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Added license header to problems, and added the max occurrence problem
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -1,24 +1,40 @@ | ||
| module Occurrence where | ||
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| import qualified Data.Map as M | ||
| import Data.List (maximumBy, foldl1) | ||
| import Data.Function (on) | ||
| import Data.Maybe | ||
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| -- problem 1: find the element occurs most | ||
| maxOccur xs = maximumBy (compare `on` snd) $ M.toList $ M.fromListWith (+) $ zip xs $ repeat 1 | ||
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| -- problem 2: find the longest sub-string contains same element. | ||
| longestDup (x:xs) = fst $ foldl f ((x, 1), (x, 1)) xs where | ||
| f ((a, n), (a', n')) b | a' /=b = ((a, n), (b, 1)) | ||
| | n < n'+1 = ((a', n'+1), (a', n'+1)) | ||
| | otherwise = ((a, n), (a', n'+1)) | ||
| -- Divide and conquer | ||
| -- problem 1 | ||
| find [] = Nothing | ||
| find (x:xs) = Just $ maximumBy (compare `on` snd) $ (x, l):catMaybes | ||
| [find [ a| a<-xs, a < x], find [ a| a<-xs, a > x]] | ||
| where | ||
| l = length (x:[ a| a<-xs, a == x]) | ||
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| -- Boyer-Moore linear time majority vote algorithm | ||
| -- Occurrence.hs | ||
| -- Copyright (C) 2014 Liu Xinyu (liuxinyu95@gmail.com) | ||
| -- | ||
| -- This program is free software: you can redistribute it and/or modify | ||
| -- it under the terms of the GNU General Public License as published by | ||
| -- the Free Software Foundation, either version 3 of the License, or | ||
| -- (at your option) any later version. | ||
| -- | ||
| -- This program is distributed in the hope that it will be useful, | ||
| -- but WITHOUT ANY WARRANTY; without even the implied warranty of | ||
| -- MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the | ||
| -- GNU General Public License for more details. | ||
| -- | ||
| -- You should have received a copy of the GNU General Public License | ||
| -- along with this program. If not, see <http://www.gnu.org/licenses/>. | ||
|
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| module Occurrence where | ||
|
|
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| import qualified Data.Map as M | ||
| import Data.List (maximumBy, foldl1) | ||
| import Data.Function (on) | ||
| import Data.Maybe | ||
|
|
||
| -- problem 1: find the element occurs most | ||
| maxOccur xs = maximumBy (compare `on` snd) $ M.toList $ M.fromListWith (+) $ zip xs $ repeat 1 | ||
|
|
||
| -- problem 2: find the longest sub-string contains same element. | ||
| longestDup (x:xs) = fst $ foldl f ((x, 1), (x, 1)) xs where | ||
| f ((a, n), (a', n')) b | a' /=b = ((a, n), (b, 1)) | ||
| | n < n'+1 = ((a', n'+1), (a', n'+1)) | ||
| | otherwise = ((a, n), (a', n'+1)) | ||
| -- Divide and conquer | ||
| -- problem 1 | ||
| find [] = Nothing | ||
| find (x:xs) = Just $ maximumBy (compare `on` snd) $ (x, l):catMaybes | ||
| [find [ a| a<-xs, a < x], find [ a| a<-xs, a > x]] | ||
| where | ||
| l = length (x:[ a| a<-xs, a == x]) | ||
|
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||
| -- Boyer-Moore linear time majority vote algorithm |
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -1,106 +1,123 @@ | ||
| #!/usr/bin/python | ||
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| import random | ||
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| # method 1, d & c | ||
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| # [l, u) | ||
| def solve(xs): | ||
