Algorithms · Reading course
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79 reading items · 9 phases · Worked examples & practice
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Lessons, chapter reviews, and checkpoints—in reading order.
Begin hereStart here0 / 2 complete
01Phase 0Foundations0 / 8 complete
0.1.1Problems, instances and algorithms; correctness; counting basic stepsLesson0.1.2Math toolkit: logarithms, floors and ceilings, sums (arithmetic, geometric, harmonic)LessonLI-0.1What an algorithm isChapter review0.2.1Arrays, linked lists, stacks and queues: what each operation costsLesson0.2.2Trees, binary search trees and binary heaps: heights and operation costsLesson0.2.3Graphs: vocabulary, adjacency matrix vs adjacency listLessonLI-0.2Data-structure recapChapter reviewCP-0FoundationsCheckpoint
02Phase 1Asymptotic Analysis & Recurrences0 / 11 complete
1.1.1Big-O, Big-Ω and Θ: definitions with constantsLesson1.1.2Little-o and little-ω; comparing and ordering functionsLesson1.1.3Analysing loops: nested, dependent and logarithmic loopsLessonLI-1.1Growth of functionsChapter review1.2.1Recurrences from recursive code; solving by unrolling (substitution)Lesson1.2.2The recursion-tree methodLesson1.2.3The master theoremLesson1.2.4Harder recurrences: change of variables, T(n−1) forms, unequal splitsLesson1.3.1Best, worst and average case; space complexity and recursion depth; amortised costLessonLI-1.2-1.3Chapters 1.2–1.3 Lock-in — Recurrences & Cases and spaceChapter reviewCP-1Asymptotic Analysis & RecurrencesCheckpoint
03Phase 2Searching & Hashing0 / 8 complete
2.1.1Linear search and binary search: comparisons and correctnessLesson2.1.2Binary search variants and the Ω(log n) lower bound for searchingLessonLI-2.1SearchingChapter review2.2.1Hash tables, hash functions, load factor; separate chainingLesson2.2.2Open addressing: linear probing, quadratic probing, double hashingLesson2.2.3Expected probes and collision probabilitiesLessonLI-2.2HashingChapter reviewCP-2Searching & HashingCheckpoint
04Phase 3Sorting0 / 12 complete
3.1.1Bubble sort and selection sort: passes, comparisons, swapsLesson3.1.2Insertion sort and inversions; stable and in-place sortingLessonLI-3.1Elementary sortsChapter review3.2.1Merge sort: merging, recurrence, comparison countsLesson3.2.2Quicksort: partitioning, best, worst and average casesLesson3.2.3Heapsort: build-heap in O(n), heapify, extract-maxLessonLI-3.2Divide-and-conquer sortsChapter review3.3.1The Ω(n log n) lower bound for comparison sorting; comparing all sortsLesson3.3.2Counting sort, radix sort and bucket sortLesson3.3.3Selection: minimum and maximum, second largest, k-th smallestLessonLI-3.3Beyond comparison sortingChapter reviewCP-3SortingCheckpoint
05Phase 4Divide & Conquer and Greedy0 / 9 complete
4.1.1Divide and conquer: fast exponentiation, counting inversions, maximum subarrayLesson4.1.2Karatsuba and Strassen multiplication; closest pair (brief)LessonLI-4.1Divide and conquerChapter review4.2.1The greedy method; activity selectionLesson4.2.2Fractional knapsack; job sequencing with deadlinesLesson4.2.3Huffman codingLesson4.2.4Optimal merge pattern; when greedy failsLessonLI-4.2Greedy algorithmsChapter reviewCP-4Divide & Conquer and GreedyCheckpoint
