# Minimum coin change problem using recursion in JavaScript

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], amount = 4 Output: 2 Explanation: 4 =
2 + 2,4=1+1+2

## The recursion formual for coin change as below

$coinchange(j,a) = \begin{cases} \infty, & \text{if j<0} \\ 0, & \text{if j =0} \\ 1+\min(\sum_{i=k}^n c[j-a_i]) & \text{if j >1} \end{cases}$

function coin_change(amount) {
// if remaining  coin is zero return
if (amount == 0) return 0
// if coin is negative return some large value
if (amount < 0) return Infinity

let ans = Infinity
for (const coin of coins)
ans = Math.min(
ans,
1 + coin_change(amount - coin)
)
return ans
}


## Recursion Tree

This article only show you how to write recursive program. I know this is not optimized way to write coin change problem{alertError}