Algorithms — DSA Core

1Complexity & analysis

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Every answer ends with "…so it's O(n)". Being fluent in Big-O and able to justify it is table stakes.

Reason about cost

Big-O / Ω / Θ; time and space; amortised analysis (why a dynamic array push is O(1) amortised).

Big-O Cheat Sheet.

Complexity of the common data structures: array, hashmap, heap, BST, trie.

Big-O Cheat Sheet — data structures table.

Recurrences & the Master Theorem for divide-and-conquer costs.

Master theorem.

2Sorting & searching

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You rarely re-implement these, but you must know their tradeoffs and when each wins.

Know the tradeoffs

Merge sort, quicksort, heapsort — average/worst case, stability, in-place or not.

VisuAlgo — Sorting — animated.

Why O(n log n) is the comparison-sort lower bound; when counting/radix sort beats it.

Comparison sort — lower bound.

Binary search template + variants (rotated array, search on the answer space).

LeetCode — Binary Search.

Quickselect for kth-smallest in average O(n).

Quickselect.

3Recursion, divide & conquer, backtracking

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The engine behind trees, permutations, and "try all options with pruning".

Core techniques

Recursion mechanics: base case, recursive case, the call stack (and stack overflow).

Python Tutor — step through the stack visually.

Divide & conquer: split, solve, combine (merge sort, quickselect, D&C on arrays).

Divide and conquer.

Backtracking template: choose → explore → un-choose; prune early. Subsets, permutations, N-Queens.

LeetCode — Subsets.

4Graph algorithms

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A dense, high-value area. Know the core traversal and shortest-path/ordering algorithms and when each applies.

The essential graph toolkit

BFS (shortest unweighted path) and DFS (reachability, components); multi-source BFS.

VisuAlgo — BFS/DFS.

Topological sort (Kahn's + DFS) for dependency ordering & cycle detection.

Course Schedule.

Dijkstra (positive weights) and why it fails with negative edges; Bellman-Ford.

VisuAlgo — Shortest paths.

Union-Find (path compression + union by rank) for connectivity & cycle detection.

VisuAlgo — Union-Find.

MST: Kruskal (sort + union-find) and Prim (heap).

VisuAlgo — MST.

5Greedy & dynamic programming

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The two big optimisation paradigms. The interview skill is recognising which one applies and proving the greedy choice is safe.

Optimisation paradigms

Greedy: when the local choice is provably safe (exchange argument); interval scheduling.

Jump Game.

DP: identify the state and recurrence; memoise vs tabulate; optimise space.

House Robber and NeetCode — DP roadmap.

Greedy vs DP: how to tell them apart, and why a greedy that "looks right" can be wrong.

Greedy algorithm.

6Where to drill

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For the pattern-by-pattern problem catalog, use the LeetCode Patterns page; this page is the algorithm theory behind it.

Practice

Work the pattern catalog — 30 patterns, 90 problems, in our style.

Resources — LeetCode Patterns.

Follow a structured roadmap so topics build on each other.

NeetCode — Roadmap.

Visualise any algorithm you're shaky on.

VisuAlgo.