[LeetCode] Problem 322 - Coin Change

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You are given coins of different denominations and a total amount of money amount. Write a function to compute the fewest number of coins that you need to make up that amount. If that amount of money cannot be made up by any combination of the coins, return -1.

Example

No.1

Input: coins = [1, 2, 5], amount = 11

Output: 3

Explanation: 11 = 5 + 5 + 1

No.2

Input: coins = [2], amount = 3

Output: -1

Note

You may assume that you have an infinite number of each kind of coin.

Code

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// dp[i] = min{dp[i - coins[j]] + 1}
public int coinChange(int[] coins, int amount) {
    int[] dp = new int[amount + 1];
    Arrays.fill(dp, amount + 1);
    dp[0] = 0;

    for (int i = 1; i <= amount; i++) {
        for (int j = 0; j < coins.length; j++) {
            if (i - coins[j] >= 0)
                dp[i] = Math.min(dp[i], dp[i - coins[j]] + 1);
        }
    }

    return dp[amount] > amount ? -1 : dp[amount];
}