### Coin Changing Problem

##### Given an infinite number of different domination coins, calculate the number of ways of representing n rupees

**Solution :**

- One simple ways try to make N money with M type of coins this ways
- N money with M-1 types of coins +
- N – Amount[M] with M types of coins

##### Recursive Algorithm:

- If
`money == 0`

then- return 1 (i.e. only way to make money 0 with any kind of coins)

- If
`index >= total`

coins then`return 0`

- Iterate till computedAmount <= money
- recursively call to make computedAmount with M-1 coins
- remaining amount with with N coins

Latest Source Code:

Github: CoinChangingProblem.java

**Output:**

Total ways (recursive): 5 Total ways (with memo): 5