| l = 0 | ||
| u = len(xs) | ||
| while l<u: | ||
| m = (l+u)/2 | ||
| left = [x for x in xs if x < m] | ||
| right = [x for x in xs if x >= m] | ||
| if len(left) < m - l: | ||
| lost = (m - 1 + l)*(m - l)/2 - sum(left) | ||
| dup = sum(right) - (u - 1 + m)*(u - m)/2 | ||
| return (lost, dup) | ||
| elif len(left) > m - l: | ||
| lost = (u - 1 + m)*(u - m)/2 - sum(right) | ||
| dup = sum(left) - (m - 1 + l)*(m - l)/2 | ||
| return (lost, dup) | ||
| else: | ||
| if sum(left) == (m -1 + l)*(m - l)/2: | ||
| l = m | ||
| xs = right | ||
| else: | ||
| u = m | ||
| xs = left | ||
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| # method 1', in-place D & C | ||
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| def partition(xs, l, u, x): | ||
| left = l | ||
| for right in range(l, u): | ||
| if xs[right] < x: | ||
| (xs[left], xs[right]) = (xs[right], xs[left]) | ||
| left = left + 1 | ||
| return left | ||
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| def solve_inplace(xs): | ||
| (l, u) = (0, len(xs)) | ||
| while l<u: | ||
| m = (l+u)/2 | ||
| m1 = partition(xs, l, u, m) | ||
| (nl, nr) = (m1 - l, u - m1); | ||
| (sl, sr) = (sum(xs[l:m1]), sum(xs[m1:u])) | ||
| sl1 = (l + m - 1)*(m - l)/2 | ||
| sr1 = (m + u - 1)*(u - m)/2 | ||
| if m1 < m: | ||
| return (sl1 - sl, sr - sr1) | ||
| elif m1 > m: | ||
| return (sr1 - sr, sl - sl1) | ||
| else: | ||
| if sl == sl1: | ||
| l = m1 | ||
| else: | ||
| u = m1 | ||
|
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| # method 2, | ||
| # a = dup-lost | ||
| # b = dup^2 - lost^2 = (dup+lost)*(dup-lost)) | ||
| def solve2(xs): | ||
| ys = zip(xs, range(len(xs))) | ||
| a = sum(map(lambda (a, b): a-b, ys)) | ||
| b = sum(map(lambda (a, b): a*a - b*b, ys)) | ||
| return ((b/a - a)/2, (a + b/a)/2) | ||
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| # method 3, | ||
| def solve3(xs): | ||
| (miss, dup) = (-1, -1) | ||
| for i in range(len(xs)): | ||
| while xs[i] != i: | ||
| j = xs[i] | ||
| if xs[j] == xs[i]: | ||
| dup = xs[j] | ||
| miss = i | ||
| break | ||
| else: | ||
| j = xs[i] | ||
| (xs[i], xs[j]) = (xs[j], xs[i]) | ||
| return (miss, dup) | ||
|
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| def test_solve(): | ||
| for i in range(100): | ||
| n = random.randint(0, 10000) | ||
| xs = range(n) | ||
| lost = random.choice(xs) | ||
| xs.remove(lost) | ||
| dup = random.choice(xs) | ||
| xs.append(dup) | ||
| random.shuffle(xs) | ||
| assert(solve(xs[0:n]) == (lost, dup)) | ||
| assert(solve_inplace(xs[0:n]) == (lost, dup)) | ||
| assert(solve3(xs[0:n]), (lost, dup)) | ||
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| def __assert(x, y): | ||
| if x != y: | ||
| print x, y | ||
| assert(x == y) | ||
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| def test(): | ||
| test_solve() | ||
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| if __name__=="__main__": | ||
| test() | ||
| #!/usr/bin/python | ||
|
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| # missdup.py | ||
| # Copyright (C) 2014 Liu Xinyu (liuxinyu95@gmail.com) | ||
| # | ||
| # This program is free software: you can redistribute it and/or modify | ||
| # it under the terms of the GNU General Public License as published by | ||
| # the Free Software Foundation, either version 3 of the License, or | ||
| # (at your option) any later version. | ||
| # | ||
| # This program is distributed in the hope that it will be useful, | ||
| # but WITHOUT ANY WARRANTY; without even the implied warranty of | ||
| # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the | ||
