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Count ways to express a number as sum of exactly two numbers

  • Difficulty Level : Basic
  • Last Updated : 19 May, 2021

Given a positive integer N. The task is to find the number of ways in which you can express N as a sum of exactly two numbers A and B (N = A + B) where A > 0, B > 0 and B > A.

Examples: 

Input: N = 8
Output: 3
Explanation:
N = 8 can be expressed as (1, 7), (2, 6), (3, 5)

Input: N = 14
Output: 6 

Approach: 

  • An observation here is that for every number N, if we take a number A which is less than N/2, then there must be a number B which is greater than N/2 and A + B = N. 
     
  • This leads to a simple solution of finding the count of numbers for either B or A. Hence, the floor value of (N-1)/2 will lead to the solution. 
     

C++




// C++ program to Count ways to
// express a number as sum of
// two numbers.
#include <bits/stdc++.h>
using namespace std;
 
// Function returns the count
// of ways express a number
// as sum of two numbers.
int CountWays(int n)
{
    int ans = (n - 1) / 2;
     
    return ans;
}
 
// Driver code
int main()
{
   int N = 8;
    
    cout << CountWays(N);
}

Java




// Java program to count ways to
// express a number as sum of
// two numbers.
class GFG{
 
// Function returns the count
// of ways express a number
// as sum of two numbers.
static int CountWays(int n)
{
    int ans = (n - 1) / 2;
     
    return ans;
}
 
// Driver code
public static void main(String[] args)
{
    int N = 8;
    System.out.print(CountWays(N));
}
}
 
// This code is contributed by Rajput-Ji

Python3




# Python3 program to Count ways to
# express a number as sum of
# two numbers.
 
# Function returns the count
# of ways express a number
# as sum of two numbers.
def CountWays(n) :
    ans = (n - 1) // 2
    return ans
 
# Driver code
N = 8
print(CountWays(N))
 
# This code is contributed by Sanjit_Prasad

C#




// C# program to count ways to
// express a number as sum of
// two numbers.
using System;
class GFG{
 
// Function returns the count
// of ways express a number
// as sum of two numbers.
static int CountWays(int n)
{
    int ans = (n - 1) / 2;
     
    return ans;
}
 
// Driver code
public static void Main()
{
    int N = 8;
    Console.Write(CountWays(N));
}
}
 
// This code is contributed by Code_Mech

Javascript




<script>
 
// Javascript program to count ways to
// express a number as sum of
// two numbers.
 
// Function returns the count
// of ways express a number
// as sum of two numbers.
function CountWays(n)
{
    let ans = Math.floor((n - 1) / 2);
       
    return ans;
}
 
// Driver Code
     
    let N = 8;
    document.write(CountWays(N));
         
</script>
Output: 
3

 

Time complexity: O(N)
 


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