[LeetCode] Problem 518 - Coin Change 2

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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

No.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

No.2

Input: amount = 3, coins = [2]

Output: 0

Explanation: the amount of 3 cannot be made up just with coins of 2.

No.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

Code

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// dp[i] = dp[i] + dp[i - coins[j]]
public int change(int amount, int[] coins) {
    int[] dp = new int[amount + 1];
    dp[0] = 1;

    for (int j = 0; j < coins.length; j++) {
        for (int i = coins[j]; i <= amount; i++)
            dp[i] += dp[i - coins[j]];
    }

    return dp[amount];
}