Programming, Data Structures and Algorithms

The subset of Python that matters: comprehensions, iterators, generators, decorators and typing.

ndarrays, dtypes, vectorisation, broadcasting rules, views vs copies, and why loops are slow.

Assumes: Python for Data Science

Series and DataFrames, indexing, groupby-apply-combine, joins, reshaping and time indexing.

Assumes: NumPy Essentials

Big-O, big-Theta and big-Omega, amortised analysis, and deriving recurrences with the master theorem.

Contiguous storage, dynamic array growth, two-pointer and sliding-window patterns.

Assumes: Complexity Analysis

LIFO semantics, array and linked implementations, and applications: expression evaluation, parsing, monotonic stacks.

Assumes: Arrays and Strings

FIFO queues, circular buffers, double-ended queues and priority queue contrasts.

Assumes: Stacks

Singly, doubly and circular lists, pointer manipulation, cycle detection and list reversal.

Assumes: Arrays and Strings

Hash functions, load factor, chaining vs open addressing, and the average/worst-case gap.

Assumes: Arrays and Strings

Terminology, binary tree properties, and pre-, in-, post- and level-order traversals recursively and iteratively.

Assumes: Queues and Deques

BST invariant, insert/search/delete, degenerate cases, and why balancing matters.

Assumes: Trees and Traversals

Heap property, array representation, sift up/down, heapify in linear time, and heapsort.

Assumes: Trees and Traversals

Prefix trees for string search, space/time trade-offs, and autocomplete applications.

Assumes: Trees and Traversals

Base cases, recursion trees, stack depth, memoisation, and systematic backtracking search.

Assumes: Complexity Analysis

Sequential search, binary search with correct invariants, and the off-by-one errors that plague it.

Assumes: Complexity Analysis

The three quadratic sorts traced step by step, with comparison and swap counts.

Assumes: Linear and Binary Search

Divide and conquer, the merge step, the recurrence solution, and stability and space cost.

Assumes: Selection, Bubble and Insertion Sort

Partitioning schemes, pivot selection, average vs worst case, and randomisation.

Assumes: Merge Sort

Heapsort, then counting, radix and bucket sort, and the comparison-sort lower bound they escape.

Assumes: Heaps and Priority Queues · Quick Sort

The general paradigm, binary-search variants, closest pair, and Strassen multiplication.

Assumes: Merge Sort

Exchange arguments, activity selection, Huffman coding, and when greed provably works.

Assumes: Heaps and Priority Queues

Optimal substructure, overlapping subproblems, memoisation vs tabulation, and classic DP tables.

Assumes: Recursion and Backtracking

Adjacency matrix vs adjacency list, edge lists, directed/undirected/weighted variants and space trade-offs.

Assumes: Hash Tables

BFS and DFS traced on worked graphs, the trees they induce, and edge classification.

Assumes: Graph Representations

Ordering a DAG via Kahn's algorithm and DFS finish times, plus cycle detection.

Assumes: Breadth-First and Depth-First Search

Dijkstra, Bellman–Ford and Floyd–Warshall traced numerically, with negative-weight handling.

Assumes: Breadth-First and Depth-First Search

Kruskal and Prim, the cut and cycle properties, and union–find with path compression.

Assumes: Shortest Path Algorithms