Learn algorithms
by seeing them run.

Dives as deep as possible along each branch before backtracking. Uses a stack (or recursion). Essential for cycle detection, topological sort, and connected components.

Linear ordering of vertices in a directed acyclic graph (DAG) such that for every edge u→v, u appears before v. Uses DFS or Kahn's algorithm.

Greedily grows a spanning tree one vertex at a time by always adding the cheapest edge connecting the tree to a new vertex. Closely related to Dijkstra.

Builds the MST by sorting all edges by weight and greedily adding the smallest edge that doesn't create a cycle. Uses Union-Find for efficient cycle detection.

Divide-and-conquer algorithm that partitions around a pivot. Excellent cache performance in practice despite O(n²) worst case. The backbone of most standard libraries.

Stable divide-and-conquer sort. Recursively splits the array in half, sorts each half, then merges. Guaranteed O(n log n) and widely used for linked lists.

Repeatedly steps through the list, comparing adjacent elements and swapping them if out of order. Simple to understand and visualize — great as a teaching tool.

Uses a binary heap to sort in-place. First builds a max-heap, then repeatedly extracts the maximum. Combines Merge Sort's time complexity with Quick Sort's space efficiency.

Classic DP problem: given items with weights and values, find the most valuable subset that fits within a weight limit. Solved by building a 2D table of subproblems.

Finds the longest sequence of characters common to two strings (not necessarily contiguous). Foundation of diff tools, DNA analysis, and spell checkers.

The gateway to DP thinking. Compare naïve recursion (O(2ⁿ)), top-down memoization, and bottom-up tabulation — all three approaches side-by-side with call trees.