{Blue}{return}}\textcolor{BrickRed}{(}\ \textbf{\textcolor{Black}{cross}}\textcolor{BrickRed}{(}pivot\textcolor{BrickRed}{,}\ that\textcolor{BrickRed}{,}\ self\textcolor{BrickRed}{)}\ \textcolor{BrickRed}{$<$}\ \textcolor{Purple}{0}\ \textcolor{BrickRed}{);} \\ -\mbox{}\textcolor{Red}{\}} \\ -\mbox{} \\ -\mbox{}\textbf{\textcolor{Blue}{inline}}\ \textcolor{ForestGreen}{int}\ \textbf{\textcolor{Black}{distsqr}}\textcolor{BrickRed}{(}\textbf{\textcolor{Blue}{const}}\ point\ \textcolor{BrickRed}{\&}a\textcolor{BrickRed}{,}\ \textbf{\textcolor{Blue}{const}}\ point\ \textcolor{BrickRed}{\&}b\textcolor{BrickRed}{)}\textcolor{Red}{\{} \\ -\mbox{}\ \ \textbf{\textcolor{Blue}{return}}\ \textcolor{BrickRed}{(}a\textcolor{BrickRed}{.}x\ \textcolor{BrickRed}{-}\ b\textcolor{BrickRed}{.}x\textcolor{BrickRed}{)*(}a\textcolor{BrickRed}{.}x\ \textcolor{BrickRed}{-}\ b\textcolor{BrickRed}{.}x\textcolor{BrickRed}{)}\ \textcolor{BrickRed}{+}\ \textcolor{BrickRed}{(}a\textcolor{BrickRed}{.}y\ \textcolor{BrickRed}{-}\ b\textcolor{BrickRed}{.}y\textcolor{BrickRed}{)*(}a\textcolor{BrickRed}{.}y\ \textcolor{BrickRed}{-}\ b\textcolor{BrickRed}{.}y\textcolor{BrickRed}{);} \\ +\mbox{}\ \ \textcolor{ForestGreen}{int}\ t\ \textcolor{BrickRed}{=}\ \textbf{\textcolor{Black}{cross}}\textcolor{BrickRed}{(}pivot\textcolor{BrickRed}{,}\ that\textcolor{BrickRed}{,}\ self\textcolor{BrickRed}{);} \\ +\mbox{}\ \ \textbf{\textcolor{Blue}{if}}\ \textcolor{BrickRed}{(}t\ \textcolor{BrickRed}{$<$}\ \textcolor{Purple}{0}\textcolor{BrickRed}{)}\ \textbf{\textcolor{Blue}{return}}\ \textbf{\textcolor{Blue}{true}}\textcolor{BrickRed}{;} \\ +\mbox{}\ \ \textbf{\textcolor{Blue}{if}}\ \textcolor{BrickRed}{(}t\ \textcolor{BrickRed}{==}\ \textcolor{Purple}{0}\textcolor{BrickRed}{)}\textcolor{Red}{\{} \\ +\mbox{}\ \ \ \ \textit{\textcolor{Brown}{//Self\ $<$\ that\ si\ está\ más\ cerquita}} \\ +\mbox{}\ \ \ \ \textbf{\textcolor{Blue}{return}}\ \textcolor{BrickRed}{(}\textbf{\textcolor{Black}{distsqr}}\textcolor{BrickRed}{(}pivot\textcolor{BrickRed}{,}\ self\textcolor{BrickRed}{)}\ \textcolor{BrickRed}{$<$}\ \textbf{\textcolor{Black}{distsqr}}\textcolor{BrickRed}{(}pivot\textcolor{BrickRed}{,}\ that\textcolor{BrickRed}{));} \\ +\mbox{}\ \ \textcolor{Red}{\}} \\ +\mbox{}\ \ \textbf{\textcolor{Blue}{return}}\ \textbf{\textcolor{Blue}{false}}\textcolor{BrickRed}{;} \\ \mbox{}\textcolor{Red}{\}} \\ \mbox{} \\ -\mbox{}\textit{\textcolor{Brown}{//vector\ p\ tiene\ los\ puntos\ ordenados\ anticlockwise}} \\ \mbox{}vector\textcolor{BrickRed}{$<$}point\textcolor{BrickRed}{$>$}\ \textbf{\textcolor{Black}{graham}}\textcolor{BrickRed}{(}vector\textcolor{BrickRed}{$<$}point\textcolor{BrickRed}{$>$}\ p\textcolor{BrickRed}{)}\textcolor{Red}{\{} \\ +\mbox{}\ \ \textit{\textcolor{Brown}{//Metemos\ el\ más\ abajo\ más\ a\ la\ izquierda\ en\ la\ posición\ 0}} \\ +\mbox{}\ \ \textbf{\textcolor{Blue}{for}}\ \textcolor{BrickRed}{(}\textcolor{ForestGreen}{int}\ i\textcolor{BrickRed}{=}\textcolor{Purple}{1}\textcolor{BrickRed}{;}\ i\textcolor{BrickRed}{$<$}p\textcolor{BrickRed}{.}\textbf{\textcolor{Black}{size}}\textcolor{BrickRed}{();}\ \textcolor{BrickRed}{++}i\textcolor{BrickRed}{)}\textcolor{Red}{\{} \\ +\mbox{}\ \ \ \ \textbf{\textcolor{Blue}{if}}\ \textcolor{BrickRed}{(}p\textcolor{BrickRed}{[}i\textcolor{BrickRed}{].}y\ \textcolor{BrickRed}{$<$}\ p\textcolor{BrickRed}{[}\textcolor{Purple}{0}\textcolor{BrickRed}{].}y\ \textcolor{BrickRed}{$|$$|$}\ \textcolor{BrickRed}{(}p\textcolor{BrickRed}{[}i\textcolor{BrickRed}{].}y\ \textcolor{BrickRed}{==}\ p\textcolor{BrickRed}{[}\textcolor{Purple}{0}\textcolor{BrickRed}{].}y\ \textcolor{BrickRed}{\&\&}\ p\textcolor{BrickRed}{[}i\textcolor{BrickRed}{].}x\ \textcolor{BrickRed}{$<$}\ p\textcolor{BrickRed}{[}\textcolor{Purple}{0}\textcolor{BrickRed}{].}x\ \textcolor{BrickRed}{))} \\ +\mbox{}\ \ \ \ \ \ \textbf{\textcolor{Black}{swap}}\textcolor{BrickRed}{(}p\textcolor{BrickRed}{[}\textcolor{Purple}{0}\textcolor{BrickRed}{],}\ p\textcolor{BrickRed}{[}i\textcolor{BrickRed}{]);} \\ +\mbox{}\ \ \textcolor{Red}{\}} \\ +\mbox{}\ \ \\ \mbox{}\ \ pivot\ \textcolor{BrickRed}{=}\ p\textcolor{BrickRed}{[}\textcolor{Purple}{0}\textcolor{BrickRed}{];} \\ \mbox{}\ \ \textbf{\textcolor{Black}{sort}}\textcolor{BrickRed}{(}p\textcolor{BrickRed}{.