Sum of multiplication of all combination of m element from an array of n elements

Question

Suppose I have an array {1, 2, 5, 4} and m = 3. I need to find:

1*2*5 + 1*2*4 + 1*5*4 + 2*5*4

i.e Sum of multipli

Answer 1

I have a Dynamic programming solution in my mind, just want to share. Time complexity is O(k*n^2) with n is total number.

The idea is, we start to fill in each position from 0 to k -1. So if we assume at position ith, the number to be filled for this position is a, so the sum of all combination start with a will be a times the total of all combination from position (i + 1)th starting with (a + 1)

Note: I have updated the solution, so it can work with any array data, My language is Java, so you can notice that the index for array is 0 based, which start from 0 to n-1.

public int cal(int n, int k , int[]data){
   int [][] dp = new int[k][n + 1];
   for(int i = 1; i <= n; i++){
       dp[k - 1][i] = data[i - 1];
   }
   for(int i = k - 2; i >= 0; i--){
       for(int j = 1 ; j <= n; j++){
           for(int m = j + 1 ; m <= n; m++){
               dp[i][j] += data[j - 1]*dp[i + 1][m];
           }
       }
   }
   int total = 0;
   for(int i = 1; i <= n; i++){
       total += dp[0][i];
   }
   return total;
}