【LeetCode】 322. Coin Change 零钱兑换（Medium）（JAVA）
题目地址: https://leetcode.com/problems/coin-change/
题目描述：
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.
题目大意
给定不同面额的硬币 coins 和一个总金额 amount。编写一个函数来计算可以凑成总金额所需的最少的硬币个数。如果没有任何一种硬币组合能组成总金额，返回 -1。
解题方法
开始采用 BFS（宽度优先搜索），直接超时；
想到要用动态规划，最重要的是找出状态转移函数 dp 函数:
dp[i] = Math.min(dp[i], dp[i - coins[j]] + 1);
class Solution {
public int coinChange(int[] coins, int amount) {
int[] dp = new int[amount + 1];
for (int i = 1; i <= amount; i++) {
dp[i] = Integer.MAX_VALUE;
for (int j = 0; j < coins.length; j++) {
if ((i - coins[j]) >= 0 && dp[i - coins[j]] < Integer.MAX_VALUE) {
dp[i] = Math.min(dp[i], dp[i - coins[j]] + 1);
}
}
}
return dp[amount] == Integer.MAX_VALUE ? -1 : dp[amount];
}
}
执行用时 : 17 ms, 在所有 Java 提交中击败了 43.27% 的用户
内存消耗 : 40.7 MB, 在所有 Java 提交中击败了 5.01% 的用户
