65 lines
1.9 KiB
Rust
65 lines
1.9 KiB
Rust
/*
|
|
* File: coin_change_ii.rs
|
|
* Created Time: 2023-07-09
|
|
* Author: codingonion (coderonion@gmail.com)
|
|
*/
|
|
|
|
/* Coin change II: Dynamic programming */
|
|
fn coin_change_ii_dp(coins: &[i32], amt: usize) -> i32 {
|
|
let n = coins.len();
|
|
// Initialize dp table
|
|
let mut dp = vec![vec![0; amt + 1]; n + 1];
|
|
// Initialize first column
|
|
for i in 0..=n {
|
|
dp[i][0] = 1;
|
|
}
|
|
// State transition
|
|
for i in 1..=n {
|
|
for a in 1..=amt {
|
|
if coins[i - 1] > a as i32 {
|
|
// If exceeding the target amount, do not choose coin i
|
|
dp[i][a] = dp[i - 1][a];
|
|
} else {
|
|
// The sum of the two options of not choosing and choosing coin i
|
|
dp[i][a] = dp[i - 1][a] + dp[i][a - coins[i - 1] as usize];
|
|
}
|
|
}
|
|
}
|
|
dp[n][amt]
|
|
}
|
|
|
|
/* Coin change II: Space-optimized dynamic programming */
|
|
fn coin_change_ii_dp_comp(coins: &[i32], amt: usize) -> i32 {
|
|
let n = coins.len();
|
|
// Initialize dp table
|
|
let mut dp = vec![0; amt + 1];
|
|
dp[0] = 1;
|
|
// State transition
|
|
for i in 1..=n {
|
|
for a in 1..=amt {
|
|
if coins[i - 1] > a as i32 {
|
|
// If exceeding the target amount, do not choose coin i
|
|
dp[a] = dp[a];
|
|
} else {
|
|
// The sum of the two options of not choosing and choosing coin i
|
|
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;
|
|
|
|
// Dynamic programming
|
|
let res = coin_change_ii_dp(&coins, amt);
|
|
println!("The number of coin combinations to make up the target amount is {res}");
|
|
|
|
// Space-optimized dynamic programming
|
|
let res = coin_change_ii_dp_comp(&coins, amt);
|
|
println!("The number of coin combinations to make up the target amount is {res}");
|
|
}
|