Given a number N, the task is to find the number of unique ways in which N can be represented as a sum of two positive integers.
Examples:
Input: N = 7
Output: 3
(1 + 6), (2 + 5) and (3 + 4).
Input: N = 200
Output: 100
Approach: The number of ways in which the number can be expressed as the sum of two positive integers are 1 + (N – 1), 2 + (N – 2), …, (N – 1) + 1 and (N – 2) + 2. There are N – 1 terms in the series and they appear in identical pairs i.e. (X + Y, Y + X). So the required count will be N / 2.
Below is the implementation of the above approach:
// C++ implementation of the approach #include <bits/stdc++.h> using namespace std;
// Function to return the number of // distinct ways to represent n // as the sum of two integers int ways( int n)
{ return n / 2;
} // Driver code int main()
{ int n = 2;
cout << ways(n);
return 0;
} |
// Java implementation of the approach class GFG
{ // Function to return the number of
// distinct ways to represent n
// as the sum of two integers
static int ways( int n)
{
return n / 2 ;
}
// Driver code
public static void main(String args[])
{
int n = 2 ;
System.out.println(ways(n));
}
} // This code is contributed by AnkitRai01 |
# Python3 implementation of the approach # Function to return the number of # distinct ways to represent n # as the sum of two integers def ways(n):
return n / / 2
# Driver code n = 2
print (ways(n))
# This code is contributed by Mohit Kumar |
// C# implementation of the approach using System;
class GFG
{ // Function to return the number of // distinct ways to represent n // as the sum of two integers static int ways( int n)
{ return n / 2;
} // Driver code public static void Main()
{ int n = 2;
Console.WriteLine(ways(n));
} } // This code is contributed by Nidhi_Biet |
<script> // Javascript implementation of the approach // Function to return the number of // distinct ways to represent n // as the sum of two integers function ways(n)
{ return parseInt(n / 2);
} // Driver code var n = 2;
document.write(ways(n)); // This code is contributed by noob2000. </script> |
1
Time Complexity: O(1)
Auxiliary Space: O(1)