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
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
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