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65 lines
1.9 KiB
65 lines
1.9 KiB
/**
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* File: unbounded_knapsack.cpp
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* Created Time: 2023-07-11
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* Author: krahets (krahets@163.com)
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*/
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#include "../utils/common.hpp"
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/* 完全背包：動態規劃 */
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int unboundedKnapsackDP(vector<int> &wgt, vector<int> &val, int cap) {
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int n = wgt.size();
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// 初始化 dp 表
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vector<vector<int>> dp(n + 1, vector<int>(cap + 1, 0));
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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] = max(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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return dp[n][cap];
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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(vector<int> &wgt, vector<int> &val, int cap) {
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int n = wgt.size();
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// 初始化 dp 表
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vector<int> dp(cap + 1, 0);
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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] = max(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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return dp[cap];
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}
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/* Driver code */
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int main() {
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vector<int> wgt = {1, 2, 3};
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vector<int> val = {5, 11, 15};
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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);
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cout << "不超過背包容量的最大物品價值為 " << res << endl;
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// 空間最佳化後的動態規劃
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res = unboundedKnapsackDPComp(wgt, val, cap);
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cout << "不超過背包容量的最大物品價值為 " << res << endl;
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return 0;
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}
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