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

Tutorial: Solving the 2 Sum Problem for Interviews

1. Understanding the Problem:

   • The 2 Sum problem involves finding two elements in an array that sum up to a target value.
   • There are two variations of the problem:
     • The first variation requires a simple yes or no answer if such a pair exists.
     • The second variation asks for the indexes of the two elements that sum up to the target.

2. Brute Force Approach:

   • Start by picking one element and checking it with every other element in the array to see if they sum up to the target.
   • Repeat this process for all elements in the array.
   • Implement nested loops to iterate through the array elements and check for the sum.
   • Time complexity: O(n^2).

3. Optimizing the Brute Force Approach:

   • Instead of checking all elements again, start checking from the next element each time.
   • This optimization slightly reduces the time complexity but is still around O(n^2).

4. Hashing Approach (Better Solution):

   • Use a hash map to store elements and their indexes as keys and values.
   • Iterate through the array and for each element, check if the required complement exists in the hash map.
   • If found, return the indexes or a yes; otherwise, continue iterating.
   • This approach reduces the time complexity to O(n).

5. Greedy Approach (Optimal Solution):

   • Sort the array to apply a greedy approach.
   • Initialize two pointers, one at the start and one at the end of the sorted array.
   • Move the pointers towards each other based on the sum of the elements at the pointers compared to the target.
   • If a pair is found, return yes; otherwise, return no.
   • This solution has a time complexity of O(n log n) due to sorting.

6. Coding the Solutions:

   • Implement the Brute Force, Hashing, and Greedy approaches in your preferred programming language.
   • Refer to the provided links for C++, Java, and Python code for all three approaches.

7. Additional Notes:

   • Consider explaining the space complexity when using different approaches during an interview.
   • Provide the necessary output format based on the problem variation (yes/no or indexes).
   • Test your implementations on platforms like LeetCode to validate correctness.

8. Conclusion:

   • The 2 Sum problem is a common interview question that can be approached using different strategies.
   • Each approach offers a trade-off between time complexity and space complexity.
   • Practice coding these solutions to enhance your problem-solving skills for technical interviews.

By following these steps, you can effectively solve the 2 Sum problem and be well-prepared for similar interview questions.