算法——Coin Change

最新推荐文章于 2024-03-30 22:41:56 发布

转载最新推荐文章于 2024-03-30 22:41:56 发布 · 393 阅读

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本文介绍了一种求解最少硬币数量以凑成指定金额的算法。通过递归方式，结合动态规划思想，实现了对不同面额硬币的最优组合计算。文章提供了完整的Java实现代码，并通过两个例子展示了其正确性和实用性。

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:
coins = [1, 2, 5], amount = 11
return 3 (11 = 5 + 5 + 1)

Example 2:
coins = [2], amount = 3
return -1.

java代码如下：

public class Solution {
    int total = Integer.MAX_VALUE;
    public int coinChange(int[] coins, int amount) {
        if (amount == 0) return 0;
        Arrays.sort(coins);
        count(amount, coins.length-1, coins, 0);
        return total == Integer.MAX_VALUE?-1:total;
    }
    void count(int amount, int index, int[] coins, int count){
        if (index<0 || count>=total-1) return;
        int c = amount/coins[index];
        for (int i = c;i>=0;i--){
            int newCount = count + i;
            int rem = amount - i*coins[index];

            if (rem>0 && newCount<total)
                count(rem, index-1, coins, newCount);
            else if (newCount<total)
                total = newCount;
            else if (newCount>=total-1)
                break;
        }
    }
}