0518.cpp

class Solution {
public:
    int change(int amount, vector<int>& coins) {
        
        vector<vector<int>> dp(coins.size() + 1, vector<int>(amount + 1, 0));
        
        //fill 1st column by 1, because 0 can always be formed
        for(int i = 0; i <= coins.size(); i++)
            dp[i][0] = 1;
        
        
        for(int i = 1; i <= coins.size(); i++){
            for(int j = 1; j <= amount; j++){
                
                if(j >= coins[i - 1])
                    dp[i][j] = dp[i][j - coins[i-1]] + dp[i - 1][j];
                
                else
                    dp[i][j] = dp[i - 1][j];
            }
        }
        
        return dp[coins.size()][amount];
    }
};