硬币问题 动态规划 算法入门经典

递归

#include <stdio.h>#include <string.h>#define maxn 100#define maxm 100int d[maxn];int v[maxm];int s, n;int dpmin(int t){int *ans = &d[t];if(*ans != -1) return *ans;*ans = 1<<30;int j, tmp;for(j = 0; j < n; ++j) if(t >= v[j] && *ans > (tmp = dpmin(t - v[j])+1)) *ans = tmp; return *ans;}int dpmax(int t){int *ans = &d[t];if(*ans != -1) return *ans;*ans = -1<<30;int j, tmp;for(j = 0; j < n; ++j) if(t >= v[j] && *ans < (tmp = dpmax(t - v[j])+1)) *ans = tmp; return *ans;}int main(){int i, tmp;scanf("%d%d", &n, &s);for(i = 0; i < n; ++i)  scanf("%d", &v[i]);memset(d, -1, sizeof(d));d[0] = 0;if((tmp = dpmin(s)) < 1<<30) printf("min = %d\n", tmp);memset(d, -1, sizeof(d));d[0] = 0; if((tmp = dpmax(s)) > 0)printf("max = %d\n", tmp);return 0;}

递归

#include <stdio.h>#include <string.h>#define maxn 100#define maxm 100int d[maxn];int v[maxm];int vis[maxn];int s, n;int dpmin(int t){int *ans = &d[t];if(vis[t]) return *ans;vis[t] = 1;*ans = 1<<30;int j, tmp;for(j = 0; j < n; ++j) if(t >= v[j] && *ans > (tmp = dpmin(t - v[j])+1)) *ans = tmp; return *ans;}int dpmax(int t){int *ans = &d[t];if(vis[t]) return *ans;vis[t] = 1; *ans = -1<<30;int j, tmp;for(j = 0; j < n; ++j) if(t >= v[j] && *ans < (tmp = dpmax(t - v[j])+1)) *ans = tmp; return *ans;}int main(){int i, tmp;scanf("%d%d", &n, &s);for(i = 0; i < n; ++i)  scanf("%d", &v[i]);memset(vis, 0, sizeof(vis));d[0] = 0;  vis[0] = 1;if((tmp = dpmin(s)) < 1<<30) printf("min = %d\n", tmp);memset(vis, 0, sizeof(vis));d[0] = 0;  vis[0] = 1;if((tmp = dpmin(s)) < 1<<30) printf("min = %d\n", tmp);return 0;}

递推

#include <stdio.h>#include <string.h>#define maxn 100#define maxm 100#define INF 0x7fffint min[maxn];int max[maxn];int v[maxm]; int n, s;void dpfunc(){int i, j, tmp;for(i = 1; i <= s; ++i){min[i] = INF;max[i] = -INF;}min[0] = 0;max[0] = 0;for(i = 1; i <= s; ++i)for(j = 0; j < n; ++j){if(i >= v[j]){if(min[i] > (tmp = min[i-v[j]] + 1)) min[i] = tmp;if(max[i] < (tmp = max[i-v[j]] + 1)) max[i] = tmp;}}}int main(){scanf("%d%d", &n, &s);int i;for(i = 0; i < n; ++i) scanf("%d", &v[i]);dpfunc();if(min[s] < INF) printf("min = %d\n", min[s]);if(max[s] > 0)   printf("max = %d\n", max[s]);return 0;}