hard10 marks

Algorithms

Searching, sorting, hashing, asymptotic complexity, algorithm design techniques (greedy, dynamic programming, divide-and-conquer), graph traversals, MST, shortest paths.

11 Topics

45h prep

13.89% subject weight

11 Topics

Searching

Algorithms: linear search, binary search, ternary search.

1m1/10

📌 Key FormulaBinary search: O(log n) comparisons.

Sorting

Arranging elements in order: bubble, insertion, selection, merge, quick, heap, counting sort, radix sort.

2m3/10

📌 Key FormulaTime complexities: best, average, worst.

Hashing

Key to index mapping for O(1) average access.

1m2/10

📌 Key FormulaLoad factor = n/m. Collision resolution: chaining, open addressing.

Asymptotic worst case time and space complexity

Big-O, Omega, Theta notations; analysis of algorithms.

2m3/10

📌 Key FormulaO(1) < O(log n) < O(n) < O(n log n) < O(n^2) < O(2^n).

Algorithm design techniques

Brute force, divide & conquer, greedy, dynamic programming, backtracking, branch & bound.

1m3/10

📌 Key FormulaOptimal substructure for DP.

Greedy techniques

Make locally optimal choice at each step.

1m2/10

📌 Key FormulaFractional knapsack, Huffman coding, Dijkstra's (greedy).

Gynamic programming techniques

DP solves problems by breaking into overlapping subproblems and storing results.

1m4/10

📌 Key FormulaRecurrence for LCS, knapsack, matrix chain.

Divide-and-conquer

Divide problem into subproblems, solve recursively, combine.

1m2/10

📌 Key FormulaMaster theorem: T(n) = aT(n/b) + f(n).

Graph traversals

BFS (queue) and DFS (stack/recursion).

1m2/10

📌 Key FormulaBFS shortest path in unweighted graph.

Minimum spanning trees

Tree connecting all vertices with minimum total weight.

1m2/10

📌 Key FormulaKruskal: sort edges, union-find. Prim: priority queue.

Shortest paths

Algorithms: Dijkstra (non-negative weights), Bellman-Ford (negative allowed), Floyd-Warshall (all pairs).

1m3/10

📌 Key FormulaDijkstra: O(E log V) with heap. Bellman-Ford: O(VE).

hard10 marks

Algorithms

Searching, sorting, hashing, asymptotic complexity, algorithm design techniques (greedy, dynamic programming, divide-and-conquer), graph traversals, MST, shortest paths.

11 Topics

45h prep

13.89% subject weight

11 Topics

Searching

Algorithms: linear search, binary search, ternary search.

1m1/10

📌 Key FormulaBinary search: O(log n) comparisons.

Sorting

Arranging elements in order: bubble, insertion, selection, merge, quick, heap, counting sort, radix sort.

2m3/10

📌 Key FormulaTime complexities: best, average, worst.

Hashing

Key to index mapping for O(1) average access.

1m2/10

📌 Key FormulaLoad factor = n/m. Collision resolution: chaining, open addressing.

Asymptotic worst case time and space complexity

Big-O, Omega, Theta notations; analysis of algorithms.

2m3/10

📌 Key FormulaO(1) < O(log n) < O(n) < O(n log n) < O(n^2) < O(2^n).

Algorithm design techniques

Brute force, divide & conquer, greedy, dynamic programming, backtracking, branch & bound.

1m3/10

📌 Key FormulaOptimal substructure for DP.

Greedy techniques

Make locally optimal choice at each step.

1m2/10

📌 Key FormulaFractional knapsack, Huffman coding, Dijkstra's (greedy).

Gynamic programming techniques

DP solves problems by breaking into overlapping subproblems and storing results.

1m4/10

📌 Key FormulaRecurrence for LCS, knapsack, matrix chain.

Divide-and-conquer

Divide problem into subproblems, solve recursively, combine.

1m2/10

📌 Key FormulaMaster theorem: T(n) = aT(n/b) + f(n).

Graph traversals

BFS (queue) and DFS (stack/recursion).

1m2/10

📌 Key FormulaBFS shortest path in unweighted graph.

Minimum spanning trees

Tree connecting all vertices with minimum total weight.

1m2/10

📌 Key FormulaKruskal: sort edges, union-find. Prim: priority queue.

Shortest paths

Algorithms: Dijkstra (non-negative weights), Bellman-Ford (negative allowed), Floyd-Warshall (all pairs).

1m3/10

📌 Key FormulaDijkstra: O(E log V) with heap. Bellman-Ford: O(VE).