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61 lines
1.8 KiB
61 lines
1.8 KiB
/*
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* File: unbounded_knapsack.rs
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* Created Time: 2023-07-09
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* Author: codingonion (coderonion@gmail.com)
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*/
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/* 完全背包：動態規劃 */
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fn unbounded_knapsack_dp(wgt: &[i32], val: &[i32], cap: usize) -> i32 {
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let n = wgt.len();
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// 初始化 dp 表
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let mut dp = vec![vec![0; cap + 1]; n + 1];
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// 狀態轉移
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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 as i32 {
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// 若超過背包容量，則不選物品 i
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dp[i][c] = dp[i - 1][c];
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} else {
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// 不選和選物品 i 這兩種方案的較大值
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dp[i][c] = std::cmp::max(dp[i - 1][c], dp[i][c - wgt[i - 1] as usize] + 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：空間最佳化後的動態規劃 */
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fn unbounded_knapsack_dp_comp(wgt: &[i32], val: &[i32], cap: usize) -> i32 {
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let n = wgt.len();
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// 初始化 dp 表
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let mut dp = vec![0; cap + 1];
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// 狀態轉移
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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 as i32 {
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// 若超過背包容量，則不選物品 i
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dp[c] = dp[c];
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} else {
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// 不選和選物品 i 這兩種方案的較大值
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dp[c] = std::cmp::max(dp[c], dp[c - wgt[i - 1] as usize] + val[i - 1]);
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}
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}
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}
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dp[cap]
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}
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/* Driver Code */
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pub fn 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: usize = 4;
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// 動態規劃
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let res = unbounded_knapsack_dp(&wgt, &val, cap);
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println!("不超過背包容量的最大物品價值為 {res}");
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// 空間最佳化後的動態規劃
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let res = unbounded_knapsack_dp_comp(&wgt, &val, cap);
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println!("不超過背包容量的最大物品價值為 {res}");
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}
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