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Feature/chapter dynamic programming swift (#608)
* feat: add Swift codes for intro_to_dynamic_programming article * feat: add Swift codes for dp_problem_features article * feat: add Swift codes for dp_solution_pipeline article * feat: add Swift codes for knapsack_problem article * feat: add Swift codes for unbounded_knapsack_problem article * feat: add Swift codes for edit_distance_problem article
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/**
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* File: unbounded_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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/* 完全背包:动态规划 */
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func unboundedKnapsackDP(wgt: [Int], val: [Int], cap: Int) -> Int {
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let n = wgt.count
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// 初始化 dp 表
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var dp = Array(repeating: Array(repeating: 0, count: cap + 1), count: n + 1)
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// 状态转移
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for i in stride(from: 1, through: n, by: 1) {
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for c in stride(from: 1, through: cap, by: 1) {
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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:状态压缩后的动态规划 */
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func unboundedKnapsackDPComp(wgt: [Int], val: [Int], cap: Int) -> Int {
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let n = wgt.count
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// 初始化 dp 表
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var dp = Array(repeating: 0, count: cap + 1)
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// 状态转移
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for i in stride(from: 1, through: n, by: 1) {
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for c in stride(from: 1, through: cap, by: 1) {
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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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@main
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enum UnboundedKnapsack {
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/* Driver Code */
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static func main() {
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let wgt = [1, 2, 3]
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let val = [5, 11, 15]
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let cap = 4
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// 动态规划
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var res = unboundedKnapsackDP(wgt: wgt, val: val, cap: 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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// 状态压缩后的动态规划
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res = unboundedKnapsackDPComp(wgt: wgt, val: val, cap: 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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}
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}
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