}\textbf{\textcolor{Black}{begin}}\textcolor{BrickRed}{(),}\ p\textcolor{BrickRed}{.}\textbf{\textcolor{Black}{end}}\textcolor{BrickRed}{(),}\ angleCmp\textcolor{BrickRed}{);} \\ +\mbox{} \\ \mbox{}\ \ \textit{\textcolor{Brown}{//Ordenar\ por\ ángulo\ y\ eliminar\ repetidos.}} \\ -\mbox{}\ \ \textit{\textcolor{Brown}{//Si\ varios\ puntos\ tienen\ el\ mismo\ angulo\ se\ borran\ todos\ excepto\ el\ que\ esté\ más\ lejos}} \\ -\mbox{}\ \ \textbf{\textcolor{Blue}{for}}\ \textcolor{BrickRed}{(}\textcolor{ForestGreen}{int}\ i\textcolor{BrickRed}{=}\textcolor{Purple}{1}\textcolor{BrickRed}{;}\ i\textcolor{BrickRed}{$<$}p\textcolor{BrickRed}{.}\textbf{\textcolor{Black}{size}}\textcolor{BrickRed}{()-}\textcolor{Purple}{1}\textcolor{BrickRed}{;}\ \textcolor{BrickRed}{++}i\textcolor{BrickRed}{)}\textcolor{Red}{\{}\ \ \ \ \\ -\mbox{}\ \ \ \ \textbf{\textcolor{Blue}{if}}\ \textcolor{BrickRed}{(}\textbf{\textcolor{Black}{cross}}\textcolor{BrickRed}{(}p\textcolor{BrickRed}{[}\textcolor{Purple}{0}\textcolor{BrickRed}{],}\ p\textcolor{BrickRed}{[}i\textcolor{BrickRed}{],}\ p\textcolor{BrickRed}{[}i\textcolor{BrickRed}{+}\textcolor{Purple}{1}\textcolor{BrickRed}{])}\ \textcolor{BrickRed}{==}\ \textcolor{Purple}{0}\textcolor{BrickRed}{)}\textcolor{Red}{\{}\ \textit{\textcolor{Brown}{//Si\ son\ colineales...}} \\ -\mbox{}\ \ \ \ \ \ \textbf{\textcolor{Blue}{if}}\ \textcolor{BrickRed}{(}\textbf{\textcolor{Black}{distsqr}}\textcolor{BrickRed}{(}p\textcolor{BrickRed}{[}\textcolor{Purple}{0}\textcolor{BrickRed}{],}\ p\textcolor{BrickRed}{[}i\textcolor{BrickRed}{])}\ \textcolor{BrickRed}{$<$}\ \textbf{\textcolor{Black}{distsqr}}\textcolor{BrickRed}{(}p\textcolor{BrickRed}{[}\textcolor{Purple}{0}\textcolor{BrickRed}{],}\ p\textcolor{BrickRed}{[}i\textcolor{BrickRed}{+}\textcolor{Purple}{1}\textcolor{BrickRed}{]))}\textcolor{Red}{\{}\ \textit{\textcolor{Brown}{//Borrar\ el\ mas\ cercano}} \\ -\mbox{}\ \ \ \ \ \ \ \ p\textcolor{BrickRed}{.}\textbf{\textcolor{Black}{erase}}\textcolor{BrickRed}{(}p\textcolor{BrickRed}{.}\textbf{\textcolor{Black}{begin}}\textcolor{BrickRed}{()}\ \textcolor{BrickRed}{+}\ i\textcolor{BrickRed}{);} \\ -\mbox{}\ \ \ \ \ \ \textcolor{Red}{\}}\textbf{\textcolor{Blue}{else}}\textcolor{Red}{\{} \\ -\mbox{}\ \ \ \ \ \ \ \ p\textcolor{BrickRed}{.}\textbf{\textcolor{Black}{erase}}\textcolor{BrickRed}{(}p\textcolor{BrickRed}{.}\textbf{\textcolor{Black}{begin}}\textcolor{BrickRed}{()}\ \textcolor{BrickRed}{+}\ i\ \textcolor{BrickRed}{+}\ \textcolor{Purple}{1}\textcolor{BrickRed}{);} \\ -\mbox{}\ \ \ \ \ \ \textcolor{Red}{\}} \\ -\mbox{}\ \ \ \ \ \ i\textcolor{BrickRed}{-\/-;} \\ -\mbox{}\ \ \ \ \textcolor{Red}{\}} \\ -\mbox{}\ \ \textcolor{Red}{\}} \\ -\mbox{}\ \ \\ +\mbox{}\ \ \textit{\textcolor{Brown}{//Si\ varios\ puntos\ tienen\ el\ mismo\ angulo\ el\ más\ lejano\ queda\ después\ en\ la\ lista}} \\ \mbox{}\ \ vector\textcolor{BrickRed}{$<$}point\textcolor{BrickRed}{$>$}\ \textbf{\textcolor{Black}{chull}}\textcolor{BrickRed}{(}p\textcolor{BrickRed}{.}\textbf{\textcolor{Black}{begin}}\textcolor{BrickRed}{(),}\ p\textcolor{BrickRed}{.}\textbf{\textcolor{Black}{begin}}\textcolor{BrickRed}{()+}\textcolor{Purple}{3}\textcolor{BrickRed}{);} \\ \mbox{} \\ \mbox{}\ \ \textit{\textcolor{Brown}{//Ahora\ sí!!!}} \\ \mbox{}\ \ \textbf{\textcolor{Blue}{for}}\ \textcolor{BrickRed}{(}\textcolor{ForestGreen}{int}\ i\textcolor{BrickRed}{=}\textcolor{Purple}{3}\textcolor{BrickRed}{;}\ i\textcolor{BrickRed}{$<$}p\textcolor{BrickRed}{.}\textbf{\textcolor{Black}{size}}\textcolor{BrickRed}{();}\ \textcolor{BrickRed}{++}i\textcolor{BrickRed}{)}\textcolor{Red}{\{} \\ -\mbox{}\ \ \ \ \textbf{\textcolor{Blue}{while}}\ \textcolor{BrickRed}{(}\ chull\textcolor{BrickRed}{.}\textbf{\textcolor{Black}{size}}\textcolor{BrickRed}{()}\ \textcolor{BrickRed}{$>$=}\ \textcolor{Purple}{2}\ \textcolor{BrickRed}{\&\&}\ \textbf{\textcolor{Black}{cross}}\textcolor{BrickRed}{(}chull\textcolor{BrickRed}{[}chull\textcolor{BrickRed}{.