Make A, B and C equal by adding total value N to them

Given 3 integers A, B, and C, and an integer N, the task is to distribute N among all the other 3 numbers such that at the end A = B = C. If the distribution is possible then print “Yes” otherwise output “No”.

Examples:

Input: A = 5, B = 3, C = 2, N = 8
Output: Yes
Explanation:
We can distribute N = 8 by adding 1 to A, 3 to B and 4 to C to get all of them as 6. Hence the distribution is possible.



Input: A = 10, B = 20, C = 15, N = 14
Output: No
Explanation:
Distribution of N among all three integers to make them equal is not possible.

Approach:

To solve the problem mentioned above we have to follow the steps given below:

  • Find maximum out of all the three integers A, B and C. Let that be integer K
  • Multiply the integer K by 3 and then subtract it by the sum of the three integers.
  • Check if the difference of that number and N is divisible by 3 or not.
  • If it is, then the output is “Yes”, otherwise it is not possible to distribute the number.

Below is the implementation of the above approach:

C++

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// C++ program to distribute integer N 
// among A, B, C such that they become equal 
#include<bits/stdc++.h>
using namespace std;
  
void distributeN(int A, int B, int C, int n)
{
    // Find maximum among the three elements 
    int max1 = max(A, B);
    int max2 = max(B, C);
    int maximum = max(max1, max2);
      
    // Summation of three elements 
    int sum = A + B + C;
    int p = (3 * maximum) - sum;
    int diff = n - p;
      
    // Check if difference is divisible by 3 
    if (diff < 0 || diff % 3) 
        cout << "No";
    else
        cout << "Yes";
}
          
// Driver code
int main()
{
    int A = 10, B = 20;
    int C = 15, n = 14;
      
    distributeN(A, B, C, n);
    return 0;
}
  
// This code is contributed by PratikBasu

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Python3

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# Python Program to Distribute integer N 
# among A, B, C such that they become equal
  
def distributeN(A, B, C, n):
      
    # find maximum among the three elements
    maximum = max(A, B, C)
      
    # summation of three elements
    sum = A + B+C
      
      
    p = (3 * maximum)-sum
      
    diff = n-p
      
    # check if difference is divisible by 3
    if diff < 0 or diff % 3
        print "No" 
    else:
        print "Yes"
          
          
# Driver code 
A = 10
B = 20
C = 15 
n = 14 
distributeN(A, B, C, n)

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Output:

No

Time Complexity: O(1)

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Improved By : PratikBasu