Problem Introduction

In many software engineering interviews, candidates are often asked to solve algorithmic problems that test their analytical and coding skills. One such problem is the "Two Sum" problem. It's a classic algorithmic challenge that is popular among interviewers for its simplicity yet ability to test basic coding and problem-solving skills.

Problem Statement: Given an array of integers nums and an integer target, return the indices of the two numbers such that they add up to target.

Constraints:

• Each input would have exactly one solution.

• You may not use the same element twice.

• The solution can be returned in any order.

Examples:

• Example 1:

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

  • Output: [0,1]

  • Explanation: Because nums[0] + nums[1] == 9, we return [0, 1].

• Example 2:

  • Input: nums = [3,2,4], target = 6

  • Output: [1,2]

• Example 3:

  • Input: nums = [3,3], target = 6

  • Output: [0,1]

High-Level Solution

The essence of solving the "Two Sum" problem efficiently lies in reducing the need to compare each number with every other number. This is achieved by utilizing a hash table (or map) to store each number's value as we iterate through the array. Here's a step-by-step approach:

1. Iterate through each element in the array.

2. For each element, calculate the complement by subtracting the current element's value from the target.

3. Check if this complement exists in the hash table.

   • If it does, we've found the two numbers that add up to the target. Return their indices.

   • If it doesn't, add the current element's value and its index to the hash table.

4. Continue this process until a solution is found.

This method allows for a time-efficient solution with a linear complexity of O(n), where n is the number of elements in the input array.

Solution in Python

class Solution:
    def twoSum(self, nums: List[int], target: int) -> List[int]:
        seen = dict()
        for index, value in enumerate(nums):
            pairValue = target - value
            if pairValue in seen:
                return [seen[pairValue], index]
            seen[value] = index

Solution in TypeScript

function twoSum(nums: number[], target: number): number[] {
    const map = new Map<number, number>();
    for (let i = 0; i < nums.length; i++) {
        const complement = target - nums[i];
        if (map.has(complement)) {
            return [map.get(complement)!, i];
        }
        map.set(nums[i], i);
    }
    return [];
};

Solution in Java

class Solution {
    public int[] twoSum(int[] nums, int target) {
        HashMap<Integer, Integer> map = new HashMap<>();
        for (int i = 0; i < nums.length; i++) {
            int complement = target - nums[i];
            if (map.containsKey(complement)) {
                return new int[] { map.get(complement), i };
            }
            map.put(nums[i], i);
        }
        return new int[0];
    }
}

Conclusion

The "Two Sum" problem is a fundamental challenge that tests a candidate's grasp of data structures and algorithmic thinking. By understanding and practicing such problems, aspiring software engineers can sharpen their problem-solving skills and prepare themselves for technical interviews.