2Sum - Complete Tutorial

The 2-Sum problem is a popular algorithmic challenge where the goal is to identify two distinct elements in an array whose sum equals a specific target. The problem emphasizes understanding array manipulation and optimizing search operations through hashing. It's a foundational problem used to assess problem-solving skills, particularly in handling array-based tasks and improving performance with hash-based techniques.

2Sum on Unsorted Input

When the array is unsorted, we don’t know anything about the order of the numbers. This means we have to consider every possible pair of numbers to check if they sum up to the target. Hashing and sometimes sorting with two pointer help us in solving these problems efficiently.

• 2Sum (Pair with given sum)
  
• Count pairs with given sum
• Pair with given product
• Sum of two elements whose sum is closest to zero
• Smallest Difference pair of values between two unsorted Arrays
• Pairs with given sum in doubly linked list
• All pairs with a given sum in two unsorted arrays
• Count pairs with absolute difference equal to k

2Sum on Sorted Input

When the input is sorted, we can take advantage of the order to find the solution more efficiently. Instead of brute force, a more better approach" Two-Pointer Technique" can be used. This method involves using two pointers that move towards each other from the start and end of the array until they find the pair that adds up to the target.

• 2Sum II (Pair with given sum in sorted array)
• Pair with sum is closest to x
• Closest number in Sorted array
• Pairs with sum is less than target
• Pair Sum in an Absolute Sorted array
• Pair with given sum in a Balanced BST
• Two Sum in BST - Pair with given sum
• Find the closest pair from two sorted arrays