490. Given an array, Find the number of all pairs with even sum

Objective: Given an array of integers, write a program to find the number of pairs with even sum.

Example:

Given Input: [1, 2, 3, 4]
Number of even pairs: 2
Note: (1, 3) and (2, 4)

Given Input: [6, 7, 1, 3, 2, 5, 4]
Number of even pairs: 9

>Naive approach: Use nested loops and check the sum of each possible pair and if sum is even then add it to the result.

Time Complexity: O(N²)

Better approach:

Iterate through the array and count the number of odd elements and even elements.
We know the even + even = even and odd + odd = even, we will use this property.
Number of pairs with even count = evenCount*(evenCount-1)/2 + oddCount*(oddCount-1)/2.
NOTE: Number of ways to choose 2 elements out of n = nC2 = n*(n-1)/2

Time Complexity: O(N)

Output:

Given Input: [6, 7, 1, 3, 2, 5, 4]
Number of even pairs: 9