76 lines
2.1 KiB
Rust
76 lines
2.1 KiB
Rust
/*
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* File: coin_change.rs
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* Created Time: 2023-07-09
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* Author: codingonion (coderonion@gmail.com)
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*/
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/* Coin change: Dynamic programming */
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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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// Initialize dp table
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let mut dp = vec![vec![0; amt + 1]; n + 1];
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// State transition: first row and first column
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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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// State transition: the rest of the rows and columns
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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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// If exceeding the target amount, do not choose coin i
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dp[i][a] = dp[i - 1][a];
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} else {
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// The smaller value between not choosing and choosing coin i
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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 {
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return dp[n][amt] as i32;
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} else {
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-1
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}
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}
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/* Coin change: Space-optimized dynamic programming */
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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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// Initialize dp table
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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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// State transition
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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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// If exceeding the target amount, do not choose coin i
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dp[a] = dp[a];
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} else {
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// The smaller value between not choosing and choosing coin i
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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 {
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return dp[amt] as i32;
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} else {
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-1
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}
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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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// Dynamic programming
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let res = coin_change_dp(&coins, amt);
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println!("Minimum number of coins required to reach the target amount = {res}");
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// Space-optimized dynamic programming
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let res = coin_change_dp_comp(&coins, amt);
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println!("Minimum number of coins required to reach the target amount = {res}");
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}
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