Advanced Algorithm (March-2023)

Maulana Azad National Urdu University M.Tech I Semester Examination, March 2023 Paper - MTCS111PCT : Advanced Algorithm

6 , p :

Time : 3 hrs Marks : 70

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(10 x 1 = 10 Marks)

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(5 x 6 = 30 Marks)

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(3 x 10 = 30 Marks)

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(1)

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Best-case Time Complexity

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^{Quick Sort (i)}

O (nlogn) (d) O (n) (c) O(logn) (b) O(n²) (a)

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^Method

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Prim's Algorithm (ii) Dynamic Programming (d) Greedy (c) Branch and Bond (b) Divide and Conquer (a)

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^Solve

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Dynamic Programming

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^Problems

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Binary Search (b) Merge Sort (a)

Quck Sort (d) Longest Common Subsequence (c)

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Elementary Number Theoritical Notation

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Rabin-Karp Algorithm (iv)

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^PRAM

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Parallel Computing (v)

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^(d) Pre-RAM (c) Processing RAM (b) Parallel RAM (a)

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Master's Theorem (vi)

Solving Iterative Relations (b) Solving Recurrency(a) Calculating time complexity of any code (d) Analysis Loops (c)

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Worst Case Complexity

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KMP Algorithm (vii)

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^(d) O (n+m) (c) O(nm) (b) O(n) (a)

1/3

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^Arrays

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^Implement

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Boyer-Moore Algorithm

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^Text

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^{Pattern (viii)}

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^{(d) 3 (c) 2 (b) 1 (a)}

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^Solutions

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^Problems

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Bellman Ford Algorithm (ix)

Sorting (b) All Pur Shortest path (a)

Network Flow (d) Single Source Shortest Path (c)

Comparision

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^Sort

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Array arr{1, 5, 6, 8, 2}

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Counting Sort (x)

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0 (d) 9 (c) 7 (b) 5 (a)

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^{Worst Case}

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Averge Case, Best Case

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^Array

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Cocktail Sort (2)

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Time Complexity

5 1 4 2 8 0 7 6

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^Match

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^{Valid Hits}

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Spurious Hits

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Rabin-karp Algorithm (3)

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^Pattern

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^Text

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q=11 "string matching modula' Text = T = < 3 1 4 1 5 9 2 6 5 3 5 8 9 7 9 3>

Pattern = P = < 2 6>

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Master's Method (4)

Recurrence :

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Order of Paranthesization

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Optimal Chain Multiplication

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^Matrices

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NP Complete

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P, NP, NP-hard (6)

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=

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

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Cook's Theorem (7)

Longest Common

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Input Strings

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X=<a,a,ab,a,b>

g Zz

Y=<b,a,a,b,>,

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Susbsequence

Time Complexity

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^{Worst Case}

g Zz

Average Case, Best Case

» k gZ Zz K

^Algorithm

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^{Quick-sort (9)}

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X

^Sort

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^Data

‰ b Š n X N C

42 34 75 23 21 18 90 67 78

2/3

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X

Johnson's All Pair Shortest Path

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^Graph

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Johnson's Algorithms (10)

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B ‚

Parallel Merge Sorting Algorithm

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(Best) Sorting Algorithm

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^{Parallel (11)}

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Best Complements

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Step-by-Step

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Knuth-Moris Pratt Algorithm (12)

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Spanning Tree

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Minimum cost

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^Graph

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Krushkal's Algorithm (a) (13)

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^Problem

q - Z Ã

^{PRAM Model (b)}

Shortest Path

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^Graph

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Dijkstra Algorithm

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^Algorithm

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Bellman's Ford (14)

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/ /

2/3 /