111 lines
3.9 KiB
Swift
111 lines
3.9 KiB
Swift
/**
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* File: knapsack.swift
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* Created Time: 2023-07-15
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* Author: nuomi1 (nuomi1@qq.com)
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*/
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/* 0-1 Knapsack: Brute force search */
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func knapsackDFS(wgt: [Int], val: [Int], i: Int, c: Int) -> Int {
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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: wgt, val: val, i: i - 1, c: 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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let no = knapsackDFS(wgt: wgt, val: val, i: i - 1, c: c)
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let yes = knapsackDFS(wgt: wgt, val: val, i: i - 1, c: 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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func knapsackDFSMem(wgt: [Int], val: [Int], mem: inout [[Int]], i: Int, c: Int) -> Int {
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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: wgt, val: val, mem: &mem, i: i - 1, c: 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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let no = knapsackDFSMem(wgt: wgt, val: val, mem: &mem, i: i - 1, c: c)
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let yes = knapsackDFSMem(wgt: wgt, val: val, mem: &mem, i: i - 1, c: 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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func knapsackDP(wgt: [Int], val: [Int], cap: Int) -> Int {
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let n = wgt.count
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// Initialize dp table
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var dp = Array(repeating: Array(repeating: 0, count: cap + 1), count: n + 1)
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// State transition
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for i in 1 ... n {
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for c in 1 ... cap {
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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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func knapsackDPComp(wgt: [Int], val: [Int], cap: Int) -> Int {
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let n = wgt.count
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// Initialize dp table
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var dp = Array(repeating: 0, count: cap + 1)
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// State transition
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for i in 1 ... n {
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// Traverse in reverse order
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for c in (1 ... cap).reversed() {
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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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@main
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enum Knapsack {
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/* Driver Code */
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static func main() {
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let wgt = [10, 20, 30, 40, 50]
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let val = [50, 120, 150, 210, 240]
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let cap = 50
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let n = wgt.count
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// Brute force search
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var res = knapsackDFS(wgt: wgt, val: val, i: n, c: cap)
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print("Maximum value of items within the backpack capacity = \(res)")
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// Memoized search
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var mem = Array(repeating: Array(repeating: -1, count: cap + 1), count: n + 1)
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res = knapsackDFSMem(wgt: wgt, val: val, mem: &mem, i: n, c: cap)
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print("Maximum value of items within the backpack capacity = \(res)")
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// Dynamic programming
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res = knapsackDP(wgt: wgt, val: val, cap: cap)
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print("Maximum value of items within the backpack capacity = \(res)")
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// Space-optimized dynamic programming
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res = knapsackDPComp(wgt: wgt, val: val, cap: cap)
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print("Maximum value of items within the backpack capacity = \(res)")
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}
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}
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