Factoring

a. Convert (11101)2 to base 16. b. Use the Euclidean algorithm to find gcd(34,21).

I need help, with the Big O

Attached

Big-Oh

Use the definition of the big-oh to prove that ... (see attachment)

Graphs and Their Representations

If all the nodes of a simple, connected, planar graph have degree 4 and the number of arcs is 12, into how many regions does it divide the plane?

Graphs and Their Representations

Describe the adjacency matrix for Kn, the simple complete graph with n nodes.

Trees and Their Representations

Write in prefix and infix notation: x 2 w + yz * -1

Directed Graphs

Given the adjacency relation p = {(1,4), (1,5) (1,6), (6,2), (6,3), (6,5)} on the set N ={1,2,3,4,5,6}, find the corresponding directed graph and adjacency matrix.

Big-oh

A.Use the definition of big-oh to prove that (3n-8-4n^3)/(2n-1)is O(n^2) B.Use the definition of big-oh to prove that 1 • 2 + 2 • 3 + 3 • 4 + ... + (n - 1) • n is O(n^3).

Directed Graphs & Binary Relations

Find products A^2 & A^(2) A= [ 1 1 0 1 0 0 1 0 1 0 0 1 1 0 1 0 ]

Directed Graphs & Binary Relations

A = [ 0 0 0 0 0 1 0 0 0 1 0 1 0 1 0 0 1 0 0 0 0 0 0 1 0 ] Compute the reachability matrix R by using washall's algorithm and also by using the formula R = A V A(2) V... V A(n)