## DEV Community

Abhishek Chaudhary

Posted on

# Coin Change

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] <= 231 - 1
• 0 <= amount <= 104

SOLUTION:

class Solution:
def coinChangeRec(self, amount):
if amount < 0:
return -1
if amount == 0:
return 0
if amount in self.memo:
return self.memo[amount]
numCoins = float('inf')
for coin in self.coins:
currMin = 1 + self.coinChangeRec(amount - coin)
if currMin == 0:
continue
numCoins = min(numCoins, currMin)
if numCoins == float('inf'):
numCoins = -1
self.memo[amount] = numCoins
return numCoins

def coinChange(self, coins: List[int], amount: int) -> int:
self.memo = {}
self.coins = coins
return self.coinChangeRec(amount)