| # GNU General Public License for more details. | ||
| # | ||
| # You should have received a copy of the GNU General Public License | ||
| # along with this program. If not, see <http://www.gnu.org/licenses/>. | ||
|
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||
|
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| import random | ||
|
|
||
| # method 1, d & c | ||
|
|
||
| # [l, u) | ||
| def solve(xs): | ||
| l = 0 | ||
| u = len(xs) | ||
| while l<u: | ||
| m = (l+u)/2 | ||
| left = [x for x in xs if x < m] | ||
| right = [x for x in xs if x >= m] | ||
| if len(left) < m - l: | ||
| lost = (m - 1 + l)*(m - l)/2 - sum(left) | ||
| dup = sum(right) - (u - 1 + m)*(u - m)/2 | ||
| return (lost, dup) | ||
| elif len(left) > m - l: | ||
| lost = (u - 1 + m)*(u - m)/2 - sum(right) | ||
| dup = sum(left) - (m - 1 + l)*(m - l)/2 | ||
| return (lost, dup) | ||
| else: | ||
| if sum(left) == (m -1 + l)*(m - l)/2: | ||
| l = m | ||
| xs = right | ||
| else: | ||
| u = m | ||
| xs = left | ||
|
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| # method 1', in-place D & C | ||
|
|
||
| def partition(xs, l, u, x): | ||
| left = l | ||
| for right in range(l, u): | ||
| if xs[right] < x: | ||
| (xs[left], xs[right]) = (xs[right], xs[left]) | ||
| left = left + 1 | ||
| return left | ||
|
|
||
| def solve_inplace(xs): | ||
| (l, u) = (0, len(xs)) | ||
| while l<u: | ||
| m = (l+u)/2 | ||
| m1 = partition(xs, l, u, m) | ||
| (nl, nr) = (m1 - l, u - m1); | ||
| (sl, sr) = (sum(xs[l:m1]), sum(xs[m1:u])) | ||
| sl1 = (l + m - 1)*(m - l)/2 | ||
| sr1 = (m + u - 1)*(u - m)/2 | ||
| if m1 < m: | ||
| return (sl1 - sl, sr - sr1) | ||
| elif m1 > m: | ||
| return (sr1 - sr, sl - sl1) | ||
| else: | ||
| if sl == sl1: | ||
| l = m1 | ||
| else: | ||
| u = m1 | ||
|
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||
| # method 2, | ||
| # a = dup-lost | ||
| # b = dup^2 - lost^2 = (dup+lost)*(dup-lost)) | ||
| def solve2(xs): | ||
| ys = zip(xs, range(len(xs))) | ||
| a = sum(map(lambda (a, b): a-b, ys)) | ||
| b = sum(map(lambda (a, b): a*a - b*b, ys)) | ||
| return ((b/a - a)/2, (a + b/a)/2) | ||
|
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| # method 3, | ||
| def solve3(xs): | ||
| (miss, dup) = (-1, -1) | ||
| for i in range(len(xs)): | ||
| while xs[i] != i: | ||
| j = xs[i] | ||
| if xs[j] == xs[i]: | ||
| dup = xs[j] | ||
| miss = i | ||
| break | ||
| else: | ||
| j = xs[i] | ||
| (xs[i], xs[j]) = (xs[j], xs[i]) | ||
| return (miss, dup) | ||
|
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| def test_solve(): | ||
| for i in range(100): | ||
| n = random.randint(0, 10000) | ||
| xs = range(n) | ||
| lost = random.choice(xs) | ||
| xs.remove(lost) | ||
| dup = random.choice(xs) | ||
| xs.append(dup) | ||
| random.shuffle(xs) | ||
| assert(solve(xs[0:n]) == (lost, dup)) | ||
| assert(solve_inplace(xs[0:n]) == (lost, dup)) | ||
| assert(solve3(xs[0:n]), (lost, dup)) | ||
|
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| def __assert(x, y): | ||
| if x != y: | ||
| print x, y | ||
| assert(x == y) | ||
|
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| def test(): | ||
| test_solve() | ||
|
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| if __name__=="__main__": | ||
| test() |
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others/problems/number-theory/linear-congruence/poj-1061/frog.c
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17 changes: 17 additions & 0 deletions
17
others/problems/number-theory/linear-congruence/poj-1061/frog1.c
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