Coin Change 2

June 7, 2020

Introduction

You are given coins of different denominations and a total amount of money. Write a function to compute the number of combinations that make up that amount. You may assume that you have infinite number of each kind of coin.

Example 1:

Input: amount = 5, coins = [1, 2, 5] Output: 4 Explanation: there are four ways to make up the amount:

5=5
5=2+2+1
5=2+1+1+1
5=1+1+1+1+1

Example 2:

Input: amount = 3, coins = [2]
Output: 0
Explanation: the amount of 3 cannot be made up just with coins of 2.

Example 3:

Input: amount = 10, coins = [10] Output: 1

Note:

You can assume that

0 <= amount <= 5000
1 <= coin <= 5000
the number of coins is less than 500
the answer is guaranteed to fit into signed 32-bit integer

Solution

Let’s dynamic programming to solve this problem.

func change(amount int, coins []int) int {
    dp := make([]int, amount + 1)
    dp[0] = 1
    n := len(coins)
    for i := 0; i < n; i++ {
        for j := coins[i]; j <= amount; j++ {
            dp[j] += dp[j - coins[i]]
         }
    }
    return dp[amount]
}

Performance of this solution is:

Runtime: 0 ms
Memory Usage: 2.3 MB

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