64 lines
1.9 KiB
JavaScript
64 lines
1.9 KiB
JavaScript
/**
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* File: unbounded_knapsack.js
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* Created Time: 2023-08-23
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* Author: Gaofer Chou (gaofer-chou@qq.com)
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*/
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/* Complete knapsack: Dynamic programming */
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function unboundedKnapsackDP(wgt, val, cap) {
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const n = wgt.length;
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// Initialize dp table
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const dp = Array.from({ length: n + 1 }, () =>
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Array.from({ length: cap + 1 }, () => 0)
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);
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// State transition
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for (let i = 1; i <= n; i++) {
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for (let c = 1; c <= cap; c++) {
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if (wgt[i - 1] > c) {
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// If exceeding the knapsack capacity, do not choose item i
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dp[i][c] = dp[i - 1][c];
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} else {
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// The greater value between not choosing and choosing item i
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dp[i][c] = Math.max(
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dp[i - 1][c],
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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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}
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return dp[n][cap];
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}
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/* Complete Knapsack: Space-optimized dynamic programming */
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function unboundedKnapsackDPComp(wgt, val, cap) {
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const n = wgt.length;
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// Initialize dp table
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const dp = Array.from({ length: cap + 1 }, () => 0);
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// State transition
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for (let i = 1; i <= n; i++) {
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for (let c = 1; c <= cap; c++) {
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if (wgt[i - 1] > c) {
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// If exceeding the knapsack capacity, do not choose item i
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dp[c] = dp[c];
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} else {
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// The greater value between not choosing and choosing item i
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dp[c] = Math.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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const wgt = [1, 2, 3];
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const val = [5, 11, 15];
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const cap = 4;
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// Dynamic programming
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let res = unboundedKnapsackDP(wgt, val, cap);
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console.log(`不超过背包容量的最大物品价值为 ${res}`);
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// Space-optimized dynamic programming
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res = unboundedKnapsackDPComp(wgt, val, cap);
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console.log(`不超过背包容量的最大物品价值为 ${res}`);
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