1
GATE CSE 1990
Subjective
+2
-0
Express T(n) in terms of the harmonic number Hn = $$\sum\limits_{t = 1}^n {1/i,n \ge 1}$$ where T(n) satisfies the recurrence relation, T(n) = $${{n + 1} \over 2}$$ T(n-1) + 1, for $$n \ge 2$$ and T(1) = 1 What is the the asymptotic behavior of T(n) as a function of n?
2
GATE CSE 1990
+2
-0.6
Match the pairs in the following:

List - I

(a) Straseen's matrix multiplication algorithm
(b) Kruskal's minimum spanning tree algorithm
(c) Bioconnected components algorithm
(d) Floyd's shortest path algorithm

List - II

(p) Greedy method
(q) Dynamic programming
(r) Divide and Conquer
(s) Depth first search
A
a - r, b - p, c - s, d - q
B
a - r, b - p, c - q, d - s
C
a - r, b - s, c - p, d - q
D
a - q, b - p, c - s, d - r
3
GATE CSE 1990
+2
-0.6
Match the pairs in the following:

List - I

(a) Heap construction
(b) Constructing hash table witn linear probing
(c) AVL Tree construction
(d) Digital tree construction

List - II

(p) $$\Omega \left( {n\log _{10}^n} \right)$$
(q) O(n)
(r) O(n2)
(s) $$\Omega \left( {n\log _2^n} \right)$$
A
a - r, b - q, c - s, d - p
B
a - q, b - r, c - p, d - s
C
a - q, b - r, c - s, d - p
D
a - q, b - s, c - r, d - p
4
GATE CSE 1990
+1
-0.3
Match the following:

List - I

(a) Lexical Analysis
(b) Code Optimization
(c) Code Generation
(d) Abelian Group

List - II

(p) DAG's
(q) Syntax trees
(r) Push Down automata
(s) Finite automata
A
a - s, b - p, c - q, d - r
B
a - r, b - p, c - q, d - s
C
a - s, b - q, c - p, d - r
D
a - s, b - p, c - r, d - q
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