}\textbf{\textcolor{Black}{size}}\textcolor{BrickRed}{()-}\textcolor{Purple}{2}\textcolor{BrickRed}{],}\ chull\textcolor{BrickRed}{[}chull\textcolor{BrickRed}{.}\textbf{\textcolor{Black}{size}}\textcolor{BrickRed}{()-}\textcolor{Purple}{1}\textcolor{BrickRed}{],}\ p\textcolor{BrickRed}{[}i\textcolor{BrickRed}{])}\ \textcolor{BrickRed}{$<$}\ \textcolor{Purple}{0}\textcolor{BrickRed}{)}\textcolor{Red}{\{} \\ +\mbox{}\ \ \ \ \textbf{\textcolor{Blue}{while}}\ \textcolor{BrickRed}{(}\ chull\textcolor{BrickRed}{.}\textbf{\textcolor{Black}{size}}\textcolor{BrickRed}{()}\ \textcolor{BrickRed}{$>$=}\ \textcolor{Purple}{2}\ \textcolor{BrickRed}{\&\&}\ \textbf{\textcolor{Black}{cross}}\textcolor{BrickRed}{(}chull\textcolor{BrickRed}{[}chull\textcolor{BrickRed}{.}\textbf{\textcolor{Black}{size}}\textcolor{BrickRed}{()-}\textcolor{Purple}{2}\textcolor{BrickRed}{],}\ chull\textcolor{BrickRed}{[}chull\textcolor{BrickRed}{.}\textbf{\textcolor{Black}{size}}\textcolor{BrickRed}{()-}\textcolor{Purple}{1}\textcolor{BrickRed}{],}\ p\textcolor{BrickRed}{[}i\textcolor{BrickRed}{])}\ \textcolor{BrickRed}{$<$=}\ \textcolor{Purple}{0}\textcolor{BrickRed}{)}\textcolor{Red}{\{} \\ \mbox{}\ \ \ \ \ \ chull\textcolor{BrickRed}{.}\textbf{\textcolor{Black}{erase}}\textcolor{BrickRed}{(}chull\textcolor{BrickRed}{.}\textbf{\textcolor{Black}{end}}\textcolor{BrickRed}{()}\ \textcolor{BrickRed}{-}\ \textcolor{Purple}{1}\textcolor{BrickRed}{);} \\ \mbox{}\ \ \ \ \textcolor{Red}{\}} \\ \mbox{}\ \ \ \ chull\textcolor{BrickRed}{.}\textbf{\textcolor{Black}{push$\_$back}}\textcolor{BrickRed}{(}p\textcolor{BrickRed}{[}i\textcolor{BrickRed}{]);} \\ \mbox{}\ \ \textcolor{Red}{\}} \\ -\mbox{} \\ +\mbox{}\ \ \textit{\textcolor{Brown}{//chull\ contiene\ los\ puntos\ del\ convex\ hull\ ordenados\ anti-clockwise.}} \\ +\mbox{}\ \ \textit{\textcolor{Brown}{//No\ contiene\ ningún\ punto\ repetido.}} \\ +\mbox{}\ \ \textit{\textcolor{Brown}{//El\ primer\ punto\ no\ es\ el\ mismo\ que\ el\ último,\ i.e,\ la\ última\ arista}} \\ +\mbox{}\ \ \textit{\textcolor{Brown}{//va\ de\ chull[chull.size()-1]\ a\ chull[0]}} \\ \mbox{}\ \ \textbf{\textcolor{Blue}{return}}\ chull\textcolor{BrickRed}{;} \\ \mbox{}\textcolor{Red}{\}} \\ -\mbox{} \\ -\mbox{}\textcolor{ForestGreen}{int}\ \textbf{\textcolor{Black}{main}}\textcolor{BrickRed}{()}\textcolor{Red}{\{} \\ -\mbox{}\ \ \textcolor{ForestGreen}{int}\ n\textcolor{BrickRed}{;} \\ -\mbox{}\ \ \textcolor{ForestGreen}{int}\ tileNo\ \textcolor{BrickRed}{=}\ \textcolor{Purple}{1}\textcolor{BrickRed}{;} \\ -\mbox{}\ \ \textbf{\textcolor{Blue}{while}}\ \textcolor{BrickRed}{(}cin\ \textcolor{BrickRed}{$>$$>$}\ n\ \textcolor{BrickRed}{\&\&}\ n\textcolor{BrickRed}{)}\textcolor{Red}{\{} \\ -\mbox{}\ \ \ \ vector\textcolor{BrickRed}{$<$}point\textcolor{BrickRed}{$>$}\ p\textcolor{BrickRed}{;} \\ -\mbox{}\ \ \ \ point\ \textbf{\textcolor{Black}{min}}\textcolor{BrickRed}{(}\textcolor{Purple}{10000}\textcolor{BrickRed}{,}\ \textcolor{Purple}{10000}\textcolor{BrickRed}{);} \\ -\mbox{}\ \ \ \ \textcolor{ForestGreen}{int}\ minPos\textcolor{BrickRed}{;} \\ -\mbox{}\ \ \ \ \textbf{\textcolor{Blue}{for}}\ \textcolor{BrickRed}{(}\textcolor{ForestGreen}{int}\ i\textcolor{BrickRed}{=}\textcolor{Purple}{0}\textcolor{BrickRed}{;}\ i\textcolor{BrickRed}{$<$}n\textcolor{BrickRed}{;}\ \textcolor{BrickRed}{++}i\textcolor{BrickRed}{)}\textcolor{Red}{\{} \\ -\mbox{}\ \ \ \ \ \ \textcolor{ForestGreen}{int}\ x\textcolor{BrickRed}{,}\ y\textcolor{BrickRed}{;} \\ -\mbox{}\ \ \ \ \ \ cin\ \textcolor{BrickRed}{$>$$>$}\ x\ \textcolor{BrickRed}{$>$$>$}\ y\textcolor{BrickRed}{;} \\ -\mbox{}\ \ \ \ \ \ p\textcolor{BrickRed}{.}\textbf{\textcolor{Black}{push$\_$back}}\textcolor{BrickRed}{(}\textbf{\textcolor{Black}{point}}\textcolor{BrickRed}{(}x\textcolor{BrickRed}{,}y\textcolor{BrickRed}{));}\ \ \ \ \ \ \\ -\mbox{}\ \ \ \ \ \ \textbf{\textcolor{Blue}{if}}\ \textcolor{BrickRed}{(}y\ \textcolor{BrickRed}{$<$}\ min\textcolor{BrickRed}{.}y\ \textcolor{BrickRed}{$|$$|$}\ \textcolor{BrickRed}{(}y\ \textcolor{BrickRed}{==}\ min\textcolor{BrickRed}{.}y\ \textcolor{BrickRed}{\&\&}\ x\ \textcolor{BrickRed}{$<$}\ min\textcolor{BrickRed}{.