06Phase 5Dynamic Programming0 / 9 complete
5.1.1Overlapping subproblems: memoisation vs tabulation; counting callsLesson5.1.20/1 knapsackLesson5.1.3Longest common subsequenceLessonLI-5.1DP foundationsChapter review5.2.1Matrix-chain multiplicationLesson5.2.2Subset sum, coin change and rod cuttingLesson5.2.3Longest increasing subsequence, edit distance and other sequence DPsLessonLI-5.2More DP problemsChapter reviewCP-5Dynamic ProgrammingCheckpoint
07Phase 6Graph Algorithms0 / 13 complete
6.1.1Breadth-first search: levels and unweighted shortest pathsLesson6.1.2Depth-first search: discovery and finish times, edge classificationLesson6.1.3Topological sort, cycle detection, connected and strongly connected componentsLessonLI-6.1Graph traversalsChapter review6.2.1Minimum spanning trees: cut and cycle properties, uniquenessLesson6.2.2Kruskal's algorithm and union–findLesson6.2.3Prim's algorithm; MST complexitiesLessonLI-6.2Minimum spanning treesChapter review6.3.1Relaxation and Dijkstra's algorithmLesson6.3.2Bellman–Ford, negative cycles, shortest paths in DAGsLesson6.3.3All-pairs shortest paths: Floyd–WarshallLessonLI-6.3Shortest pathsChapter reviewCP-6Graph AlgorithmsCheckpoint
08Phase 7Integration & Final Testrule sheet · 3 practice sets · drill · final test0 / 7 complete
7.1.17.1.1 — Master Rule Sheet (all rule cards merged)Revision7.2.17.2.1 — Mixed practice set 1Revision7.2.27.2.2 — Mixed practice set 2Revision7.2.37.2.3 — Mixed practice set 3Revision7.3.17.3.1 — GATE pattern drill: recurring patterns and fastest methodsRevision7.4.1Final end-to-end testFinal test7.4-keyFinal Test — Answer Key🛑Stop here until you have finished the 90-minute final test.🔑 Open the full answer keyQ1 Answer: (C)1 markReaching the last node means walking the whole list.(A) is wrong: Constant time.(B) is wrong: Constant time.(D) is wrong: Constant time.Re-read: Lesson 0.2.1 — Arrays, linked lists, stacks and queues: what each operation costsQ2 Answer: 61 mark⌊log 100⌋.Re-read: Lesson 0.2.2 — Trees, binary search trees and binary heaps: heights and operation costsQ3 Answer: (D)1 mark2²ⁿ / 2ⁿ = 2ⁿ → ∞.(A) is wrong: The ratio log n / n → 0.(B) is wrong: Constant factor 2.(C) is wrong: 2 log n.Re-read: Lesson 1.1.2 — Little-o and little-ω; comparing and ordering functionsQ4 Answer: 101 mark1024 → 512 → … → 2 → 1: 10 halvings.Re-read: Lesson 1.1.3 — Analysing loops: nested, dependent and logarithmic loopsQ5 Answer: (B)1 markn^(log₂ 8) = n³ dominates n².(A) is wrong: Equal case only.(C) is wrong: Ignores the leaves.(D) is wrong: No log factor.Re-read: Lesson 1.2.3 — The master theoremQ6 Answer: 101 mark⌊log 1000⌋ + 1.Re-read: Lesson 2.1.1 — Linear search and binary search: comparisons and correctnessQ7 Answer: 41 mark2000 / 500.Re-read: Lesson 2.2.1 — Hash tables, hash functions, load factor; separate chainingQ8 Answer: (B) (C)1 markSelection and heapsort move equal keys past each other.(A) is wrong: Root swaps.(D) is wrong: Long-distance swaps.Re-read: Lesson 3.1.2 — Insertion sort and inversions; stable and in-place sortingQ9 Answer: 681 markn + ⌈log n⌉ − 2.Re-read: Lesson 3.3.3 — Selection: minimum and maximum, second largest, k-th smallestQ10 Answer: (B)1 markOne pass over the input, one over the counts.