Understanding and Solving the Two-Sum LeetCode Problem: A Guide for Beginners

Problem Statement: You are given an array of integers nums and an integer target. You need to return the indices of two numbers in the array that add up to target.

Prerequisites: Basic knowledge of arrays and loops.

Relevance: This problem tests your ability to work with arrays and find specific elements within them. It's a foundational skill in computer science and programming.

Step-by-Step Solution: Breaking Down the Solution and Including Logic Behind Each Step

1. Create a Dictionary: To store the numbers and their corresponding indices.

2. Iterate Through the Array: Using a loop, go through each number in the array.

3. Find the Complement: For each number, calculate the complement by subtracting it from the target.

4. Check if Complement Exists: See if the complement is in the dictionary.

5. Return the Indices: If the complement exists, return the current index and the index of the complement.

Pseudo-Code:

Create an empty dictionary
For each index, number in the array:
  Compute the complement = target - number
  If complement is in the dictionary:
    Return current index and index of complement from dictionary
  Add the number and its index to the dictionary
End loop

Code Explanation: Explaining Each Line with Complexity Analysis

def twoSum(nums, target):
    num_dict = {} # Create an empty dictionary

    for i, num in enumerate(nums): # Iterate through the array
        complement = target - num # Compute the complement
        if complement in num_dict: # Check if complement is in the dictionary
        return [num_dict[complement], i] # Return the indices
        num_dict[num] = i # Add the number and its index to the dictionary

Complexity Analysis:

• Time Complexity: O(n), as we are iterating through the array once.

• Space Complexity: O(n), for storing the elements in the dictionary.

Analogies & Examples: Understanding Through Simple Examples

Think of the array as a row of numbered boxes. You are looking for two boxes whose numbers add up to a specific value. You keep track of the boxes you have seen so far (using a dictionary), so if you find a box that, when added to one you've already seen, equals the target number, you've found your solution!

Example:

• Input: nums = [3,5,2,4], target = 7

• Output: [1,2]

Other Approaches and Resources:

1. Brute Force Approach: You can use nested loops to compare all pairs, but this would be less efficient (O(n^2)).

2. Resources: LeetCode's own tutorials and solutions can be a great help.

Potential Misunderstandings and How to Avoid Them

Make sure not to confuse the indices with the actual numbers in the array. We are looking for the positions of the numbers in the array, not the numbers themselves.

You've learned how to solve a classic problem using arrays and dictionaries. Keep practicing and applying these skills to more complex problems. Happy coding!