01背包 + 数学（平衡） 之 uva 562

//  [7/21/2014 Sjm]/*题目关键：Given a bag with a maximum of 100 coins, determine the most fair division between two persons.This means that the difference between the amount each person obtains should be minimised.  思路：两个人分硬币，要公平。那就让一个人所获得的硬币无限接近总的硬币的数目的一半（01背包求解），剩下的硬币给另外一个人。此时，即可做到："the difference between the amount each person obtains should be minimised. " */

#include <iostream>#include <cstdlib>#include <cstdio>#include <algorithm>#include <cstring>using namespace std;const int MAX = 50005;int arr[105];int dp[MAX];int m, sum, Val;int Solve() {memset(dp, 0, sizeof(dp));for (int i = 1; i <= m; ++i) {for (int j = Val; j >= arr[i]; --j) {dp[j] = max(dp[j], dp[j - arr[i]] + arr[i]);}}return abs(sum - 2 * dp[Val]);}int main(){//freopen("input.txt", "r", stdin);int T;scanf("%d", &T);while (T--) {sum = 0;scanf("%d", &m);for (int i = 1; i <= m; ++i) {scanf("%d", &arr[i]);sum += arr[i];}Val = sum / 2;printf("%d\n", Solve());}return 0;}