hello-algo/codes/rust/chapter_dynamic_programming/coin_change_ii.rs
sjinzh b1f8857212
rust and zig : add codes for chapter_dynamic_programming (#606)
* rust : add codes for chapter_dynamic_programming

* zig : add codes for chapter_dynamic_programming

* rust : add codes for chapter_backtracking

* Update n_queens.rs

---------

Co-authored-by: Yudong Jin <krahets@163.com>
2023-07-15 23:16:02 +08:00

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/*
* File: coin_change_ii.rs
* Created Time: 2023-07-09
* Author: sjinzh (sjinzh@gmail.com)
*/
/* 零钱兑换 II动态规划 */
fn coin_change_ii_dp(coins: &[i32], amt: usize) -> i32 {
let n = coins.len();
// 初始化 dp 表
let mut dp = vec![vec![0; amt + 1]; n + 1];
// 初始化首列
for i in 0..= n {
dp[i][0] = 1;
}
// 状态转移
for i in 1..=n {
for a in 1..=amt {
if coins[i - 1] > a as i32 {
// 若超过背包容量,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] = dp[i - 1][a] + dp[i][a - coins[i - 1] as usize];
}
}
}
dp[n][amt]
}
/* 零钱兑换 II状态压缩后的动态规划 */
fn coin_change_dp_ii_comp(coins: &[i32], amt: usize) -> i32 {
let n = coins.len();
// 初始化 dp 表
let mut dp = vec![0; amt + 1];
dp[0] = 1;
// 状态转移
for i in 1..=n {
for a in 1..=amt {
if coins[i - 1] > a as i32 {
// 若超过背包容量,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] = dp[a] + dp[a - coins[i - 1] as usize];
}
}
}
dp[amt]
}
/* Driver Code */
pub fn main() {
let coins = [ 1, 2, 5 ];
let amt: usize = 5;
// 动态规划
let res = coin_change_ii_dp(&coins, amt);
println!("凑出目标金额的硬币组合数量为 {res}");
// 状态压缩后的动态规划
let res = coin_change_dp_ii_comp(&coins, amt);
println!("凑出目标金额的硬币组合数量为 {res}");
}