Maximum value with the choice of either dividing or considering as it is in C++ program

In this problem, we are given a number N. Our task is to create a program to find to Maximum value with the choice of either dividing or considering as it is in C++.

Problem Description

To find the maximum, we can consider any two values, either by take the value as it is or we could get the maximum value by dividing.The value could be extracted as F(N/2) + F(N/3) + F(N/4) + F(N/5).

Let’s take an example to understand the problem,

Input:N = 8

Output:9

Explanation

F(8) =F(8/2) + F(8/3) + F(8/4) + F(8/5) = F(4) + F(2) + F(2) + F(1) = 4 + 2 + 2 + 1 = 9

Solution Approach

The idea is simply to call the same function multiple times for the value of division. For this we have used the concept dynamic programming and created an array to solve the values of F(i) from 0 to N, for recusing them for finding the solution.

Example

 Live Demo

#include <iostream>
using namespace std;
int calcMaximumValue(int N) {
   int F[N + 1];
   int divVal = 0;
   F[0] = 0;
   F[1] = 1;
   for (int i = 2; i <= N; i++) {
      divVal = ( F[i / 2] + F[i / 3] + F[i / 4] + F[i / 5] );
      if(divVal > i)
         F[i] = divVal;
      else
         F[i] = i;
   }
   return F[N];
}
int main() {
   int N = 8;
   cout<<"Maximum value with the choice of either dividing or considering as it is = "<<calcMaximumValue(N);
   return 0;
}

Output

Maximum value with the choice of either dividing or considering as it is = 9