Two Sum and Sorted Two Sum

Introduction

The Two Sum problem is one of the most popular questions in programming interviews. It helps in understanding arrays, hashing, and two-pointer techniques.

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Problem Statement

Two Sum

Given an array of integers and a target value, return the indices of the two numbers such that they add up to the target.

Two Sum II (Sorted Array)

Given a sorted array, find two numbers such that they add up to a target. Return their indices.

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💡 Approach 1: Two Sum (Using Hash Map)

1. Create a dictionary to store numbers and their indices
2. For each element:
   • Find complement = target - element
   • Check if complement exists in dictionary
3. If yes → return indices

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Python Code (Two Sum)

python
def two_sum(nums, target):
    hashmap = {}

    for i, num in enumerate(nums):
        complement = target - num

        if complement in hashmap:
            return [hashmap[complement], i]

        hashmap[num] = i

Approach 2: Two Sum II (Sorted Array - Two Pointer)
Use two pointers:
left = 0
right = n - 1
Calculate sum:
If sum == target → return indices
If sum < target → move left
If sum > target → move right

python code (sorted Two sum)

def two_sum_sorted(nums, target):
    left, right = 0, len(nums) - 1

    while left < right:
        total = nums[left] + nums[right]

        if total == target:
            return [left, right]
        elif total < target:
            left += 1
        else:
            right -= 1


## Input
 nums = [2, 7, 11, 15]
 target = 9

## output
 [0,1]