Day-07-Coin Change 2.cpp

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.



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


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






class Solution {
public:

    int change(int amount, vector<int>& coins) {
        int n=coins.size();
        int dp[n+1][amount+1];

        for(int i=0;i<n+1;i++) dp[i][0]=1;
        for(int j=1;j<amount+1;j++) dp[0][j]=0;

        for(int i=1;i<n+1;i++){
            for(int j=1;j<amount+1;j++){
                if(coins[i-1]<=j){
                    dp[i][j] = dp[i][j-coins[i-1]] + dp[i-1][j];
                } else {
                    dp[i][j]  = dp[i-1][j];
                }
            }
        }
        return dp[n][amount];
    }
};