}x\ \textcolor{BrickRed}{))}\textcolor{Red}{\{} \\ -\mbox{}\ \ \ \ \ \ \ \ min\ \textcolor{BrickRed}{=}\ \textbf{\textcolor{Black}{point}}\textcolor{BrickRed}{(}x\textcolor{BrickRed}{,}y\textcolor{BrickRed}{);} \\ -\mbox{}\ \ \ \ \ \ \ \ minPos\ \textcolor{BrickRed}{=}\ i\textcolor{BrickRed}{;} \\ -\mbox{}\ \ \ \ \ \ \textcolor{Red}{\}} \\ -\mbox{}\ \ \ \ \textcolor{Red}{\}} \\ -\mbox{}\ \ \ \ \textcolor{ForestGreen}{double}\ tileArea\ \textcolor{BrickRed}{=}\ \textbf{\textcolor{Black}{fabs}}\textcolor{BrickRed}{(}\textbf{\textcolor{Black}{area}}\textcolor{BrickRed}{(}p\textcolor{BrickRed}{));} \\ -\mbox{} \\ -\mbox{}\ \ \ \ \textit{\textcolor{Brown}{//Destruye\ el\ orden\ cw$|$ccw\ poligono,\ pero\ hay\ que\ hacerlo\ por\ que\ Graham\ necesita\ el\ pivote\ en\ p[0]}} \\ -\mbox{}\ \ \ \ \textbf{\textcolor{Black}{swap}}\textcolor{BrickRed}{(}p\textcolor{BrickRed}{[}\textcolor{Purple}{0}\textcolor{BrickRed}{],}\ p\textcolor{BrickRed}{[}minPos\textcolor{BrickRed}{]);} \\ -\mbox{}\ \ \ \ pivot\ \textcolor{BrickRed}{=}\ p\textcolor{BrickRed}{[}\textcolor{Purple}{0}\textcolor{BrickRed}{];} \\ -\mbox{}\ \ \ \ \textcolor{ForestGreen}{double}\ chullArea\ \textcolor{BrickRed}{=}\ \textbf{\textcolor{Black}{fabs}}\textcolor{BrickRed}{(}\textbf{\textcolor{Black}{area}}\textcolor{BrickRed}{(}\textbf{\textcolor{Black}{graham}}\textcolor{BrickRed}{(}p\textcolor{BrickRed}{)));} \\ -\mbox{}\ \ \ \ \\ -\mbox{}\ \ \ \ \textbf{\textcolor{Black}{printf}}\textcolor{BrickRed}{(}\texttt{\textcolor{Red}{"{}Tile\ \#\%d}}\texttt{\textcolor{CarnationPink}{\textbackslash{}n}}\texttt{\textcolor{Red}{"{}}}\textcolor{BrickRed}{,}\ tileNo\textcolor{BrickRed}{++);} \\ -\mbox{}\ \ \ \ \textbf{\textcolor{Black}{printf}}\textcolor{BrickRed}{(}\texttt{\textcolor{Red}{"{}Wasted\ Space\ =\ \%.2f\ }}\texttt{\textcolor{CarnationPink}{\textbackslash{}\%\textbackslash{}n\textbackslash{}n}}\texttt{\textcolor{Red}{"{}}}\textcolor{BrickRed}{,}\ \ \textcolor{BrickRed}{(}chullArea\ \textcolor{BrickRed}{-}\ tileArea\textcolor{BrickRed}{)}\ \textcolor{BrickRed}{*}\ \textcolor{Purple}{100.0}\ \textcolor{BrickRed}{/}\ chullArea\textcolor{BrickRed}{);} \\ -\mbox{}\ \ \ \\ -\mbox{}\ \ \textcolor{Red}{\}} \\ -\mbox{}\ \ \textbf{\textcolor{Blue}{return}}\ \textcolor{Purple}{0}\textcolor{BrickRed}{;} \\ -\mbox{}\textcolor{Red}{\}} \\ } \normalfont\normalsize Mi manual de algoritmos/version_maraton_interuniversitaria_2008-2/src/geometria/grahamscan.tex @@ -1,51 +1,20 @@ -#include <iostream> -#include <climits> -#include <algorithm> - -using namespace std; - +/* + g[i][j] = Distancia entre el nodo i y el j. + */ unsigned long long g[101][101]; -int main(){ - int casos; - cin >> casos; - bool first = true; - while (casos--){ - if (!first) cout << endl; - first = false; +void floyd(){ + //Llenar g + //... - int n, e, t; - cin >> n >> e >> t; + for (int k=0; k<n; ++k){ for (int i=0; i<n; ++i){ for (int j=0; j<n; ++j){ - g[i][j] = INT_MAX; - } - g[i][i] = 0; - } - - int m; - cin >> m; - while (m--){ - int i, j, k; - cin >> i >> j >> k; - g[i-1][j-1] = k; - } - - for (int k=0; k<n; ++k){ - for (int i=0; i<n; ++i){ - for (int j=0; j<n; ++j){ - g[i][j] = min(g[i][j], g[i][k] + g[k][j]); - } + g[i][j] = min(g[i][j], g[i][k] + g[k][j]); } } - - int r=0; - e -= 1; - for (int i=0; i<n; ++i){ - r += ((g[i][e] <= t) ? 1 : 0); - } - - cout << r << endl; } - return 0; + /* + Acá se cumple que g[i][j] = Longitud de la ruta más corta de i a j. + */ } Mi manual de algoritmos/version_maraton_interuniversitaria_2008-2/src/grafos/floyd.cpp @@ -2,56 +2,25 @@ {\ttfamily \raggedright { \noindent -\mbox{}\textbf{\textcolor{RoyalBlue}{\#include}}\ \texttt{\textcolor{Red}{$<$iostream$>$}} \\ -\mbox{}\textbf{\textcolor{RoyalBlue}{\#include}}\ \texttt{\textcolor{Red}{$<$climits$>$}} \\ -\mbox{}\textbf{\textcolor{RoyalBlue}{\#include}}\ \texttt{\textcolor{Red}{$<$algorithm$>$}} \\ -\mbox{} \\ -\mbox{}\textbf{\textcolor{Blue}{using}}\ \textbf{\textcolor{Blue}{namespace}}\ std\textcolor{BrickRed}{;} \\ -\mbox{} \\ +\mbox{}\textit{\textcolor{Brown}{/*}} \\ +\mbox{}\textit{\textcolor{Brown}{\ \ g[i][j]\ =\ Distancia\ entre\ el\ nodo\ i\ y\ el\ j.