leetcode Dynamic Programming

leetcode 322题

Posted by franki on February 7, 2021

leetcode 322题 零钱兑换

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。

示例1:

输入: coins = [1, 2, 5], amount = 11
输出: 3
解释: 11 = 5 + 5 + 1
示例 2:

输入: coins = [2], amount = 3
输出: -1

思路

动态规划

代码

var coinChange = function(coins, amount) {
  let dp = new Array( amount + 1 ).fill( Infinity );
  dp[0] = 0;
  
  for (let i = 1; i <= amount; i++) {
    for (let coin of coins) {
      if (i - coin >= 0) {
        dp[i] = Math.min(dp[i], dp[i - coin] + 1);
      }
    }
  }
  
  return dp[amount] === Infinity ? -1 : dp[amount];
}

复杂度分析

  • 时间复杂度: O(N^2)
  • 空间复杂度: O(N)
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