(A) is wrong: No.(C) is wrong: No.(D) is wrong: That is comparison sorting.Re-read: Lesson 3.3.2 — Counting sort, radix sort and bucket sortQ11 Answer: 101 mark63 = 111111₂: 5 squarings + 5 extra.Re-read: Lesson 4.1.1 — Divide and conquer: fast exponentiation, counting inversions, maximum subarrayQ12 Answer: (B)1 markWhole items can leave wasted capacity.(A) is wrong: Optimal there.(C) is wrong: 0/1 fails.(D) is wrong: Fractional is optimal.Re-read: Lesson 4.2.4 — Optimal merge pattern; when greedy failsQ13 Answer: 411 mark2F(8) − 1 = 2 × 21 − 1.Re-read: Lesson 5.1.1 — Overlapping subproblems: memoisation vs tabulation; counting callsQ14 Answer: (A) (B) (D)1 markBFS uses a queue.(C) is wrong: A stack gives DFS.Re-read: Lesson 6.1.1 — Breadth-first search: levels and unweighted shortest pathsQ15 Answer: (B)1 markRelaxing all edges V − 1 times handles negative edges.(A) is wrong: Needs non-negative weights.(C) is wrong: Ignores weights.(D) is wrong: Builds an MST, not paths.Re-read: Lesson 6.3.2 — Bellman–Ford, negative cycles, shortest paths in DAGsQ16 Answer: 802 marksn log n + n = 64 + 16.Re-read: Lesson 1.2.1 — Recurrences from recursive code; solving by unrolling (substitution)Q17 Answer: 52 marks65536 → 256 → 16 → 4 → 2: four steps, plus T(2) = 1.Re-read: Lesson 1.2.4 — Harder recurrences: change of variables, T(n−1) forms, unequal splitsQ18 Answer: 92 marks23: 1; 43: 2; 13: 3; 27: 1; 37: 2.Re-read: Lesson 2.2.2 — Open addressing: linear probing, quadratic probing, double hashingQ19 Answer: 3.48 to 3.492 marks10 × (0.9)¹⁰ ≈ 3.487.Re-read: Lesson 2.2.3 — Expected probes and collision probabilitiesQ20 Answer: 172 marksPairs 4 × 1; merging into fours 3 + 3; final merge 7.Re-read: Lesson 3.2.1 — Merge sort: merging, recurrence, comparison countsQ21 Answer: 62 marksPivot 7: 4; then [4, 1, 3] with pivot 3: 2; single elements need none.Re-read: Lesson 3.2.2 — Quicksort: partitioning, best, worst and average casesQ22 Answer: 32 marks20↔40; 10↔40; 10↔30. Result [40, 30, 15, 10, 20].Re-read: Lesson 3.2.3 — Heapsort: build-heap in O(n), heapify, extract-maxQ23 Answer: 952 marks40 from the first item (ratio 10), then 11 units at ratio 5 = 55.Re-read: Lesson 4.2.2 — Fractional knapsack; job sequencing with deadlinesQ24 Answer: 2.172 marksMerges 17, 42, 58, 100 sum to 217.Re-read: Lesson 4.2.3 — Huffman codingQ25 Answer: 652 marks(1, 15) + (5, 50).Re-read: Lesson 5.1.2 — 0/1 knapsackQ26 Answer: 92 marksTens 2: 1 way; tens 1: fives 0–2 (3 ways); tens 0: fives 0–4 (5 ways).Re-read: Lesson 5.2.2 — Subset sum, coin change and rod cuttingQ27 Answer: 13442 marksOrder ((A₁A₂)((A₃A₄)A₅)).Re-read: Lesson 5.2.1 — Matrix-chain multiplicationQ28 Answer: (A) (B) (D)2 marksTimes: 1 1/8, 2 2/5, 4 3/4, 3 6/7; 1 → 3 is a tree edge.(C) is wrong: 3 is still white when 1 → 3 is explored.Re-read: Lesson 6.1.2 — Depth-first search: discovery and finish times, edge classificationQ29 Answer: 392 marksEdges added: A–D 5, D–F 6, A–B 7, B–E 7, E–C 5, E–G 9.Re-read: Lesson 6.2.3 — Prim's algorithm; MST complexitiesQ30 Answer: 202 marks1–3–6–5 = 9 + 2 + 9.Re-read: Lesson 6.3.1 — Relaxation and Dijkstra's algorithmAnswer key
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