Program to find number of combinations of coins to reach target in Python

Suppose we have a list of coins and another value amount, we have to find the number of combinations there are that sum to amount. If the answer is very large, then mod the result by 10^9 + 7.

So, if the input is like coins = [2, 5] amount = 10, then the output will be 2, as we can make these combinations − [2, 2, 2, 2, 2], [5, 5]

To solve this, we will follow these steps −

• m := 10^9 + 7
• dp := a list of size same as amount + 1, and fill it with 0
• dp[0] := 1
• for each d in coins, do
  • for i in range 1 to size of dp, do
    • if i - d >= 0, then
      • dp[i] := dp[i] + dp[i - d]
• return (last element of dp) mod m

Let us see the following implementation to get better understanding −

Example

 Live Demo

class Solution:
   def solve(self, coins, amount):
      dp = [0] * (amount + 1)
      dp[0] = 1
      for d in coins:
         for i in range(1, len(dp)):
            if i - d >= 0:
               dp[i] += dp[i - d]
      return dp[-1] % (10 ** 9 + 7)
ob = Solution()
coins = [2, 5]
amount = 10
print(ob.solve(coins, amount))

Input

[2, 5], 10

Output

2