Number of ways to choose a pair containing an even and an odd number from 1 to N
Given a number N the task is to find the number of pairs containing an even and an odd number from numbers between 1 and N inclusive.
Note: The order of numbers in the pair does not matter. That is (1, 2) and (2, 1) are the same.
Examples:
Input: N = 3 Output: 2 The pairs are (1, 2) and (2, 3).
Input: N = 6 Output: 9 The pairs are (1, 2), (1, 4), (1, 6), (2, 3), (2, 5), (3, 4), (3, 6), (4, 5), (5, 6).
Approach: The number of ways to form the pairs is (Total number of Even numbers*Total number of Odd numbers).
Thus
- if N is an even number of even numbers = number of odd numbers = N/2
- if N is an odd number of even numbers = N/2 and the number of odd numbers = N/2+1
Below is the implementation of the above approach:
C++
// C++ implementation of the above approach #include <iostream> using namespace std; // Driver code int main() { int N = 6; int Even = N / 2; int Odd = N - Even; cout << Even * Odd; return 0; // This code is contributed // by ANKITRAI1 } |
Java
// Java implementation of the above approach import java.util.*; import java.lang.*; import java.io.*; class GFG{ // Driver code public static void main(String args[]) { int N = 6 ; int Even = N / 2 ; int Odd = N - Even ; System.out.println( Even * Odd ); } } |
Python3
# Python implementation of the above approach N = 6 # number of even numbers Even = N / / 2 # number of odd numbers Odd = N - Even print (Even * Odd) |
C#
// C# implementation of the // above approach using System; class GFG { // Driver code public static void Main() { int N = 6; int Even = N / 2 ; int Odd = N - Even ; Console.WriteLine(Even * Odd); } } // This code is contributed // by Akanksha Rai(Abby_akku) |
PHP
<?php // PHP implementation of the // above approach // Driver code $N = 6; $Even = $N / 2 ; $Odd = $N - $Even ; echo $Even * $Odd ; // This code is contributed // by ChitraNayal ?> |
Javascript
<script> // Javascript implementation of the above approach // Driver code let N = 6; let Even = Math.floor(N / 2) ; let Odd = N - Even ; document.write( Even * Odd ); // This code is contributed by avanitrachhadiya2155 </script> |
Output:
9
Time Complexity: O(1)
Space Complexity: O(1)
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