117 lines
3.5 KiB
Dart
117 lines
3.5 KiB
Dart
/**
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* File: 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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/* 0-1 Knapsack: Brute force search */
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int knapsackDFS(List<int> wgt, List<int> val, int i, int c) {
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// If all items have been chosen or the knapsack has no remaining capacity, return value 0
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if (i == 0 || c == 0) {
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return 0;
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}
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// If exceeding the knapsack capacity, can only choose not to put it in the knapsack
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if (wgt[i - 1] > c) {
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return knapsackDFS(wgt, val, i - 1, c);
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}
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// Calculate the maximum value of not putting in and putting in item i
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int no = knapsackDFS(wgt, val, i - 1, c);
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int yes = knapsackDFS(wgt, val, i - 1, c - wgt[i - 1]) + val[i - 1];
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// Return the greater value of the two options
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return max(no, yes);
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}
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/* 0-1 Knapsack: Memoized search */
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int knapsackDFSMem(
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List<int> wgt,
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List<int> val,
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List<List<int>> mem,
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int i,
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int c,
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) {
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// If all items have been chosen or the knapsack has no remaining capacity, return value 0
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if (i == 0 || c == 0) {
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return 0;
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}
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// If there is a record, return it
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if (mem[i][c] != -1) {
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return mem[i][c];
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}
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// If exceeding the knapsack capacity, can only choose not to put it in the knapsack
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if (wgt[i - 1] > c) {
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return knapsackDFSMem(wgt, val, mem, i - 1, c);
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}
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// Calculate the maximum value of not putting in and putting in item i
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int no = knapsackDFSMem(wgt, val, mem, i - 1, c);
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int yes = knapsackDFSMem(wgt, val, mem, i - 1, c - wgt[i - 1]) + val[i - 1];
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// Record and return the greater value of the two options
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mem[i][c] = max(no, yes);
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return mem[i][c];
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}
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/* 0-1 Knapsack: Dynamic programming */
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int knapsackDP(List<int> wgt, List<int> val, int cap) {
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int n = wgt.length;
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// Initialize dp table
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List<List<int>> dp = List.generate(n + 1, (index) => List.filled(cap + 1, 0));
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// State transition
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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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// 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] = max(dp[i - 1][c], dp[i - 1][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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/* 0-1 Knapsack: Space-optimized dynamic programming */
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int knapsackDPComp(List<int> wgt, List<int> val, int cap) {
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int n = wgt.length;
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// Initialize dp table
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List<int> dp = List.filled(cap + 1, 0);
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// State transition
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for (int i = 1; i <= n; i++) {
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// Traverse in reverse order
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for (int c = cap; c >= 1; c--) {
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if (wgt[i - 1] <= c) {
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// The greater value between not choosing and choosing item i
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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 = [10, 20, 30, 40, 50];
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List<int> val = [50, 120, 150, 210, 240];
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int cap = 50;
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int n = wgt.length;
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// Brute force search
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int res = knapsackDFS(wgt, val, n, cap);
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print("Maximum value of items without exceeding bag capacity = $res");
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// Memoized search
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List<List<int>> mem =
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List.generate(n + 1, (index) => List.filled(cap + 1, -1));
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res = knapsackDFSMem(wgt, val, mem, n, cap);
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print("Maximum value of items without exceeding bag capacity = $res");
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// Dynamic programming
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res = knapsackDP(wgt, val, cap);
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print("Maximum value of items without exceeding bag capacity = $res");
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// Space-optimized dynamic programming
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res = knapsackDPComp(wgt, val, cap);
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print("Maximum value of items without exceeding bag capacity = $res");
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}
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