Create coin-change-2.py

Author: kamyu104

Python/coin-change-2.py

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+# Time:  O(n * m)
+# Space: O(m)
+
+# 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
+        """
+        dp = [0] * (amount+1)
+        dp[0] = 1;
+        for coin in coins:
+            for i in xrange(coin, amount+1):
+                dp[i] += dp[i-coin]
+        return dp[amount]