518. Coin Change 2

• Difficulty: Medium

• Topics:

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Problem:

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.

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

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

Solutions:

class Solution {
public:
    int change(int amount, vector<int>& coins) {
        int n = coins.size();
        if (n == 0) return amount == 0 ? 1 : 0;
        vector<vector<int>> dp(n, vector<int>(amount + 1, 0));
        for (int i = 0; i < n; ++i) {
            dp[i][0] = 1;
        }

        for (int i = 0; i < coins.size(); ++i) {
            for (int j = 1; j <= amount; ++j) {
                dp[i][j] = (i - 1 >= 0 ? dp[i-1][j] : 0) + 
                    (j - coins[i] >= 0 ? dp[i][j - coins[i]] : 0);
            }
        }  

        return dp[n-1][amount];
    }
};