2835 - A Round Peg in a Ground Hole (Geometría, polígono convexo, dis…

…tancia de un punto a una recta)

2835 - A Round Peg in a Ground Hole/2835.2.cpp

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+/*
+  Author: Andrés Mejía-Posada + Sebastián Arcila-Valenzuela
+  http://blogaritmo.factorcomun.org
+
+  Accepted
+ */
+#include <iostream>
+#include <math.h>
+#include <vector>
+#include <algorithm>
+#include <stdio.h>
+#include <stdlib.h>
+#include <assert.h>
+using namespace std;
+
+struct point{
+  double x,y;
+};
+
+int n;
+
+/*
+  Returns positive if a-b-c make a left turn.
+  Returns negative if a-b-c make a right turn.
+  Returns 0.0 if a-b-c are colineal.
+ */
+double turn(const point &a, const point &b, const point &c){
+  double z = (b.x - a.x)*(c.y - a.y) - (b.y - a.y)*(c.x - a.x);
+  if (fabs(z) < 1e-9) return 0.0;
+  return z;
+}
+
+inline double dist(const point &a, const point &b){
+  return sqrt((a.x-b.x)*(a.x-b.x) + (a.y-b.y)*(a.y-b.y));
+}
+
+inline double distsqr(const point &a, const point &b){
+  return (a.x-b.x)*(a.x-b.x) + (a.y-b.y)*(a.y-b.y);
+}
+
+
+/*
+  Returns true if polygon p is convex.
+  False if it's concave or it can't be determined.
+ */
+bool isConvex(const vector<point> &p){
+  int mask = 0;
+  for (int i=0; i<n; ++i){
+    int j=(i+1)%n;
+    int k=(i+2)%n;
+    double z = turn(p[i], p[j], p[k]);
+    if (z < 0.0){
+      mask |= 1;
+    }else if (z > 0.0){
+      mask |= 2;
+    }
+    if (mask == 3) return false;
+  }
+  return mask != 0;
+}
+
+/*
+  Returns true if point a is inside polygon p.
+  Note that if point a lies on the border of p it
+  is considered outside.
+ */
+bool inside(const vector<point> &p, const point &a){
+  int mask = 0;
+  for (int i=0; i<n; ++i){
+    int j = (i+1)%n;
+    double z = turn(p[i], p[j], a);
+    if (z < 0.0){
+      mask |= 1;
+    }else if (z > 0.0){
+      mask |= 2;
+    }else if (z == 0.0) return false;
+    if (mask == 3) return false;
+  }
+  return mask != 0;
+
+}
+
+/*
+  Returns the closest distance between point pnt and the line that passes through points a & b
+  Idea by: http://local.wasp.uwa.edu.au/%7Epbourke/geometry/pointline/
+ */
+double distance_point_to_line(const point &a, const point &b, const point &pnt){
+  double u = ((pnt.x - a.x)*(b.x - a.x) + (pnt.y - a.y)*(b.y - a.y)) / distsqr(a, b);
+  point intersection;
+  intersection.x = a.x + u*(b.x - a.x);
+  intersection.y = a.y + u*(b.y - a.y);
+  return dist(pnt, intersection);
+}
+
+/*
+  Returns true if I can place circle at point "peg" with radius "radius"
+  such that it's inside polygon "p".
+ */
+bool check(const vector<point> &p, const point &peg, const double &radius){
+  if (!inside(p, peg)) return false;
+  //Revisar aquí que la distancia entre el punto peg y la arista (p[i], p[(i+1)%n]) sea <=  radius.
+  for (int i=0; i<n; ++i){
+    int j = (i+1)%n;
+    double z = distance_point_to_line(p[i], p[j], peg);
+    if (z < radius){
+      return false;
+    }
+  }
+  return true;
+}
+
+int main(){
+  while (scanf("%d", &n) == 1 && n >= 3){
+    double pegRadius;
+    point peg;
+    scanf("%lf %lf %lf", &pegRadius, &peg.x, &peg.y);
+    vector<point> p(n);
+    for (int i=0; i<n; ++i){
+      scanf("%lf %lf", &p[i].x,  &p[i].y);
+    }
+    if (!isConvex(p)){
+      puts("HOLE IS ILL-FORMED");
+    }else{
+      printf("PEG WILL %sFIT\n", (check(p, peg, pegRadius) ? "" : "NOT "));
+    }
+
+  }
+  return 0;
+}

