Algorithms & Data Structures

Repeatedly compares adjacent pairs and swaps them if out of order. After each full pass the largest remaining element 'bubbles' to the end.

Divide-and-conquer sort: recursively split the array in half, sort each half, then merge the two sorted halves back together in linear time.

Pick a pivot, partition elements into 'less than' and 'greater than' groups, then recursively sort each partition. Uses Lomuto partitioning here.

Search a sorted array in O(log n) by repeatedly halving the search range — compare the target with the middle element and discard the half it can't be in.

Explore a graph layer by layer using a queue. Guarantees shortest path in an unweighted graph because nodes are visited in order of their distance from the source.

Explore a graph as deeply as possible before backtracking. Uses a stack (or recursion). Natural fit for topological sort, cycle detection, and maze exploration.

Greedy single-source shortest path on non-negative weighted graphs. Always expands the unvisited node with the smallest tentative distance, relaxing edges to its neighbours.

BFS on a 2D grid — the shortest-path workhorse behind maze solving and flood fill. Each walkable cell is a node; edges connect 4-neighbours. Shortest path by cell count is guaranteed.

DFS on a 2D grid — explores as far as possible along one direction before backtracking. Great for maze generation, connected-component labelling, and 'can I reach X?' checks.

Dijkstra on a grid where each cell has its own entry cost (digit 1–9). Finds the lowest-total-cost path from S to E. '.' cells cost 1, walls '#' are blocked.

Insert values into a Binary Search Tree one at a time. At each node, go left if the new value is smaller, right if larger — place it in the first empty slot.

Depth-first traversals of a binary search tree. In-order yields sorted values; pre-order is useful for copying; post-order for tree deletion and expression evaluation.

Append, prepend, delete, and reverse operations on a singly linked list. Reversal flips every next-pointer with three moving references (prev / curr / next).

A stack is a Last-In-First-Out container. push adds to the top, pop removes from the top, peek reads the top without removing. All three operations are O(1).

Compute the nth Fibonacci number by filling a table from the bottom up. Each entry depends only on its two predecessors — the textbook introduction to dynamic programming.