LeetCode - Coin Change 2 - LeetCode

Question Definition

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

Java Solution

public int change(int amount, int[] coins) {
    int[][] dp = new int[coins.length + 1][amount + 1];
    dp[0][0] = 1;
    for (int i = 1; i <= coins.length; ++i) {
        dp[i][0] = 1;
        for (int j = 1; j <= amount; ++j) {
            dp[i][j] = dp[i - 1][j] + (j >= coins[i - 1] ? dp[i][j - coins[i - 1]] : 0);
        }
    }
    return dp[coins.length][amount];
}