C++ Program to Find Maximum Value of any Algebraic Expression

C++Server Side ProgrammingProgramming

This is a C++ Program to Find Maximum Value of any Algebraic Expression.An algebraic expression of the form (x1 + x2 + x3 + . . . + xa) * (y1 + y2 + . . . + yb) and (a + b) integers is given.consider all possible combinations of a numbers and remaining b numbers and calculating their values, from which maximum value can be derived.

Algorithm

Begin
   function MaxValue() :
   Arguments:
   a[]=array which store the elements.
   x, y=integers.
   Body of the function:
   1) Find the sum of array elements.
   2) Initialize s = 0.
   3) Make for loop i = 0 to (x + y-1) Shift the integers by 25 so that they become positive .
   4) Declare a boolean array p[i][j] that represents true if sum j can be reachable by choosing i numbers.
   5) Initialization of the array.
   6) Make for loop i = 0 to (x + y)-1 to determine If p[i][j] is true, that means it is possible to select i numbers from (x + y) numbers to sum upto j.
   7) Initialize max_value = -INF.
   8) Make for loop i = 0 to (MAX * MAX + 1)-1 to Check if a particular sum can be reachable by choosing n numbers.
   if (p[x][i])
      Get the actual sum as we shifted the numbers by 25 to avoid negative indexing in array .
   9) Print the max_value.
End

Example

#include <bits/stdc++.h>
using namespace std;
#define INF 1e9
#define MAX 25
int MaxValue(int a[], int x, int y) {
   int s= 0;
   for (int i = 0; i < (x + y); i++) {
      s+= a[i];
      a[i] += 25;
   }
   bool p[MAX+1][MAX * MAX + 1];
   //Initialize the array to 01.
   memset(p, 0, sizeof(p));
   p[0][0] = 1;
   for (int i = 0; i < (x + y); i++) {
      //k can be at max x because the
      // left expression has x numbers
      for (int k = min(x, i + 1); k >= 1; k--) {
         for (int j = 0; j < MAX * MAX + 1; j++) {
            if (p[k - 1][j])
            p[k][j + a[i]] = 1;
         }
      }
   }
   int max_value = -INF;
   for (int i = 0; i < MAX * MAX + 1; i++) {
      if (p[x][i]) {
         int tmp = i - 25 * x;
         max_value = max(max_value, tmp * (s - tmp));
      }
   }
   cout << "Maximum Value: " << max_value ;
}
int main() {
   int x = 2, y = 2; //input is taken of
   x and y.
   int ar[] = { 7,6,4,3 };
   MaxValue(ar, x, y);
   return 0;
}

Output

Maximum Value: 100
raja
Published on 30-Apr-2019 08:51:46
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