GATE Engineering - Computer Science & Information Technology (CS/IT)

Asymptotic Analysis, Trees, Graphs, Automata & Turing Machines question bank (Algorithms, Data Structures & Theory of Computation)

Practice 48 free GATE Engineering - Computer Science & Information Technology (CS/IT) Algorithms, Data Structures & Theory of Computation - Asymptotic Analysis, Trees, Graphs, Automata & Turing Machines questions with answers and step-by-step solutions.

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Q1.

Computer Networks (Subnetting): An organization is allocated the network block 192.168.10.0/24 in 'Asymptotic Analysis: Big-O, Omega, Theta, Recurrence Relations and Master Theorem'. If it requires 4 equal subnets, what is the subnet mask and maximum usable host count per subnet?

(A)

Subnet Mask: 255.255.255.192 (/26); 62 usable hosts per subnet ($2^6 - 2 = 62$) (Asymptotic Analysis: Big-O, Omega, Theta, Recurrence Relations and Master Theorem)

(B)

Mask: 255.255.255.128 (/25); 126 usable hosts

(C)

Mask: 255.255.255.224 (/27); 30 usable hosts

(D)

Mask: 255.255.255.240 (/28); 14 usable hosts

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Q2.

Algorithms (Graph Theory): What is the tightest worst-case time complexity of finding Single-Source Shortest Paths in a directed graph with $V$ vertices, $E$ edges, and NON-NEGATIVE weights using a Fibonacci Heap in 'Asymptotic Analysis: Big-O, Omega, Theta, Recurrence Relations and Master Theorem'?

(A)

$O(V \log V + E)$ (Asymptotic Analysis: Big-O, Omega, Theta, Recurrence Relations and Master Theorem)

(B)

$O((V + E) \log V)$

(C)

$O(V^2)$

(D)

$O(V E)$

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