Request senior-level coding problems focused on algorithms and complexity

Request senior-level coding problems focused on algorithms and complexity

CODING

1. Merge K Sorted Linked Lists

Problem: Given k sorted linked lists, merge them into one sorted linked list.
Key Algorithm: Use a min-heap (priority queue) to efficiently find the smallest head among k lists.
Time Complexity: O(Nlog⁡k)O(N \log k)O(Nlogk) where NNN is total number of nodes, kkk is number of lists.

2. Trapping Rain Water

Problem: Given an array of elevations, compute how much water it can trap after raining.
Key Algorithm: Two-pointer approach maintaining left_max and right_max to compute trapped water in O(N).
Time Complexity: O(N)O(N)O(N), Space Complexity: O(1)O(1)O(1).

3. Word Break (DP)

Problem: Given a string and a dictionary, determine if the string can be segmented into valid words.
Key Algorithm: Use dynamic programming with a boolean DP array indicating if substrings can be segmented.
Time Complexity: O(N2)O(N^2)O(N2), with NNN as length of string.

4. LRU Cache Implementation

Problem: Design an LRU cache with O(1) get and put operations.
Key Data Structures: Use OrderedDict or combine doubly linked list and hashmap for O(1) operations.
Time Complexity: O(1) for both get and put.

5. Median in Data Stream

Problem: Find the median at any point as numbers are streamed.
Key Algorithm: Use two heaps (max-heap and min-heap) to balance lower and upper halves.
Time Complexity: O(log N) per insertion.

6. Number of Islands (Graph DFS)

Problem: Count connected components of '1's in 2D grid.
Key Algorithm: DFS or BFS traversal of grid to mark visited cells.
Time Complexity: O(M×N)O(M \times N)O(M×N), where MMM and NNN are grid dimensions.

Complexity Analysis and Approach Strategy

  • Always start with a brute force solution: analyze its time and space complexity (often O(N2)O(N^2)O(N2) or worse).

  • Brainstorm optimizations: introducing data structures like heaps, tries, balanced trees, or using DP/memoization.

  • Consider input constraints to choose between solutions (e.g., N≤105N \leq 10^5N≤105 favors O(Nlog⁡N)O(N \log N)O(NlogN) or better).

  • Use known algorithmic patterns: sliding windows (O(N)), divide and conquer (O(N log N)), two pointers (O(N)).

  • Articulate space-time tradeoffs clearly during interviews.

Recommended Practice

  • Work on these problems on platforms like LeetCode, HackerRank, or InterviewBit.

  • After solving, write down time and space complexity, and try alternate approaches for optimization.

  • Engage in mock interviews focusing on explaining your complexity reasoning.

This approach builds both problem-solving skills and a deep understanding of complexity analysis valued at senior levels.