Picture yourself at a bustling party where each guest wears a number on their back. The host sets up a challenge: find two guests whose numbers add up to the ‘magic number,’ and you’ll take home a prize! This scenario beautifully illustrates the essence of the Two Sum Problem, a classic favorite in algorithm challenges. In this article, we’ll explore two distinct approaches to solving it. Let’s dive right in!
Let’s start to Cracking the Two Sum Problem: A Step-by-Step Solution in JavaScript for Interview Success
Introduction: Two Sum
Objective: Given an array of integers, return the indices of two numbers that add up to a specific target. For instance, if the target is 10 and the array is [5, 1, 5, 3], the output should be [0, 2] because the values at indices 0 and 2 are both 5, which add up to 10. While this problem might appear straightforward, it offers a range of solutions, from basic brute-force to more efficient, optimized approaches. The first solution may be a bit slow, but don’t worry—we’ll ramp up the efficiency in the second one!
Solution 1: The Brute Force Dance
The first approach is like a classic dance move—simple yet effective. We examine every possible pair in the array to see if their sum matches the target. Try to solve it before proceeding! What would happen if the input contained an array with a million or more elements? In that case, the code could take an excessive amount of time to run. The time complexity of the solution above is O(n^2). We can optimise it! Let’s upgrade our code to be more efficient with the use of a hash map.
Try to solve it before proceeding!
function twoSum(nums, target) {
for (let i = 0; i < nums.length; i++) {
for (let j = i + 1; j < nums.length; j++) {
if (nums[i] + nums[j] === target) {
return [i, j];
}
}
}
return null;
}
console.log(twoSum([2, 7, 11, 15], 9)); // [0, 1]Solution 2: Speed it up with Hash Map
The solution I’m about to show uses a hash map to store the indices of the elements we’ve encountered so far. A hash map (or hash table) is a data structure that stores key-value pairs, enabling fast retrieval of values based on their keys through a process called hashing. This way, we can find the complement of the current element in constant time. The reason for naming the variable ‘complement’ is that, for any given element nums[i], we are searching for another element in the array such that their sum equals the target.
This other element is the complement of the current element with respect to the target sum. Try to solve it before looking down below!
function twoSumHashMap(nums, target) {
const numToIndex = {};
for (let i = 0; i < nums.length; i++) {
const complement = target - nums[i];
if (numToIndex[complement] !== undefined) {
return [numToIndex[complement], i];
}
numToIndex[nums[i]] = i;
}
return null;
}
console.log(twoSumHashMap([2, 7, 11, 15], 9)); // [0, 1]This algorithm is much faster than the previous one, although it does require extra space for the hash map. The space complexity of this algorithm is (O(n). Since we must perform this check for every element in the array, the overall time complexity of the algorithm is O(n).
Conclusion:
That wraps up a fun and engaging algorithm challenge with two distinct solutions. We hope this article helps you feel more prepared for your next interview! Have you ever faced this algorithm in an interview? Feel free to share your experience in the comments below! If you’re an interviewer who has asked this question, we’d love to hear how the candidates did!
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