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82 lines
2.2 KiB
82 lines
2.2 KiB
/**
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* File: unbounded_knapsack.c
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* Created Time: 2023-10-02
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* Author: Zuoxun (845242523@qq.com)
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*/
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#include "../utils/common.h"
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/* 求最大值 */
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int myMax(int a, int b) {
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return a > b ? a : b;
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}
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/* 完全背包：動態規劃 */
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int unboundedKnapsackDP(int wgt[], int val[], int cap, int wgtSize) {
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int n = wgtSize;
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// 初始化 dp 表
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int **dp = malloc((n + 1) * sizeof(int *));
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for (int i = 0; i <= n; i++) {
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dp[i] = calloc(cap + 1, sizeof(int));
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}
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// 狀態轉移
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for (int i = 1; i <= n; i++) {
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for (int c = 1; c <= cap; c++) {
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if (wgt[i - 1] > c) {
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// 若超過背包容量，則不選物品 i
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dp[i][c] = dp[i - 1][c];
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} else {
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// 不選和選物品 i 這兩種方案的較大值
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dp[i][c] = myMax(dp[i - 1][c], dp[i][c - wgt[i - 1]] + val[i - 1]);
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}
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}
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}
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int res = dp[n][cap];
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// 釋放記憶體
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for (int i = 0; i <= n; i++) {
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free(dp[i]);
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}
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return res;
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}
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/* 完全背包：空間最佳化後的動態規劃 */
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int unboundedKnapsackDPComp(int wgt[], int val[], int cap, int wgtSize) {
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int n = wgtSize;
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// 初始化 dp 表
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int *dp = calloc(cap + 1, sizeof(int));
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// 狀態轉移
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for (int i = 1; i <= n; i++) {
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for (int c = 1; c <= cap; c++) {
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if (wgt[i - 1] > c) {
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// 若超過背包容量，則不選物品 i
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dp[c] = dp[c];
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} else {
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// 不選和選物品 i 這兩種方案的較大值
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dp[c] = myMax(dp[c], dp[c - wgt[i - 1]] + val[i - 1]);
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}
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}
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}
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int res = dp[cap];
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// 釋放記憶體
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free(dp);
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return res;
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}
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/* Driver code */
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int main() {
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int wgt[] = {1, 2, 3};
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int val[] = {5, 11, 15};
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int wgtSize = sizeof(wgt) / sizeof(wgt[0]);
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int cap = 4;
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// 動態規劃
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int res = unboundedKnapsackDP(wgt, val, cap, wgtSize);
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printf("不超過背包容量的最大物品價值為 %d\n", res);
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// 空間最佳化後的動態規劃
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res = unboundedKnapsackDPComp(wgt, val, cap, wgtSize);
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printf("不超過背包容量的最大物品價值為 %d\n", res);
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return 0;
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}
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