Technical Fundamentals & Core Skills Topics
Core technical concepts including algorithms, data structures, statistics, cryptography, and hardware-software integration. Covers foundational knowledge required for technical roles and advanced technical depth.
Sorting and Searching Algorithms
Comparison and non-comparison sorting (quicksort with its pivot and partition choices and hybrid cutoffs, mergesort, heapsort as a sort, insertion/selection/bubble, counting/radix/bucket), their stability, in-place behavior, stack depth and lower bounds, and choosing a sort from input constraints, including near-sorted data, library sorts (Timsort, introsort, language defaults), comparator design and expensive comparisons or copies. Also selection (quickselect, median-of-medians, nth_element), external merge sorting of data larger than memory (run generation and merge passes), and binary search with its variants: first/last occurrence, lower/upper bound, rotated arrays with or without duplicates, peak and mountain arrays, sorted matrices, unbounded search, loop-invariant correctness and off-by-one pitfalls, and binary search on an answer space (discrete or continuous, including k-th smallest by value). Includes divide-and-conquer reasoning for sorts (merge step, merging sorted arrays, median of two sorted arrays, inversion counting). Excludes heap data-structure mechanics and heap-based top-k and k-way merging, trees and tries, general graph search, distributed data-processing systems, approximate nearest-neighbor and streaming-sketch algorithms, and abstract Big-O comparison.
Algorithmic Problem-Solving and Data Structure Selection
The higher-order meta-skill of attacking an unfamiliar problem: recognizing problem archetypes and mapping them to known techniques, decomposing under constraints, and choosing, composing, or designing the right data structures to meet specified operation costs (LRU cache, min-stack, ordered maps, disjoint-set/union-find). Covers reasoning about trade-offs between competing structures and approaches, working through medium-to-hard problems methodically, handling problem variations, and communicating an approach before coding. The connective-tissue topic that ties the individual structure and algorithm topics together, rather than any single structure or algorithm.
Time and Space Complexity Analysis
Reasoning about algorithmic efficiency: Big-O/Theta/Omega notation, amortized analysis, recurrence solving, and the time-versus-space trade-off. Covers deriving bounds from code, comparing candidate approaches, and communicating complexity clearly under interview pressure. The analytical layer applied across every algorithm topic.
Heaps and Priority Queues
Binary heaps and priority queues as data structures: min-heap and max-heap, array layout, sift-up and sift-down, push/pop/peek costs, build-heap (heapify) in O(n), and indexed heaps with decrease-key versus lazy deletion of stale entries. Covers the problems where a heap is the intended tool: top-K and kth largest or smallest selection (including over a one-pass stream and under inserts and deletes), sorting an array whose elements are at most k places out of order with a window heap, the two-heap pattern for running and sliding-window medians (invariants, rebalancing, lazy deletion, testing, and extensions to percentiles, weighted medians, custom orderings and merging structures), k-way merge of sorted lists, arrays, files or streams with bounded memory, scheduling by priority with cancellation and reprioritisation, stable priority queues with tie-breaking, and implementing a heap or priority queue with a language library such as heapq or PriorityQueue (including max-heap behaviour from a min-heap). Boundary: graph shortest-path algorithms, approximate quantile sketches, production streaming-system design, and heapsort and quickselect as sorting and selection algorithms are covered elsewhere.
Code Review and Working with Existing Codebases
Reviewing others' code and navigating unfamiliar systems: giving and receiving actionable review feedback, spotting correctness and design issues, and reading and understanding large or legacy codebases before changing them. Covers collaborative coding norms, incremental change in shared repositories, and verifying changes against existing behavior. The team-facing side of day-to-day engineering.
Linear Algebra and Numerical Computing
The linear algebra and numerical methods that machine-learning and scientific code rest on. Covers vectors, matrices and their operations, eigenvalues and eigenvectors and their geometry, singular value decomposition and PCA as linear algebra (variance explained, randomized SVD), least squares, the normal equations and rank deficiency, matrix calculus and gradients of quadratic objectives, conditioning and its effect on solvers, feature scaling and gradient descent, ill-conditioned covariance matrices and the fixes for them (shrinkage, truncated pseudo-inverse, dimension reduction), floating-point error and numerically stable algorithms (compensated and pairwise summation), iterative methods such as power iteration, and the mathematics of optimization: convexity, smoothness, strong convexity, convergence rates of gradient descent, preconditioning, saddle points and Hessian tests for stationary points, Lagrange multipliers and KKT conditions. Questions are about deriving, computing and reasoning about precision and convergence. Probability and statistical inference, learning-theory bounds, neural-network training practice, and library API mechanics are covered elsewhere.
Recursion and Backtracking
Recursion mechanics (base and recursive cases, tracing call stack frames, what lives on the stack versus the heap, tail calls, recursion depth limits and stack overflow diagnosis, recursion-to-iteration conversion with an explicit stack or trampoline, recursion versus iteration trade-offs) and recursion on nested data and simple divide-and-conquer (Euclid's gcd, string reversal, flattening nested lists and dictionaries lazily with generators, recursive maximum subarray). Also backtracking search over combinatorial spaces: permutations (including duplicates and the k-th permutation), subsets, combinations, combination sum, generating balanced parentheses, N-Queens (with bitmasks and symmetry), Sudoku (with minimum-remaining-values ordering), word search, palindrome partitioning, Knight's Tour and Hamiltonian paths. Covers the choose/explore/undo template, how it differs from plain DFS, state-leakage bugs, pruning, and recursion-tree complexity (O(b^d)) including call-tree counts. Memoized recursion, tree traversals, and general graph search are covered elsewhere.
Arrays, Strings, and Hashing
Manipulating arrays and strings using the standard toolkit for entry-level coding-interview problems: two-pointer and sliding-window techniques, in-place modification (reversal, rotation, partitioning, deduplication), prefix sums, and hash-map or hash-set based techniques used to solve array or string problems in optimal time (frequency counting, lookup-based pairing such as two-sum, duplicate detection, grouping by a computed key such as anagram grouping). Hashing appears in this topic only as an applied technique for solving an array or string problem faster: how hash tables work internally (hash functions, collision resolution, load factor, resizing) and hash-based structures that are not array or string shaped (Bloom filters, HyperLogLog) belong to the separate hashing and hash tables topic, not this one. Covers the most frequent entry-level coding-interview problem shapes and the trade-offs between time, space, and readability. The default warm-up surface for any coding interview.
Dynamic Programming
Solving problems with overlapping subproblems and optimal substructure by memoization (top-down) and tabulation (bottom-up). Covers recognizing DP-amenable problems, defining state, transition and base cases, 1D and 2D sequence and grid formulations (knapsack and its variants, coin change, LIS, LCS, edit distance, sequence alignment, regular-expression and wildcard matching, counting-ways problems), interval DP (matrix chain, palindrome partitioning), space optimization with rolling arrays, solution reconstruction, longest paths in a DAG, game and expected-value DP, bitmask and tree DP, speeding up a DP (monotone queue, convex hull trick, divide-and-conquer optimization, bitsets, meet in the middle), and judging greedy versus DP. Ground covered elsewhere: probabilistic model inference, production caching and debugging practice, and general graph shortest-path algorithms.