LeetCode：322. Coin Change（硬币兑换问题）

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 1:

Input: coins = [1, 2, 5], amount = 11
Output: 3
Explanation: 11 = 5 + 5 + 1
Example 2:
Input: coins = [2], amount = 3
Output: -1
Note:
You may assume that you have an infinite number of each kind of coin.

---

方法1：(动态规划)

package leetcode;

import org.junit.Test;

public class CoinChange {
	@Test
	public void fun() {
		int coins[] = { 1, 2, 5 };
		int amount = 11;
		int method = CoinChange(coins, amount);
		System.out.println(method);
	}

	private int CoinChange(int[] coins, int amount) {
		// TODO Auto-generated method stub
		if (amount == 0) {
			return 0;
		}
		if (coins == null || coins.length == 0) {
			return -1;
		}
		int[] dp = new int[amount + 1];
		for (int i = 1; i <= amount; i++) {
			int res = Integer.MAX_VALUE;
			for (int j = 0; j < coins.length; j++) {
				if (coins[j] > i) {
					continue;
				}
				if (dp[i - coins[j]] == -1) {
					continue;
				}
				dp[i] = 1 + dp[i - coins[j]];
				res = Math.min(res, dp[i]);
			}
			dp[i] = res;
		}
		return dp[amount];
	}
}

时间复杂度：O(n^2)

空间复杂度：O(n)