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 codeint 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 codepublic 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 = 8print(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 codepublic 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(1)
Auxiliary space: O(1) because it is using constant space for variable
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