e720aa2d24
* Sync recent changes to the revised Word. * Revised the preface chapter * Revised the introduction chapter * Revised the computation complexity chapter * Revised the chapter data structure * Revised the chapter array and linked list * Revised the chapter stack and queue * Revised the chapter hashing * Revised the chapter tree * Revised the chapter heap * Revised the chapter graph * Revised the chapter searching * Reivised the sorting chapter * Revised the divide and conquer chapter * Revised the chapter backtacking * Revised the DP chapter * Revised the greedy chapter * Revised the appendix chapter * Revised the preface chapter doubly * Revised the figures
68 lines
2.0 KiB
Rust
68 lines
2.0 KiB
Rust
/*
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* File: coin_change.rs
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* Created Time: 2023-07-09
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* Author: sjinzh (sjinzh@gmail.com)
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*/
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/* 零钱兑换：动态规划 */
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fn coin_change_dp(coins: &[i32], amt: usize) -> i32 {
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let n = coins.len();
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let max = amt + 1;
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// 初始化 dp 表
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let mut dp = vec![vec![0; amt + 1]; n + 1];
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// 状态转移：首行首列
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for a in 1..= amt {
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dp[0][a] = max;
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}
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// 状态转移：其余行和列
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for i in 1..=n {
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for a in 1..=amt {
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if coins[i - 1] > a as i32 {
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// 若超过目标金额，则不选硬币 i
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dp[i][a] = dp[i - 1][a];
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} else {
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// 不选和选硬币 i 这两种方案的较小值
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dp[i][a] = std::cmp::min(dp[i - 1][a], dp[i][a - coins[i - 1] as usize] + 1);
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}
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}
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}
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if dp[n][amt] != max { return dp[n][amt] as i32; } else { -1 }
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}
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/* 零钱兑换：空间优化后的动态规划 */
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fn coin_change_dp_comp(coins: &[i32], amt: usize) -> i32 {
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let n = coins.len();
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let max = amt + 1;
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// 初始化 dp 表
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let mut dp = vec![0; amt + 1];
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dp.fill(max);
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dp[0] = 0;
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// 状态转移
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for i in 1..=n {
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for a in 1..=amt {
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if coins[i - 1] > a as i32 {
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// 若超过目标金额，则不选硬币 i
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dp[a] = dp[a];
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} else {
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// 不选和选硬币 i 这两种方案的较小值
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dp[a] = std::cmp::min(dp[a], dp[a - coins[i - 1] as usize] + 1);
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}
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}
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}
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if dp[amt] != max { return dp[amt] as i32; } else { -1 }
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}
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/* Driver Code */
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pub fn main() {
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let coins = [ 1, 2, 5 ];
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let amt: usize = 4;
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// 动态规划
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let res = coin_change_dp(&coins, amt);
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println!("凑到目标金额所需的最少硬币数量为 {res}");
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// 空间优化后的动态规划
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let res = coin_change_dp_comp(&coins, amt);
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println!("凑到目标金额所需的最少硬币数量为 {res}");
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}
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