Create Coin Change 2.py

Author: sugia

Coin Change 2.py

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+'''
+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]