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63 lines
1.7 KiB
63 lines
1.7 KiB
/**
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* File: unbounded_knapsack.dart
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* Created Time: 2023-08-11
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* Author: liuyuxin (gvenusleo@gmail.com)
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*/
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import 'dart:math';
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/* 完全背包：动态规划 */
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int unboundedKnapsackDP(List<int> wgt, List<int> val, int cap) {
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int n = wgt.length;
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// 初始化 dp 表
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List<List<int>> dp = List.generate(n + 1, (index) => List.filled(cap + 1, 0));
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// 状态转移
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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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// 若超过背包容量，则不选物品 i
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dp[i][c] = dp[i - 1][c];
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} else {
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// 不选和选物品 i 这两种方案的较大值
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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：空间优化后的动态规划 */
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int unboundedKnapsackDPComp(List<int> wgt, List<int> val, int cap) {
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int n = wgt.length;
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// 初始化 dp 表
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List<int> dp = List.filled(cap + 1, 0);
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// 状态转移
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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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// 若超过背包容量，则不选物品 i
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dp[c] = dp[c];
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} else {
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// 不选和选物品 i 这两种方案的较大值
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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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void main() {
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List<int> wgt = [1, 2, 3];
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List<int> val = [5, 11, 15];
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int cap = 4;
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// 动态规划
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int res = unboundedKnapsackDP(wgt, val, cap);
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print("不超过背包容量的最大物品价值为 $res");
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// 空间优化后的动态规划
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int resComp = unboundedKnapsackDPComp(wgt, val, cap);
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print("不超过背包容量的最大物品价值为 $resComp");
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}
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