By Piyush Wairale (M.Tech, IIT Madras) · Former Instructor, IIT Madras BS Degree Programme · Mentor to 20,000+ GATE aspirants · Updated November 2026

GATE CSE Algorithms Syllabus 2027 (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 (GATE CSE Algorithms)

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 n^log_ba. If f is polynomially smaller, T = Θ(n^log_ba); if equal, T = Θ(n^log_ba 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

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(n^2.81)), 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 (GATE CSE Algorithms)

Q1 (MCQ). Solve T(n) = 8T(n/2) + n².
Solution: n^log₂8 = n³, which dominates n² polynomially, so T(n) = Θ(n³).

Q2 (MCQ). Solve T(n) = 2T(n/2) + n.
Solution: n^log₂2 = 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.

Common Mistakes to Avoid (GATE CSE Algorithms)

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 (GATE CSE Algorithms)

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.

FAQs: GATE CSE Algorithms 2027

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

That completes this GATE CSE Algorithms guide. Full paper overview: GATE CS 2027 Syllabus, Exam Pattern & Cutoff. Practise all ten subjects in one place with the GATE CSE 2027 Test Series.