}} \\ +\mbox{}\textit{\textcolor{Brown}{\ */}} \\ \mbox{}\textcolor{ForestGreen}{unsigned}\ \textcolor{ForestGreen}{long}\ \textcolor{ForestGreen}{long}\ g\textcolor{BrickRed}{[}\textcolor{Purple}{101}\textcolor{BrickRed}{][}\textcolor{Purple}{101}\textcolor{BrickRed}{];} \\ \mbox{} \\ -\mbox{}\textcolor{ForestGreen}{int}\ \textbf{\textcolor{Black}{main}}\textcolor{BrickRed}{()}\textcolor{Red}{\{} \\ -\mbox{}\ \ \textcolor{ForestGreen}{int}\ casos\textcolor{BrickRed}{;} \\ -\mbox{}\ \ cin\ \textcolor{BrickRed}{$>$$>$}\ casos\textcolor{BrickRed}{;} \\ -\mbox{}\ \ \textcolor{ForestGreen}{bool}\ first\ \textcolor{BrickRed}{=}\ \textbf{\textcolor{Blue}{true}}\textcolor{BrickRed}{;} \\ -\mbox{}\ \ \textbf{\textcolor{Blue}{while}}\ \textcolor{BrickRed}{(}casos\textcolor{BrickRed}{-\/-)}\textcolor{Red}{\{} \\ -\mbox{}\ \ \ \ \textbf{\textcolor{Blue}{if}}\ \textcolor{BrickRed}{(!}first\textcolor{BrickRed}{)}\ cout\ \textcolor{BrickRed}{$<$$<$}\ endl\textcolor{BrickRed}{;} \\ -\mbox{}\ \ \ \ first\ \textcolor{BrickRed}{=}\ \textbf{\textcolor{Blue}{false}}\textcolor{BrickRed}{;} \\ +\mbox{}\textcolor{ForestGreen}{void}\ \textbf{\textcolor{Black}{floyd}}\textcolor{BrickRed}{()}\textcolor{Red}{\{} \\ +\mbox{}\ \ \textit{\textcolor{Brown}{//Llenar\ g}} \\ +\mbox{}\ \ \textit{\textcolor{Brown}{//...}} \\ \mbox{} \\ -\mbox{}\ \ \ \ \textcolor{ForestGreen}{int}\ n\textcolor{BrickRed}{,}\ e\textcolor{BrickRed}{,}\ t\textcolor{BrickRed}{;} \\ -\mbox{}\ \ \ \ cin\ \textcolor{BrickRed}{$>$$>$}\ n\ \textcolor{BrickRed}{$>$$>$}\ e\ \textcolor{BrickRed}{$>$$>$}\ t\textcolor{BrickRed}{;} \\ +\mbox{}\ \ \textbf{\textcolor{Blue}{for}}\ \textcolor{BrickRed}{(}\textcolor{ForestGreen}{int}\ k\textcolor{BrickRed}{=}\textcolor{Purple}{0}\textcolor{BrickRed}{;}\ k\textcolor{BrickRed}{$<$}n\textcolor{BrickRed}{;}\ \textcolor{BrickRed}{++}k\textcolor{BrickRed}{)}\textcolor{Red}{\{} \\ \mbox{}\ \ \ \ \textbf{\textcolor{Blue}{for}}\ \textcolor{BrickRed}{(}\textcolor{ForestGreen}{int}\ i\textcolor{BrickRed}{=}\textcolor{Purple}{0}\textcolor{BrickRed}{;}\ i\textcolor{BrickRed}{$<$}n\textcolor{BrickRed}{;}\ \textcolor{BrickRed}{++}i\textcolor{BrickRed}{)}\textcolor{Red}{\{} \\ \mbox{}\ \ \ \ \ \ \textbf{\textcolor{Blue}{for}}\ \textcolor{BrickRed}{(}\textcolor{ForestGreen}{int}\ j\textcolor{BrickRed}{=}\textcolor{Purple}{0}\textcolor{BrickRed}{;}\ j\textcolor{BrickRed}{$<$}n\textcolor{BrickRed}{;}\ \textcolor{BrickRed}{++}j\textcolor{BrickRed}{)}\textcolor{Red}{\{} \\ -\mbox{}\ \ \ \ \ \ \ \ g\textcolor{BrickRed}{[}i\textcolor{BrickRed}{][}j\textcolor{BrickRed}{]}\ \textcolor{BrickRed}{=}\ INT$\_$MAX\textcolor{BrickRed}{;} \\ -\mbox{}\ \ \ \ \ \ \textcolor{Red}{\}} \\ -\mbox{}\ \ \ \ \ \ g\textcolor{BrickRed}{[}i\textcolor{BrickRed}{][}i\textcolor{BrickRed}{]}\ \textcolor{BrickRed}{=}\ \textcolor{Purple}{0}\textcolor{BrickRed}{;} \\ -\mbox{}\ \ \ \ \textcolor{Red}{\}} \\ -\mbox{} \\ -\mbox{}\ \ \ \ \textcolor{ForestGreen}{int}\ m\textcolor{BrickRed}{;} \\ -\mbox{}\ \ \ \ cin\ \textcolor{BrickRed}{$>$$>$}\ m\textcolor{BrickRed}{;} \\ -\mbox{}\ \ \ \ \textbf{\textcolor{Blue}{while}}\ \textcolor{BrickRed}{(}m\textcolor{BrickRed}{-\/-)}\textcolor{Red}{\{} \\ -\mbox{}\ \ \ \ \ \ \textcolor{ForestGreen}{int}\ i\textcolor{BrickRed}{,}\ j\textcolor{BrickRed}{,}\ k\textcolor{BrickRed}{;} \\ -\mbox{}\ \ \ \ \ \ cin\ \textcolor{BrickRed}{$>$$>$}\ i\ \textcolor{BrickRed}{$>$$>$}\ j\ \textcolor{BrickRed}{$>$$>$}\ k\textcolor{BrickRed}{;} \\ -\mbox{}\ \ \ \ \ \ g\textcolor{BrickRed}{[}i\textcolor{BrickRed}{-}\textcolor{Purple}{1}\textcolor{BrickRed}{][}j\textcolor{BrickRed}{-}\textcolor{Purple}{1}\textcolor{BrickRed}{]}\ \textcolor{BrickRed}{=}\ k\textcolor{BrickRed}{;} \\ -\mbox{}\ \ \ \ \textcolor{Red}{\}} \\ -\mbox{} \\ -\mbox{}\ \ \ \ \textbf{\textcolor{Blue}{for}}\ \textcolor{BrickRed}{(}\textcolor{ForestGreen}{int}\ k\textcolor{BrickRed}{=}\textcolor{Purple}{0}\textcolor{BrickRed}{;}\ k\textcolor{BrickRed}{$<$}n\textcolor{BrickRed}{;}\ \textcolor{BrickRed}{++}k\textcolor{BrickRed}{)}\textcolor{Red}{\{} \\ -\mbox{}\ \ \ \ \ \ \textbf{\textcolor{Blue}{for}}\ \textcolor{BrickRed}{(}\textcolor{ForestGreen}{int}\ i\textcolor{BrickRed}{=}\textcolor{Purple}{0}\textcolor{BrickRed}{;}\ i\textcolor{BrickRed}{$<$}n\textcolor{BrickRed}{;}\ \textcolor{BrickRed}{++}i\textcolor{BrickRed}{)}\textcolor{Red}{\{} \\ -\mbox{}\ \ \ \ \ \ \ \ \textbf{\textcolor{Blue}{for}}\ \textcolor{BrickRed}{(}\textcolor{ForestGreen}{int}\ j\textcolor{BrickRed}{=}\textcolor{Purple}{0}\textcolor{BrickRed}{;}\ j\textcolor{BrickRed}{$<$}n\textcolor{BrickRed}{;}\ \textcolor{BrickRed}{++}j\textcolor{BrickRed}{)}\textcolor{Red}{\{} \\ -\mbox{}\ \ \ \ \ \ \ \ \ \ g\textcolor{BrickRed}{[}i\textcolor{BrickRed}{][}j\textcolor{BrickRed}{]}\ \textcolor{BrickRed}{=}\ \textbf{\textcolor{Black}{min}}\textcolor{BrickRed}{(}g\textcolor{BrickRed}{[}i\textcolor{BrickRed}{][}j\textcolor{BrickRed}{],}\ g\textcolor{BrickRed}{[}i\textcolor{BrickRed}{][}k\textcolor{BrickRed}{]}\ \textcolor{BrickRed}{+}\ g\textcolor{BrickRed}{[}k\textcolor{BrickRed}{][}j\textcolor{BrickRed}{]);} \\ -\mbox{}\ \ \ \ \ \ \ \ \textcolor{Red}{\}} \\ +\mbox{}\ \ \ \ \ \ \ \ g\textcolor{BrickRed}{[}i\textcolor{BrickRed}{][}j\textcolor{BrickRed}{]}\ \textcolor{BrickRed}{=}\ \textbf{\textcolor{Black}{min}}\textcolor{BrickRed}{(}g\textcolor{BrickRed}{[}i\textcolor{BrickRed}{][}j\textcolor{BrickRed}{],}\ g\textcolor{BrickRed}{[}i\textcolor{BrickRed}{][}k\textcolor{BrickRed}{]}\ \textcolor{BrickRed}{+}\ g\textcolor{BrickRed}{[}k\textcolor{BrickRed}{][}j\textcolor{BrickRed}{]);} \\ \mbox{}\ \ \ \ \ \ \textcolor{Red}{\}} \\ \mbox{}\ \ \ \ \textcolor{Red}{\}} \\ -\mbox{}\ \ \ \ \\ -\mbox{}\ \ \ \ \textcolor{ForestGreen}{int}\ r\textcolor{BrickRed}{=}\textcolor{Purple}{0}\textcolor{BrickRed}{;} \\ -\mbox{}\ \ \ \ e\ \textcolor{BrickRed}{-=}\ \textcolor{Purple}{1}\textcolor{BrickRed}{;} \\ -\mbox{}\ \ \ \ \textbf{\textcolor{Blue}{for}}\ \textcolor{BrickRed}{(}\textcolor{ForestGreen}{int}\ i\textcolor{BrickRed}{=}\textcolor{Purple}{0}\textcolor{BrickRed}{;}\ i\textcolor{BrickRed}{$<$}n\textcolor{BrickRed}{;}\ \textcolor{BrickRed}{++}i\textcolor{BrickRed}{)}\textcolor{Red}{\{} \\ -\mbox{}\ \ \ \ \ \ r\ \textcolor{BrickRed}{+=}\ \textcolor{BrickRed}{((}g\textcolor{BrickRed}{[}i\textcolor{BrickRed}{][}e\textcolor{BrickRed}{]}\ \textcolor{BrickRed}{$<$=}\ t\textcolor{BrickRed}{)}\ \textcolor{BrickRed}{?}\ \textcolor{Purple}{1}\ \textcolor{BrickRed}{:}\ \textcolor{Purple}{0}\textcolor{BrickRed}{);}\ \ \ \ \ \ \\ -\mbox{}\ \ \ \ \textcolor{Red}{\}} \\ -\mbox{} \\ -\mbox{}\ \ \ \ cout\ \textcolor{BrickRed}{$<$$<$}\ r\ \textcolor{BrickRed}{$<$$<$}\ endl\textcolor{BrickRed}{;} \\ \mbox{}\ \ \textcolor{Red}{\}} \\ -\mbox{}\ \ \textbf{\textcolor{Blue}{return}}\ \textcolor{Purple}{0}\textcolor{BrickRed}{;} \\ +\mbox{}\ \ \textit{\textcolor{Brown}{/*}} \\ +\mbox{}\textit{\textcolor{Brown}{\ \ \ \ Acá\ se\ cumple\ que\ g[i][j]\ =\ Longitud\ de\ la\ ruta\ más\ corta\ de\ i\ a\ j.}} \\ +\mbox{}\textit{\textcolor{Brown}{\ \ \ */}} \\ \mbox{}\textcolor{Red}{\}} \\ } \normalfont\normalsize Mi manual de algoritmos/version_maraton_interuniversitaria_2008-2/src/grafos/floyd.tex @@ -1,6 +1,11 @@ - int cap[MAXN+1][MAXN+1], flow[MAXN+1][MAXN+1], prev[MAXN+1]; +/* + cap[i][j] = Capacidad de la arista (i, j). + flow[i][j] = Flujo actual de i a j. + prev[i] = Predecesor del nodo i en un camino de aumentación. + */ + int fordFulkerson(int n, int s, int t){ int ans = 0; for (int i=0; i<n; ++i) fill(flow[i], flow[i]+n, 0); Mi manual de algoritmos/version_maraton_interuniversitaria_2008-2/src/grafos/ford_fulkerson.cpp @@ -2,9 +2,14 @@ {\ttfamily \raggedright { \noindent -\mbox{} \\ \mbox{}\textcolor{ForestGreen}{int}\ cap\textcolor{BrickRed}{[}MAXN\textcolor{BrickRed}{+}\textcolor{Purple}{1}\textcolor{BrickRed}{][}MAXN\textcolor{BrickRed}{+}\textcolor{Purple}{1}\textcolor{BrickRed}{],}\ flow\textcolor{BrickRed}{[}MAXN\textcolor{BrickRed}{+}\textcolor{Purple}{1}\textcolor{BrickRed}{][}MAXN\textcolor{BrickRed}{+}\textcolor{Purple}{1}\textcolor{BrickRed}{],}\ prev\textcolor{BrickRed}{[}MAXN\textcolor{BrickRed}{+}\textcolor{Purple}{1}\textcolor{BrickRed}{];} \\ \mbox{} \\ +\mbox{}\textit{\textcolor{Brown}{/*}} \\ +\mbox{}\textit{\textcolor{Brown}{\ \ cap[i][j]\ =\ Capacidad\ de\ la\ arista\ (i,\ j).}} \\ +\mbox{}\textit{\textcolor{Brown}{\ \ flow[i][j]\ =\ Flujo\ actual\ de\ i\ a\ j.