Algorithms

⏱ 6 min read Tree DP Pattern Many tree problems require computing an answer that depends on both subtrees. The key pattern: define a […] Read article

⏱ 6 min read What Makes an Algorithm Greedy A greedy algorithm makes the locally optimal choice at each step, hoping this leads to Read article

⏱ 6 min read Palindrome Check A palindrome reads the same forward and backward. Brute force check: O(n). Two-pointer: left=0, right=n-1; while left < Read article

⏱ 6 min read The String Matching Problem Given a text T of length n and a pattern P of length m, find all Read article

⏱ 6 min read Topological Sort A topological ordering of a directed acyclic graph (DAG) is a linear ordering of vertices such that for Read article

⏱ 5 min read When Number Theory Appears in Interviews Number theory problems appear in interviews at companies like Google, Facebook, and competitive programming Read article

⏱ 7 min read What Is a Minimum Spanning Tree? A Minimum Spanning Tree (MST) of a weighted undirected graph is a spanning tree Read article

⏱ 5 min read Choosing the Right Algorithm Decision tree: non-negative weights? -> Dijkstra (O((V+E) log V)). Negative weights, no negative cycles? -> Bellman-Ford Read article

⏱ 6 min read Monotonic Stack Concept A monotonic stack maintains elements in strictly increasing or decreasing order. Elements that violate the order are Read article

⏱ 6 min read What Is Amortized Analysis? Amortized analysis gives the average cost per operation over a sequence of operations, even when individual Read article

⏱ 6 min read Why Randomized Algorithms? Randomized algorithms use random choices to achieve good expected performance, simplify implementation, or avoid worst-case inputs that Read article

⏱ 7 min read When to Use DP on Graphs DP on graphs works when the graph has structure that prevents cycles in the Read article

⏱ 7 min read Naive String Matching For each position i in text (0 to n-m): check if text[i:i+m] == pattern. O(n*m) in the Read article

⏱ 7 min read Bellman-Ford Algorithm Finds shortest paths from a source to all nodes, handling negative edge weights. Algorithm: initialize dist[source]=0, dist[all others]=inf. Read article

⏱ 5 min read GCD and LCM Greatest Common Divisor (GCD): the largest number that divides both a and b. Euclidean algorithm: gcd(a, b) Read article