Coin Change 2.py

'''
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.

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

 

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

'''

class Solution(object):
    def change(self, amount, coins):
        """
        :type amount: int
        :type coins: List[int]
        :rtype: int
        """
        f = [0 for i in xrange(amount + 1)]
        f[0] = 1
        
        for c in coins:
            for i in range(c, len(f)):
                f[i] += f[i-c]
                    
        return f[-1]