}} \\ +\mbox{}\textit{\textcolor{Brown}{\ \ prev[i]\ =\ Predecesor\ del\ nodo\ i\ en\ un\ camino\ de\ aumentación.}} \\ +\mbox{}\textit{\textcolor{Brown}{\ */}} \\ +\mbox{} \\ \mbox{}\textcolor{ForestGreen}{int}\ \textbf{\textcolor{Black}{fordFulkerson}}\textcolor{BrickRed}{(}\textcolor{ForestGreen}{int}\ n\textcolor{BrickRed}{,}\ \textcolor{ForestGreen}{int}\ s\textcolor{BrickRed}{,}\ \textcolor{ForestGreen}{int}\ t\textcolor{BrickRed}{)}\textcolor{Red}{\{} \\ \mbox{}\ \ \textcolor{ForestGreen}{int}\ ans\ \textcolor{BrickRed}{=}\ \textcolor{Purple}{0}\textcolor{BrickRed}{;} \\ \mbox{}\ \ \textbf{\textcolor{Blue}{for}}\ \textcolor{BrickRed}{(}\textcolor{ForestGreen}{int}\ i\textcolor{BrickRed}{=}\textcolor{Purple}{0}\textcolor{BrickRed}{;}\ i\textcolor{BrickRed}{$<$}n\textcolor{BrickRed}{;}\ \textcolor{BrickRed}{++}i\textcolor{BrickRed}{)}\ \textbf{\textcolor{Black}{fill}}\textcolor{BrickRed}{(}flow\textcolor{BrickRed}{[}i\textcolor{BrickRed}{],}\ flow\textcolor{BrickRed}{[}i\textcolor{BrickRed}{]+}n\textcolor{BrickRed}{,}\ \textcolor{Purple}{0}\textcolor{BrickRed}{);} \\ Mi manual de algoritmos/version_maraton_interuniversitaria_2008-2/src/grafos/ford_fulkerson.tex @@ -17,7 +17,6 @@ struct edge{ }; - /* Union find */ int p[10001], rank[10001]; void make_set(int x){ p[x] = x, rank[x] = 0; } @@ -48,7 +47,7 @@ int main(){ for (int i=0; i<e.size(); ++i){ int u = e[i].start, v = e[i].end, w = e[i].weight; if (find_set(u) != find_set(v)){ - //xprintf("Joining %d with %d using weight %d\n", u, v, w); + //printf("Joining %d with %d using weight %d\n", u, v, w); total -= w; merge(u, v); } Mi manual de algoritmos/version_maraton_interuniversitaria_2008-2/src/grafos/kruskal.cpp @@ -21,7 +21,6 @@ \mbox{}\textcolor{Red}{\}}\textcolor{BrickRed}{;} \\ \mbox{} \\ \mbox{} \\ -\mbox{} \\ \mbox{}\textit{\textcolor{Brown}{/*\ Union\ find\ */}} \\ \mbox{}\textcolor{ForestGreen}{int}\ p\textcolor{BrickRed}{[}\textcolor{Purple}{10001}\textcolor{BrickRed}{],}\ rank\textcolor{BrickRed}{[}\textcolor{Purple}{10001}\textcolor{BrickRed}{];} \\ \mbox{}\textcolor{ForestGreen}{void}\ \textbf{\textcolor{Black}{make$\_$set}}\textcolor{BrickRed}{(}\textcolor{ForestGreen}{int}\ x\textcolor{BrickRed}{)}\textcolor{Red}{\{}\ p\textcolor{BrickRed}{[}x\textcolor{BrickRed}{]}\ \textcolor{BrickRed}{=}\ x\textcolor{BrickRed}{,}\ rank\textcolor{BrickRed}{[}x\textcolor{BrickRed}{]}\ \textcolor{BrickRed}{=}\ \textcolor{Purple}{0}\textcolor{BrickRed}{;}\ \textcolor{Red}{\}} \\ @@ -52,7 +51,7 @@ \mbox{}\ \ \ \ \textbf{\textcolor{Blue}{for}}\ \textcolor{BrickRed}{(}\textcolor{ForestGreen}{int}\ i\textcolor{BrickRed}{=}\textcolor{Purple}{0}\textcolor{BrickRed}{;}\ i\textcolor{BrickRed}{$<$}e\textcolor{BrickRed}{.}\textbf{\textcolor{Black}{size}}\textcolor{BrickRed}{();}\ \textcolor{BrickRed}{++}i\textcolor{BrickRed}{)}\textcolor{Red}{\{} \\ \mbox{}\ \ \ \ \ \ \textcolor{ForestGreen}{int}\ u\ \textcolor{BrickRed}{=}\ e\textcolor{BrickRed}{[}i\textcolor{BrickRed}{].}start\textcolor{BrickRed}{,}\ v\ \textcolor{BrickRed}{=}\ e\textcolor{BrickRed}{[}i\textcolor{BrickRed}{].}end\textcolor{BrickRed}{,}\ w\ \textcolor{BrickRed}{=}\ e\textcolor{BrickRed}{[}i\textcolor{BrickRed}{].}weight\textcolor{BrickRed}{;} \\ \mbox{}\ \ \ \ \ \ \textbf{\textcolor{Blue}{if}}\ \textcolor{BrickRed}{(}\textbf{\textcolor{Black}{find$\_$set}}\textcolor{BrickRed}{(}u\textcolor{BrickRed}{)}\ \textcolor{BrickRed}{!=}\ \textbf{\textcolor{Black}{find$\_$set}}\textcolor{BrickRed}{(}v\textcolor{BrickRed}{))}\textcolor{Red}{\{} \\ -\mbox{}\ \ \ \ \ \ \ \ \textit{\textcolor{Brown}{//xprintf("{}Joining\ \%d\ with\ \%d\ using\ weight\ \%d\textbackslash{}n"{},\ u,\ v,\ w);}} \\ +\mbox{}\ \ \ \ \ \ \ \ \textit{\textcolor{Brown}{//printf("{}Joining\ \%d\ with\ \%d\ using\ weight\ \%d\textbackslash{}n"{},\ u,\ v,\ w);}} \\ \mbox{}\ \ \ \ \ \ \ \ total\ \textcolor{BrickRed}{-=}\ w\textcolor{BrickRed}{;} \\ \mbox{}\ \ \ \ \ \ \ \ \textbf{\textcolor{Black}{merge}}\textcolor{BrickRed}{(}u\textcolor{BrickRed}{,}\ v\textcolor{BrickRed}{);} \\ \mbox{}\ \ \ \ \ \ \textcolor{Red}{\}} \\ Mi manual de algoritmos/version_maraton_interuniversitaria_2008-2/src/grafos/kruskal.tex @@ -9,13 +9,12 @@ void buildCriba(){ memset(criba, false, sizeof(criba)); criba[0] = criba[1] = true; - for (int i=2; i<=SIZE; i += 2){ + for (int i=4; i<=SIZE; i += 2){ criba[i] = true; } - - for (int i=3; i<=SIZE; i += 2){ + for (int i=3; i*i<=SIZE; i += 2){ if (!criba[i]){ - for (int j=i+i; j<=SIZE; j += i){ + for (int j=i*i; j<=SIZE; j += i){ criba[j] = true; } } Mi manual de algoritmos/version_maraton_interuniversitaria_2008-2/src/number_theory/criba.cpp @@ -13,13 +13,12 @@ \mbox{}\ \ \textbf{\textcolor{Black}{memset}}\textcolor{BrickRed}{(}criba\textcolor{BrickRed}{,}\ \textbf{\textcolor{Blue}{false}}\textcolor{BrickRed}{,}\ \textbf{\textcolor{Blue}{sizeof}}\textcolor{BrickRed}{(}criba\textcolor{BrickRed}{));} \\ \mbox{} \\ \mbox{}\ \ criba\textcolor{BrickRed}{[}\textcolor{Purple}{0}\textcolor{BrickRed}{]}\ \textcolor{BrickRed}{=}\ criba\textcolor{BrickRed}{[}\textcolor{Purple}{1}\textcolor{BrickRed}{]}\ \textcolor{BrickRed}{=}\ \textbf{\textcolor{Blue}{true}}\textcolor{BrickRed}{;} \\ -\mbox{}\ \ \textbf{\textcolor{Blue}{for}}\ \textcolor{BrickRed}{(}\textcolor{ForestGreen}{int}\ i\textcolor{BrickRed}{=}\textcolor{Purple}{2}\textcolor{BrickRed}{;}\ i\textcolor{BrickRed}{$<$=}SIZE\textcolor{BrickRed}{;}\ i\ \textcolor{BrickRed}{+=}\ \textcolor{Purple}{2}\textcolor{BrickRed}{)}\textcolor{Red}{\{} \\ +\mbox{}\ \ \textbf{\textcolor{Blue}{for}}\ \textcolor{BrickRed}{(}\textcolor{ForestGreen}{int}\ i\textcolor{BrickRed}{=}\textcolor{Purple}{4}\textcolor{BrickRed}{;}\ i\textcolor{BrickRed}{$<$=}SIZE\textcolor{BrickRed}{;}\ i\ \textcolor{BrickRed}{+=}\ \textcolor{Purple}{2}\textcolor{BrickRed}{)}\textcolor{Red}{\{} \\ \mbox{}\ \ \ \ criba\textcolor{BrickRed}{[}i\textcolor{BrickRed}{]}\ \textcolor{BrickRed}{=}\ \textbf{\textcolor{Blue}{true}}\textcolor{BrickRed}{;} \\ \mbox{}\ \ \textcolor{Red}{\}} \\ -\mbox{}\ \ \\ -\mbox{}\ \ \textbf{\textcolor{Blue}{for}}\ \textcolor{BrickRed}{(}\textcolor{ForestGreen}{int}\ i\textcolor{BrickRed}{=}\textcolor{Purple}{3}\textcolor{BrickRed}{;}\ i\textcolor{BrickRed}{$<$=}SIZE\textcolor{BrickRed}{;}\ i\ \textcolor{BrickRed}{+=}\ \textcolor{Purple}{2}\textcolor{BrickRed}{)}\textcolor{Red}{\{} \\ +\mbox{}\ \ \textbf{\textcolor{Blue}{for}}\ \textcolor{BrickRed}{(}\textcolor{ForestGreen}{int}\ i\textcolor{BrickRed}{=}\textcolor{Purple}{3}\textcolor{BrickRed}{;}\ i\textcolor{BrickRed}{*}i\textcolor{BrickRed}{$<$=}SIZE\textcolor{BrickRed}{;}\ i\ \textcolor{BrickRed}{+=}\ \textcolor{Purple}{2}\textcolor{BrickRed}{)}\textcolor{Red}{\{} \\ \mbox{}\ \ \ \ \textbf{\textcolor{Blue}{if}}\ \textcolor{BrickRed}{(!}criba\textcolor{BrickRed}{[}i\textcolor{BrickRed}{])}\textcolor{Red}{\{} \\ -\mbox{}\ \ \ \ \ \ \textbf{\textcolor{Blue}{for}}\ \textcolor{BrickRed}{(}\textcolor{ForestGreen}{int}\ j\textcolor{BrickRed}{=}i\textcolor{BrickRed}{+}i\textcolor{BrickRed}{;}\ j\textcolor{BrickRed}{$<$=}SIZE\textcolor{BrickRed}{;}\ j\ \textcolor{BrickRed}{+=}\ i\textcolor{BrickRed}{)}\textcolor{Red}{\{} \\ +\mbox{}\ \ \ \ \ \ \textbf{\textcolor{Blue}{for}}\ \textcolor{BrickRed}{(}\textcolor{ForestGreen}{int}\ j\textcolor{BrickRed}{=}i\textcolor{BrickRed}{*}i\textcolor{BrickRed}{;}\ j\textcolor{BrickRed}{$<$=}SIZE\textcolor{BrickRed}{;}\ j\ \textcolor{BrickRed}{+=}\ i\textcolor{BrickRed}{)}\textcolor{Red}{\{} \\ \mbox{}\ \ \ \ \ \ \ \ criba\textcolor{BrickRed}{[}j\textcolor{BrickRed}{]}\ \textcolor{BrickRed}{=}\ \textbf{\textcolor{Blue}{true}}\textcolor{BrickRed}{;} \\ \mbox{}\ \ \ \ \ \ \textcolor{Red}{\}} \\ \mbox{}\ \ \ \ \textcolor{Red}{\}} \\ Mi manual de algoritmos/version_maraton_interuniversitaria_2008-2/src/number_theory/criba.tex Mi manual de algoritmos/version_maraton_interuniversitaria_2008-2/src/c++/highlight.sh 1fa74fedda9db2d25d1d790fa0b4ddd4d28fbe8b Familia andmej@gmail.com http://github.com/andmej/acm/commit/23cd3ed841a8eed5a2d59fdec042f9584f38cc54 23cd3ed841a8eed5a2d59fdec042f9584f38cc54 2008-09-21T09:53:18-07:00 2008-09-21T09:53:18-07:00 11088 - End up with more teams (DP), 11282 - Mixing invitations & 1481 - Arrange the Numbers (Inclusión-exclusión) 527b1949c821b25180fefbe203970b613e6f4173 Familia andmej@gmail.com