LeetCode #322 Coin Change

Medium

Problem

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.

Solution

The concept of this problem is like Knapsack problem which can be solved by using dynamic programming approach.

dp[i] = min(dp[i-coin] + 1), for all coin in coins

Complexity

It takes O(m) time to run line 16, where m denotes to amount. And in each iteration, it takes O(n) time to check if i in coins, where n denotes to counts of coins. Therefore, its time complexity is O(mn).

It’s clear that it uses O(m) extra space for dp list.