65 lines
1.7 KiB
Rust
65 lines
1.7 KiB
Rust
/*
|
||
* File: coin_change_ii.rs
|
||
* Created Time: 2023-07-09
|
||
* Author: codingonion (coderonion@gmail.com)
|
||
*/
|
||
|
||
/* 零錢兌換 II：動態規劃 */
|
||
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;
|
||
}
|
||
// 狀態轉移
|
||
for i in 1..=n {
|
||
for a in 1..=amt {
|
||
if coins[i - 1] > a as i32 {
|
||
// 若超過目標金額，則不選硬幣 i
|
||
dp[i][a] = dp[i - 1][a];
|
||
} else {
|
||
// 不選和選硬幣 i 這兩種方案之和
|
||
dp[i][a] = dp[i - 1][a] + dp[i][a - coins[i - 1] as usize];
|
||
}
|
||
}
|
||
}
|
||
dp[n][amt]
|
||
}
|
||
|
||
/* 零錢兌換 II：空間最佳化後的動態規劃 */
|
||
fn coin_change_ii_dp_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;
|
||
// 狀態轉移
|
||
for i in 1..=n {
|
||
for a in 1..=amt {
|
||
if coins[i - 1] > a as i32 {
|
||
// 若超過目標金額，則不選硬幣 i
|
||
dp[a] = dp[a];
|
||
} else {
|
||
// 不選和選硬幣 i 這兩種方案之和
|
||
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;
|
||
|
||
// 動態規劃
|
||
let res = coin_change_ii_dp(&coins, amt);
|
||
println!("湊出目標金額的硬幣組合數量為 {res}");
|
||
|
||
// 空間最佳化後的動態規劃
|
||
let res = coin_change_ii_dp_comp(&coins, amt);
|
||
println!("湊出目標金額的硬幣組合數量為 {res}");
|
||
}
|