Coin Change

Question

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.

Tag

• Dynamic Programming
• BFS

Thought

There are two approaches: Dynamic Programming Breadth-First Search.

Code

DP

class Solution(object):
    def coinChange(self, coins, amount):
        """
        :type coins: List[int]
        :type amount: int
        :rtype: int
        """
        DP = [amount + 1 for i in xrange(amount + 1)]
        DP[0] = 0
        for num in xrange(1, amount + 1):
            for coin in coins:
                if coin <= num:
                    DP[num] = min(DP[num], DP[num - coin] + 1)
        if DP[-1] == amount + 1:
            return -1
        else:
            return DP[-1]

BFS

"""
https://discuss.leetcode.com/topic/32589/fast-python-bfs-solution/3
"""
class Solution(object):
    def coinChange(self, coins, amount):
        """
        :type coins: List[int]
        :type amount: int
        :rtype: int
        """
        level = seen = {0}
        number = 0
        while level:
            if amount in level:
                return number
            level = {a+c for a in level for c in coins if a+c <= amount} - seen
            seen |= level
            number += 1
        return -1