hello-algo/codes/rust/chapter_dynamic_programming/coin_change.rs
codingonion 7ffef7e1d6
update the author info sjinzh -> codingonion (#1017)
* update author information

* Update index.md

---------

Co-authored-by: Yudong Jin <krahets@163.com>
2024-01-02 01:25:37 +08:00

67 lines
2 KiB
Rust

/*
* File: coin_change.rs
* Created Time: 2023-07-09
* Author: codingonion (coderonion@gmail.com)
*/
/* 零钱兑换:动态规划 */
fn coin_change_dp(coins: &[i32], amt: usize) -> i32 {
let n = coins.len();
let max = amt + 1;
// 初始化 dp 表
let mut dp = vec![vec![0; amt + 1]; n + 1];
// 状态转移:首行首列
for a in 1..= amt {
dp[0][a] = max;
}
// 状态转移:其余行和列
for i in 1..=n {
for a in 1..=amt {
if coins[i - 1] > a as i32 {
// 若超过目标金额,则不选硬币 i
dp[i][a] = dp[i - 1][a];
} else {
// 不选和选硬币 i 这两种方案的较小值
dp[i][a] = std::cmp::min(dp[i - 1][a], dp[i][a - coins[i - 1] as usize] + 1);
}
}
}
if dp[n][amt] != max { return dp[n][amt] as i32; } else { -1 }
}
/* 零钱兑换:空间优化后的动态规划 */
fn coin_change_dp_comp(coins: &[i32], amt: usize) -> i32 {
let n = coins.len();
let max = amt + 1;
// 初始化 dp 表
let mut dp = vec![0; amt + 1];
dp.fill(max);
dp[0] = 0;
// 状态转移
for i in 1..=n {
for a in 1..=amt {
if coins[i - 1] > a as i32 {
// 若超过目标金额,则不选硬币 i
dp[a] = dp[a];
} else {
// 不选和选硬币 i 这两种方案的较小值
dp[a] = std::cmp::min(dp[a], dp[a - coins[i - 1] as usize] + 1);
}
}
}
if dp[amt] != max { return dp[amt] as i32; } else { -1 }
}
/* Driver Code */
pub fn main() {
let coins = [ 1, 2, 5 ];
let amt: usize = 4;
// 动态规划
let res = coin_change_dp(&coins, amt);
println!("凑到目标金额所需的最少硬币数量为 {res}");
// 空间优化后的动态规划
let res = coin_change_dp_comp(&coins, amt);
println!("凑到目标金额所需的最少硬币数量为 {res}");
}