GATE CSE 2027 Algorithms: Syllabus, Weightage, Complexity, DP, Greedy, Graphs & Solved Problems
Searching, sorting, hashing, asymptotic analysis, greedy, dynamic programming, divide and conquer, graph traversal, MSTs and shortest paths: the complete GATE CSE 2027 Algorithms toolkit with solved questions.
By Piyush Wairale (M.Tech, IIT Madras) · Former Instructor, IIT Madras BS Degree Programme · Mentor to 20,000+ GATE aspirants · Updated November 2026
Quick Answer
• Algorithms is Section 5 of GATE CSE 2027 and typically carries 8 to 10 marks.
• Syllabus: searching, sorting, hashing; asymptotic worst case time and space complexity; greedy, dynamic programming and divide-and-conquer; graph traversals, minimum spanning trees and shortest paths.
• Complexity analysis (recurrences, loops) and graph algorithms (MST, Dijkstra, BFS/DFS properties) appear every year.
• Algorithms MSQs punish half-understanding. Practise them under exam conditions in the GATE CSE 2027 Test Series by Piyush Wairale.
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Official syllabus · Weightage · Asymptotic analysis · Searching, sorting, hashing · Greedy, DP, D&C · Graph algorithms · Solved problems · Strategy · FAQs
GATE CSE 2027 Algorithms Syllabus (Official, IIT Madras)
Section 5 of the CS paper: Searching, sorting, hashing. Asymptotic worst case time and space complexity. Algorithm design techniques: greedy, dynamic programming and divide-and-conquer. Graph traversals, minimum spanning trees, shortest paths.
See every section in the GATE CS 2027 syllabus and exam pattern guide.
Topic-wise Weightage and Priority
| Topic | Typical question | Priority |
|---|---|---|
| Asymptotic analysis | Solve recurrences, loop complexity, compare growth rates | Very high |
| Graph algorithms | MST weight/uniqueness, Dijkstra trace, BFS/DFS tree properties | Very high |
| Sorting & searching | Best/worst case, stability, comparisons, partition outputs | High |
| Dynamic programming | LCS, knapsack, matrix chain, fill-the-table values | High |
| Hashing | Final table after linear/quadratic probing, expected probes | Medium |
Asymptotic Worst Case Time and Space Complexity
Growth order to memorise: 1 < log log n < log n < √n < n < n log n < n² < n³ < 2n < n! < nn. Master theorem for T(n) = aT(n/b) + f(n): compare f(n) with nlogba. If f is polynomially smaller, T = Θ(nlogba); if equal, T = Θ(nlogba log n); if polynomially larger (with regularity), T = Θ(f(n)). Recurrences like T(n) = T(n−1) + n solve by substitution to Θ(n²). For nested loops where the inner variable doubles, count iterations as log n, not n.
Searching, Sorting and Hashing
| Algorithm | Best | Worst | Stable / In-place |
|---|---|---|---|
| Insertion sort | O(n) | O(n²) | Yes / Yes |
| Selection sort | O(n²) | O(n²) | No / Yes |
| Merge sort | O(n log n) | O(n log n) | Yes / No (O(n) extra) |
| Quick sort | O(n log n) | O(n²) | No / Yes |
| Heap sort | O(n log n) | O(n log n) | No / Yes |
Any comparison sort needs Ω(n log n) comparisons in the worst case. Binary search is O(log n) on a sorted array. Finding both max and min of n elements needs ⌈3n/2⌉ − 2 comparisons. In hashing with load factor α, chaining gives expected O(1 + α) search; open addressing (linear and quadratic probing, double hashing) suffers clustering as α approaches 1.
Greedy, Dynamic Programming and Divide-and-Conquer
Greedy: activity selection, fractional knapsack, Huffman coding, Kruskal and Prim. Greedy works when the problem has the greedy-choice property; it fails for 0/1 knapsack. Dynamic programming: overlapping subproblems + optimal substructure. Know LCS (O(mn)), 0/1 knapsack (O(nW), pseudo-polynomial), matrix chain multiplication (O(n³)), and Floyd-Warshall (O(V³)). Divide-and-conquer: merge sort, quick sort, binary search, Strassen (O(n2.81)), and the closest-pair style recurrences.