2835 - A Round Peg in a Ground Hole/2835.cpp

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+/*
+  Author: Andrés Mejía-Posada + Sebastián Arcila-Valenzuela
+  http://blogaritmo.factorcomun.org
+
+  Accepted
+ */
+#include <iostream>
+#include <math.h>
+#include <vector>
+#include <algorithm>
+#include <stdio.h>
+#include <stdlib.h>
+#include <assert.h>
+using namespace std;
+
+struct point{
+  double x,y;
+};
+
+/*
+  Returns positive if a-b-c make a left turn.
+  Returns negative if a-b-c make a right turn.
+  Returns 0.0 if a-b-c are colineal.
+ */
+double turn(const point &a, const point &b, const point &c){
+  double z = (b.x - a.x)*(c.y - a.y) - (b.y - a.y)*(c.x - a.x);
+  if (fabs(z) < 1e-9) return 0.0;
+  return z;
+}
+
+inline double dist(const point &a, const point &b){
+  return sqrt((a.x-b.x)*(a.x-b.x) + (a.y-b.y)*(a.y-b.y));
+}
+
+inline double distsqr(const point &a, const point &b){
+  return (a.x-b.x)*(a.x-b.x) + (a.y-b.y)*(a.y-b.y);
+}
+
+
+/*
+  Returns true if polygon p is convex.
+  False if it's concave or it can't be determined.
+ */
+bool isConvex(const vector<point> &p){
+  int n = p.size();
+  int mask = 0;
+  for (int i=0; i<n; ++i){
+    int j=(i+1)%n;
+    int k=(i+2)%n;
+    double z = turn(p[i], p[j], p[k]);
+    if (z < 0.0){
+      mask |= 1;
+    }else if (z > 0.0){
+      mask |= 2;
+    }
+    if (mask == 3) return false;
+  }
+  return mask != 0;
+}
+
+/*
+  Returns true if point a is inside polygon p.
+  Note that if point a lies on the border of p it
+  is considered outside.
+ */
+bool inside(const vector<point> &p, const point &a){
+  int n = p.size();
+  int mask = 0;
+  for (int i=0; i<n; ++i){
+    int j = (i+1)%n;
+    double z = turn(p[i], p[j], a);
+    if (z < 0.0){
+      mask |= 1;
+    }else if (z > 0.0){
+      mask |= 2;
+    }else if (z == 0.0) return false;
+    if (mask == 3) return false;
+  }
+  return mask != 0;
+
+}
+
+/*
+  Returns the closest distance between point pnt and the line that passes through points a & b
+  Idea by: http://local.wasp.uwa.edu.au/%7Epbourke/geometry/pointline/
+ */
+double distance_point_to_line(const point &a, const point &b, const point &pnt){
+  double u = ((pnt.x - a.x)*(b.x - a.x) + (pnt.y - a.y)*(b.y - a.y)) / distsqr(a, b);
+  point intersection;
+  intersection.x = a.x + u*(b.x - a.x);
+  intersection.y = a.y + u*(b.y - a.y);
+  return dist(pnt, intersection);
+}
+
+/*
+  Returns true if I can place circle at point "peg" with radius "radius"
+  such that it's inside polygon "p".
+ */
+bool check(const vector<point> &p, const point &peg, const double &radius){
+  if (!inside(p, peg)) return false;
+  //Revisar aquí que la distancia entre el punto peg y la arista (p[i], p[(i+1)%n]) sea <=  radius.
+  int n = p.size();
+  for (int i=0; i<n; ++i){
+    int j = (i+1)%n;
+    double z = distance_point_to_line(p[i], p[j], peg);
+    if (z < radius){
+      return false;
+    }
+  }
+  return true;
+}
+
+int main(){
+  int n;
+  while (cin >> n && n >= 3){
+    double pegRadius;
+    point peg;
+    cin >> pegRadius >> peg.x >> peg.y;
+    assert(pegRadius > 0.0);
+    vector<point> p(n);
+    for (int i=0; i<n; ++i){
+      cin >> p[i].x >> p[i].y;
+      if (i > 0) assert(dist(p[i-1], p[i]) > 0.0);
+    }
+    if (!isConvex(p)){
+      cout << "HOLE IS ILL-FORMED" << endl;
+    }else{
+      cout << "PEG WILL " << (check(p, peg, pegRadius) ? "" : "NOT ") << "FIT" << endl;
+    }
+
+  }
+  return 0;
+}