72 lines
2.4 KiB
C#
72 lines
2.4 KiB
C#
/**
|
|
* File: coin_change.cs
|
|
* Created Time: 2023-07-12
|
|
* Author: hpstory (hpstory1024@163.com)
|
|
*/
|
|
|
|
namespace hello_algo.chapter_dynamic_programming;
|
|
|
|
public class coin_change {
|
|
/* Coin change: Dynamic programming */
|
|
int CoinChangeDP(int[] coins, int amt) {
|
|
int n = coins.Length;
|
|
int MAX = amt + 1;
|
|
// Initialize dp table
|
|
int[,] dp = new int[n + 1, amt + 1];
|
|
// State transition: first row and first column
|
|
for (int a = 1; a <= amt; a++) {
|
|
dp[0, a] = MAX;
|
|
}
|
|
// State transition: the rest of the rows and columns
|
|
for (int i = 1; i <= n; i++) {
|
|
for (int a = 1; a <= amt; a++) {
|
|
if (coins[i - 1] > a) {
|
|
// If exceeding the target amount, do not choose coin i
|
|
dp[i, a] = dp[i - 1, a];
|
|
} else {
|
|
// The smaller value between not choosing and choosing coin i
|
|
dp[i, a] = Math.Min(dp[i - 1, a], dp[i, a - coins[i - 1]] + 1);
|
|
}
|
|
}
|
|
}
|
|
return dp[n, amt] != MAX ? dp[n, amt] : -1;
|
|
}
|
|
|
|
/* Coin change: Space-optimized dynamic programming */
|
|
int CoinChangeDPComp(int[] coins, int amt) {
|
|
int n = coins.Length;
|
|
int MAX = amt + 1;
|
|
// Initialize dp table
|
|
int[] dp = new int[amt + 1];
|
|
Array.Fill(dp, MAX);
|
|
dp[0] = 0;
|
|
// State transition
|
|
for (int i = 1; i <= n; i++) {
|
|
for (int a = 1; a <= amt; a++) {
|
|
if (coins[i - 1] > a) {
|
|
// If exceeding the target amount, do not choose coin i
|
|
dp[a] = dp[a];
|
|
} else {
|
|
// The smaller value between not choosing and choosing coin i
|
|
dp[a] = Math.Min(dp[a], dp[a - coins[i - 1]] + 1);
|
|
}
|
|
}
|
|
}
|
|
return dp[amt] != MAX ? dp[amt] : -1;
|
|
}
|
|
|
|
[Test]
|
|
public void Test() {
|
|
int[] coins = [1, 2, 5];
|
|
int amt = 4;
|
|
|
|
// Dynamic programming
|
|
int res = CoinChangeDP(coins, amt);
|
|
Console.WriteLine("The minimum number of coins required to make up the target amount is" + res);
|
|
|
|
// Space-optimized dynamic programming
|
|
res = CoinChangeDPComp(coins, amt);
|
|
Console.WriteLine("The minimum number of coins required to make up the target amount is" + res);
|
|
}
|
|
}
|