Express T(n) in terms of the harmonic number H_n = $$\sum\limits_{t = 1}^n {1/i,n \ge 1} $$ 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?

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

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) $$\Omega \left( {n\log _2^n} \right)$$

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