【DP】 0/1 knapsack problem (single copy)

刚刚博客还不能用，现在终于可以了，呵呵，感谢CSDN管理员！

今天中午上课之前，按照书上0/1背包问题的算法思想用C实现了一下。

具体DP思想见 《算法概率》P184 背包问题

附代码：

#include <stdio.h>#include <stdlib.h>#include <string.h>int knapsack(int weight[], int value[], int W, int n){int i, j;int w;int max_value;int** K = (int**)malloc(sizeof(int*) * (W + 1));for (i = 0; i < W + 1; i++){K[i] = (int*)malloc(sizeof(int) * (n + 1));}for (i = 0; i <= W; i++){K[i][0] = 0;}for (i = 0; i <= n; i++){K[0][i] = 0;}for (i = 1; i<= n; i++){for (w = 1; w <= W; w++){if (weight[i - 1] > w){K[w][i] = K[w][i - 1];}else{int pre_weight = K[w][i - 1];int indexW = w - weight[i - 1];int indexI = i - 1;K[w][i] = max(pre_weight, K[indexW][indexI] + value[i - 1]);/*K[w][i] = max(K[w][i - 1], K[w - weight[i]][i - 1] + value[i - 1]);*/}}}/*for (i = 0; i <= W; i++){for (j = 0; j <= n; j++)printf("%d ", K[i][j]);printf("/n");}*/max_value = K[W][n];for (i = 0; i <= W; i++){free((void*)K[i]);}free((void*)K);return max_value;}int main(){int weight[] = {6, 3, 4, 2};int value[] = {30, 14, 16, 9};int W = 10; /* weight that bag carries*/int n = sizeof(value) / sizeof(int); /*num of bags*/int max_value = knapsack(weight, value, W, n);printf("max value =%d", max_value);return 0;}