Given an array arr[] of n integers and a target value, check if there exists a pair whose sum equals the target.

A common solution is to use a hash set to store numbers seen so far. Iterate through the array; for each element x, compute y = target - x. If y is already in the set, a pair exists and you can return true. If not, add x to the set and continue. This runs in O(n) time and uses O(n) additional space. In Python:

def has_pair_with_sum(arr, target):
    seen = set()
    for num in arr:
        if target - num in seen:
            return True
        seen.add(num)
    return False

If you need to return the actual pair, store the numbers in a dictionary mapping value to index and retrieve the indices when a match is found.