Find Maximum Rated Parts Set in C++

Suppose, there is a manufacturer that makes specific parts for a particular product. The manufacturer has n different variations of the parts, and the parts have a specific rating on three criteria. The ratings of the n products are given in the array 'ratings' where each element is of the format (A, B, C) where A, B, and C are different rating criteria of the product. Now, an OEM wants to buy m parts for each product they make from the manufacturer of the parts. The OEM chooses the parts satisfying the below conditions −

• Two or more units of the same part should not be bought.

• Choose the set of parts such that the value V is maximized, where V = |total rating of criteria A| + |total rating of criteria B| + |total rating of criteria C|.

We have to find the maximum possible value of V from the parts that the OEM chooses.

So, if the input is like n = 6, m = 4, ratings = {{2, 3, 5}, {3, 5, 2}, {4, 8, 5}, {1, 5, 3}, {7, 2, 7}, {4, 3, 6}}, then the output will be 56.

If the OEM chooses parts 1, 3, 5, and 6, then the total ratings for each category are −

Category A = 2 + 4 + 7 + 4 = 17
Category B = 3 + 8 + 2 + 3 = 16.
Category C = 5 + 5 + 7 + 6 = 23
The total value of V is 17 + 16 + 23 = 56.

To solve this, we will follow these steps −

N := 100
Define an array arr of size: 9 x N.
Define an array ans.
for initialize i := 0, when i < n, update (increase i by 1), do:
   a := first value of ratings[i]
   b := second value of ratings[i]
   c := third value of ratings[i]
   arr[1, i] := a + b + c
   arr[2, i] := a - b - c
   arr[3, i] := a + b - c
   arr[4, i] := a - b + c
   arr[5, i] := -a + b + c
   arr[6, i] := -a - b - c
   arr[7, i] := -a + b - c
   arr[8, i] := -a - b + c
for initialize i := 1, when i <= 8, update (increase i by 1), do:
   sort the array arr[i]
for initialize i := 1, when i <= 8, update (increase i by 1), do:
   reverse the array arr[i]
if m is the same as 0, then:
   V := 0
Otherwise
   for initialize j := 1, when j <= 8, update (increase j by 1), do:
      k := 0
      for initialize i := 0, when i < m, update (increase i by 1), do:
         k := k + arr[j, i]
         V := maximum of V and k
return V

Example

Let us see the following implementation to get better understanding −

#include <bits/stdc++.h>
using namespace std;
const int INF = 1e9;
const int modval = (int) 1e9 + 7;
#define N 100
int solve(int n, int m, vector<tuple<int, int, int>> ratings) {
   int V, arr[9][N] ;
   vector<int> ans ;
   for(int i = 0 ; i < n ; i++) {
      int a, b, c;
      tie(a, b, c) = ratings[i];
      arr[1][i] = a + b + c ;
      arr[2][i] = a - b - c ;
      arr[3][i] = a + b - c ;
      arr[4][i] = a - b + c ;
      arr[5][i] = -a + b + c ;
      arr[6][i] = -a - b - c ;
      arr[7][i] = -a + b - c ;
      arr[8][i] = -a - b + c ;
   }
   for(int i = 1 ; i <= 8 ; i++)
    sort(arr[i] , arr[i] + n) ;
   for(int i = 1 ; i <= 8 ; i++)
    reverse(arr[i] , arr[i] + n) ;
   if (m == 0)
   V = 0 ;
   else {
      for (int j = 1; j <= 8; j++) {
         int k = 0;
         for (int i = 0; i < m; i++)
            k += arr[j][i];
         V = max(V, k);
      }
   }
   return V;
}
int main() {
   int n = 6, m = 4;
   vector<tuple<int, int, int>> ratings = {{2, 3, 5}, {3, 5, 2}, {4, 8, 5}, {1, 5, 3}, {7, 2, 7}, {4, 3, 6}};
   cout<< solve(n, m, ratings);
   return 0;
}

Input

6, 4, {{2, 3, 5}, {3, 5, 2}, {4, 8, 5}, {1, 5, 3}, {7, 2, 7}, {4, 3,6}}

Output

56