Graph Traversals, MSTs and Shortest Paths
BFS (queue) gives shortest paths in unweighted graphs; DFS (stack/recursion) classifies edges into tree, back, forward and cross edges, and a back edge means a cycle. Both run in O(V + E) with adjacency lists. MST: Kruskal is O(E log E), Prim with a binary heap is O((V+E) log V); if all edge weights are distinct the MST is unique, and an MST has V − 1 edges. Shortest paths: Dijkstra (no negative edges) is O((V+E) log V) with a binary heap; Bellman-Ford handles negative edges in O(VE) and detects negative cycles; Floyd-Warshall solves all pairs in O(V³).
Five GATE-Style Problems, Solved
Q1 (MCQ). Solve T(n) = 8T(n/2) + n².
Solution: nlog28 = n³, which dominates n² polynomially, so T(n) = Θ(n³).
Q2 (MCQ). Solve T(n) = 2T(n/2) + n.
Solution: nlog22 = n equals f(n), so T(n) = Θ(n log n).
Q3 (NAT). Length of the LCS of ABCBDAB and BDCABA?
Solution: Filling the DP table gives 4 (for example BCBA).
Q4 (NAT). A hash table of size 10 uses h(k) = k mod 10 with linear probing. Keys 12, 22, 32, 15 are inserted, then 13. At which index does 13 land?
Solution: 12→2, 22→3, 32→4, 15→5. Key 13 hashes to 3, then probes 4, 5 and lands at 6.
Q5 (NAT). Minimum comparisons to find both the maximum and minimum of 100 numbers?
Solution: ⌈3 × 100/2⌉ − 2 = 148.
Algorithms MSQs have no partial marks. Check yourself before GATE does.
The GATE CSE 2027 Test Series includes Algorithms subject-wise tests with recurrence, DP, hashing and graph questions in MCQ, MSQ and NAT format, plus detailed solutions.
Start practising for ₹499 →Common Mistakes to Avoid
Applying the Master theorem where it doesn’t fit (for example T(n) = 2T(n/2) + n/log n falls in the gap).
Running Dijkstra on negative edges.
Assuming quick sort is always O(n log n): sorted input with a first/last pivot gives O(n²).
Calling 0/1 knapsack DP polynomial: O(nW) is pseudo-polynomial.
Forgetting MST uniqueness conditions: equal weights can allow multiple MSTs with the same total weight.
4-Week Preparation Strategy
Week 1: Asymptotic notation, recurrences, loop analysis. Week 2: Sorting, searching and hashing. Week 3: Greedy, DP and divide-and-conquer with classic problems. Week 4: Graph algorithms, then 10 years of GATE CS PYQs and the Algorithms tests in the GATE CSE 2027 Test Series. Make sure Programming & Data Structures is done first.
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FAQs: GATE CSE 2027 Algorithms
How many marks does Algorithms carry in GATE CSE?
About 8 to 10 marks in recent GATE CS papers.
Is NP-completeness in the GATE CSE 2027 Algorithms syllabus?
No. The 2027 Algorithms syllabus does not list P, NP or NP-completeness; decidability is covered in Theory of Computation instead.
Which graph algorithms are most important?
Kruskal and Prim for MSTs, Dijkstra and Bellman-Ford for shortest paths, and BFS/DFS with their traversal-tree properties.
Which is the best test series for GATE CSE 2027?
The GATE CSE 2027 Test Series by Piyush Wairale (IIT Madras) on piyushwairale.com offers subject-wise and full-length mocks with MCQ, MSQ and NAT questions, detailed solutions and performance analysis for ₹499. See the test series.
Should I study Data Structures before Algorithms?
Yes. Heaps, trees and graph representations are prerequisites for sorting, Dijkstra, Prim and traversal algorithms.
GATE CSE 2027: All Subject-wise Guides
1. Engineering Mathematics · 2. Digital Logic · 3. Computer Organization & Architecture · 4. Programming & Data Structures · 5. Algorithms · 6. Theory of Computation · 7. Compiler Design · 8. Operating System · 9. Databases (DBMS) · 10. Computer Networks
Full paper overview: GATE CS 2027 Syllabus, Exam Pattern & Cutoff. Practise all ten subjects in one place with the GATE CSE 2027 Test Series.
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