2 Sum Problem | 2 types of the same problem for Interviews | Brute-Better-Optimal

Summary

In this video, the instructor dives into the Two Sum problem, an essential data structures and algorithms (DSA) challenge. The video covers both varieties of the problem—one where you simply check if two elements sum up to a target, and another where you return the indices of those elements. The instructor demonstrates a brute force solution, then optimizes it using hashing for better efficiency, followed by a two-pointer approach. Throughout the tutorial, viewers are guided step-by-step through the logic and coding process, with clear explanations, time complexities, and space optimization strategies.

Takeaways

• 😀 This course is an in-depth Data Structures and Algorithms (DSA) course, covering 456 modules and 400+ problems.
• 😀 Completing the course guarantees proficiency in tackling DSA problems in interviews at any company globally.
• 😀 The current video addresses the Two Sum problem, which has two varieties: one asks for a simple yes/no answer, and the other asks for the indices of the two elements.
• 😀 The first variety of the Two Sum problem asks if there are two elements that add up to a given target sum.
• 😀 The second variety requires returning the indices of the two elements that add up to the target sum.
• 😀 The brute force solution to the Two Sum problem involves checking every pair of elements, resulting in an O(n²) time complexity.
• 😀 An optimization can be achieved by only checking elements that haven't been compared yet, reducing the problem's complexity but still being close to O(n²).
• 😀 A more efficient solution uses a hash map to store elements and their indices, allowing quick lookups and reducing the time complexity to O(n).
• 😀 The time complexity of the hash map solution is O(n), assuming average O(1) time complexity for lookups in the hash map.
• 😀 If using a hash map is not allowed, the Two Pointer approach can be used, which sorts the array and moves pointers from both ends, resulting in a time complexity of O(n log n) due to sorting.

Q & A

What is the primary topic of the video?

The video covers a solution to the Two Sum problem, a common algorithmic problem often encountered in technical interviews. It explains both the brute force solution and the optimized approach using hashing and two-pointer techniques.

What are the two varieties of the Two Sum problem mentioned in the video?

The first variety asks whether two elements in an array sum up to a target value, returning a simple 'yes' or 'no'. The second variety requires returning the indices of the two elements that sum up to the target value.

How does the brute force solution for the Two Sum problem work?

The brute force solution iterates through each element in the array, then checks every other element to see if their sum equals the target value. This approach results in a time complexity of O(n^2).

What is the time complexity of the brute force solution?

The time complexity of the brute force solution is O(n^2), where n is the number of elements in the array. This is because for each element, you check it against every other element in the array.

How does hashing optimize the Two Sum problem solution?

Hashing improves the solution by storing the elements in a hash map while iterating over the array. This allows for constant time lookups (O(1)) to check if the complement of the current element (target - element) has already been seen, reducing the time complexity to O(n).

What does the hash map store in the optimized solution?

In the optimized solution, the hash map stores the elements of the array as keys and their corresponding indices as values. This allows for quick lookups to find whether a complement element (target - current element) exists.

What is the space complexity of the hash map approach?

The space complexity of the hash map approach is O(n), where n is the number of elements in the array, as we store each element and its index in the hash map.

What is the two-pointer approach, and how is it used to solve the Two Sum problem?

The two-pointer approach involves sorting the array and placing one pointer at the beginning (left) and another at the end (right). If the sum of the elements at these pointers equals the target, the solution is found. If the sum is less than the target, the left pointer is incremented, and if the sum is greater, the right pointer is decremented.

What is the time complexity of the two-pointer approach?

The time complexity of the two-pointer approach is O(n log n) because the array must be sorted first, which takes O(n log n) time. The subsequent iteration with two pointers takes O(n) time.

What is the difference between the two-pointer approach and the hashing approach?

The two-pointer approach requires sorting the array and then iterating with two pointers, while the hashing approach uses a hash map to store elements and perform constant-time lookups for the complement. The two-pointer approach has a time complexity of O(n log n), whereas the hashing approach has a time complexity of O(n).