题目大意:给出m和s, 再给出m种电子硬币,每种硬币有两种金额xi,yi。现在要在m种硬币种选若干个硬币,可以重复选同一种硬币, 使得(x1 + x2 + .... + xn) ^ 2 + (y1 + y2 + ... + yn) ^ 2 == s * s, 要求n尽量小,(n为选取硬币的个数), 如果不能选出满足条件的硬币,输出-1。
解题思路:二维的完全背包问题,注意要用long long。
#include <stdio.h> #include <string.h> const int N = 305; struct coin{ int x; int y; }val[50]; int n, s, S, dp[N][N]; void read() { memset(val, 0, sizeof(val)); scanf("%d%d", &n, &s); S = s * s; for (int i = 0; i < n; i++) scanf("%d%d", &val[i].x, &val[i].y); } int solve() { int cnt = 1 << 30; memset(dp, 0, sizeof(dp)); dp[0][0] = 1; for (int k = 0; k < n; k++) { for (int i = 0; i <= s; i++) { for (int j = 0; j <= s; j++) { if (dp[i][j]) { int p = i + val[k].x, q = j + val[k].y; if (p > s || q > s) break; if (dp[p][q] == 0 || dp[i][j] + 1 < dp[p][q]) dp[p][q] = dp[i][j] + 1; if (p * p + q * q == S && dp[p][q] < cnt) cnt = dp[p][q]; } } } } if (cnt == 1 << 30) return 0; else return cnt; } int main() { int cas; scanf("%d", &cas); while (cas--) { read(); int ans = solve(); if (ans) printf("%d ", ans - 1); else printf("not possible "); } return 0; }