322. Coin Change

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题目

You are given an integer array coins representing coins of different denominations and an integer amount representing a total amount of money.

Return 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.

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

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

Example 3:

Input: coins = [1], amount = 0

Output: 0

Constraints:

• 1 <= coins.length <= 12
• 1 <= coins[i] <= 2^31 - 1
• 0 <= amount <= 10^4

题目大意

给你一个整数数组 coins ，表示不同面额的硬币；以及一个整数 amount ，表示总金额。

计算并返回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 。

你可以认为每种硬币的数量是无限的。

解题思路

可以使用动态规化，定义一个数组dp，其中dp[i]表示凑齐金额i所需的最少硬币数。

• 初始化数组 dp 为 -666，便于后续取最小值。
• 将 base case dp[0] 设置为 0，表示凑齐金额 0 不需要任何硬币。
• 对于每个金额 i，遍历硬币的面额，计算凑齐金额 i 所需的最少硬币数。
• 状态转移方程为：dp[i] = min(dp[i], dp[i - coin] + 1)，其中 coin 为硬币的面额。
• 最终，dp[amount] 即为凑齐总金额所需的最少硬币数。

代码

/**
 * @param {number[]} coins
 * @param {number} amount
 * @return {number}
 */
var coinChange = function (coins, amount) {
	let dp = new Array(amount + 1).fill(-666);

	const helper = (num) => {
		if (num == 0) return 0;
		if (num < 0) return -1;
		if (dp[num] !== -666) return dp[num];
		let res = Infinity;
		for (let coin of coins) {
			let sub = helper(num - coin);
			if (sub == -1) continue;
			res = Math.min(res, sub + 1);
		}
		dp[num] = res == Infinity ? -1 : res;
		return dp[num];
	};
	return helper(amount);
};

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- [983. 最低票价](https://leetcode.com/problems/minimum-cost-for-tickets)
- [2218. 从栈中取出 K 个硬币的最大面值和](https://leetcode.com/problems/maximum-value-of-k-coins-from-piles)
- [2224. 转化时间需要的最少操作数](https://leetcode.com/problems/minimum-number-of-operations-to-convert-time)
- [2547. 拆分数组的最小代价](https://leetcode.com/problems/minimum-cost-to-split-an-array)
- [2902. Count of Sub-Multisets With Bounded Sum](https://leetcode.com/problems/count-of-sub-multisets-with-bounded-sum)
- [2915. Length of the Longest Subsequence That Sums to Target](https://leetcode.com/problems/length-of-the-longest-subsequence-that-sums-to-target)
- [2952. Minimum Number of Coins to be Added](https://leetcode.com/problems/minimum-number-of-coins-to-be-added)