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++
// 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 integersint ways(int n){ return n / 2;}// Driver codeint main(){ int n = 2; cout << ways(n); return 0;} |
Java
// 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
# Python3 implementation of the approach# Function to return the number of# distinct ways to represent n# as the sum of two integersdef ways(n): return n // 2# Driver coden = 2print(ways(n))# This code is contributed by Mohit Kumar |
C#
// C# implementation of the approachusing System;class GFG{ // Function to return the number of// distinct ways to represent n// as the sum of two integersstatic int ways(int n){ return n / 2;}// Driver codepublic static void Main(){ int n = 2; Console.WriteLine(ways(n));}}// This code is contributed by Nidhi_Biet |
Javascript
<script>// Javascript implementation of the approach// Function to return the number of// distinct ways to represent n// as the sum of two integersfunction ways(n){ return parseInt(n / 2);}// Driver codevar n = 2;document.write(ways(n));// This code is contributed by noob2000.</script> |
Output:
1
Time Complexity: O(1)
Auxiliary Space: O(1)
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