Leetcode 518: Coin Change 2

You are given coins of different denominations and a total amount of money. Write a function to compute the number of combinations that make up that amount. You may assume that you have infinite number of each kind of coin.

Note: You can assume that

• 0 <= amount <= 5000
• 1 <= coin <= 5000
• the number of coins is less than 500
• the answer is guaranteed to fit into signed 32-bit integer

 

Example 1:

Input: amount = 5, coins = [1, 2, 5]
Output: 4
Explanation: there are four ways to make up the amount:
5=5
5=2+2+1
5=2+1+1+1
5=1+1+1+1+1

 

Example 2:

Input: amount = 3, coins = [2]
Output: 0
Explanation: the amount of 3 cannot be made up just with coins of 2.

 

Example 3:

Input: amount = 10, coins = [10] 
Output: 1

public class Solution {
    public int Change(int amount, int[] coins) {
        if (amount < 0) return -1;
        
        // dp[i] means the minimal coins to get that amount
        var dp = new int[amount + 1];
        
        // dp[0] means there is one way to make up 0
        dp[0] = 1;
        
        /*
        // NOTE: this doesn't work due to duplicate
        
         dp[0] = 1 
         dp[1] = 1 
         dp[2] = 2 
         dp[3] = 3 
         dp[4] = 5

         2: 1 1
         2: 2

         3: 1 : 1 : 1
         3: 2 : 1
         3: 1 : 2

        for (int i = 1; i < dp.Length; i++)
        {
            for (int j = 0; j < coins.Length; j++)
            {
                if (i - coins[j] >= 0)
                {
                    dp[i] += dp[i - coins[j]];
                }
            }
        }
        */
        
        for (int j = 0; j < coins.Length; j++)
        {
            for (int i = 1; i < dp.Length; i++)
            {
                if (i - coins[j] >= 0)
                {
                    dp[i] += dp[i - coins[j]];
                }
            }
        }
        
        return dp[amount];
    }
}