Algorithmic Problem Solving Fundamentals Questions
Core foundation for solving entry level algorithmic problems. Focuses on arrays, strings, basic mathematics and number theory problems, simple bit manipulation, basic linked list and tree operations, stacks and queues, basic sorting and searching algorithms, simple recursion, and use of hash based data structures for counting and lookup. Emphasizes understanding asymptotic time and space complexity, selecting appropriate data structures for a task, and clear step by step problem solving including writing a brute force solution and analyzing correctness.
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Given a string consisting of characters '(', ')', '{', '}', '[' and ']', write a Python function to determine if it is valid. A valid string must have matching open/close types and correct nesting order. Explain why a stack is the appropriate data structure and discuss time/space complexity.
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Solve the Dutch National Flag problem: given an array of values 0, 1, and 2, sort it in-place in one pass with constant extra space. Implement in Python and explain pointer invariants for low, mid, and high indices.
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Given an integer array (can contain negative numbers) and an integer k, count the number of continuous subarrays that sum to k. Implement an O(n) time solution in Python using prefix sums and a hash map for counts. Explain why this works and how to handle large inputs.
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Implement a function in Python that determines whether a 32-bit signed integer is a power of two (positive powers only). Solve it using bit manipulation without loops. Discuss edge cases (e.g., zero, negative inputs) and time/space complexity.
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Write a function in Python that takes a text field from a dataset (a string) and returns the reversed string. If the input is given as a mutable list of characters, perform the reversal in-place. Explain time and space complexity for both immutable and mutable inputs, and mention how you would handle very large inputs or streaming data. Example: Input: 'hello' → Output: 'olleh'.
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