See attached file.
Here are some recurrence relations that come up in the analysis of Quicksort and or Select. For each recurrence, write one sentence explaining how it relates to Quicksort or Select and give its asymptotic growth rate in notation.
A. T(n) = T(n/10) + T(9n/10) + n
B. T(n) = T(n-1) + n
C. T(n) = T(n

A sorting algorithm is stable if two data items having the same value are not rearranged with respect to each other at any stage of the algorithm. For instance, in the five-element vector
55 12 33
a stable sorting algorithm guarantees that the final ordering is
12 33 55
classify each of the algorithms a

The following recurrence equation gives the expected number of comparisons for Quicksort, given that the "pivot element" is selected uniformly at random from the list:
T(n) = (n - 1) + (1/n)* SUM[i=0,n-1](T(i) + T(n-1-i)), T(0) = 0.
(a) Let S(n) = SUM[i=0,n-1](T(i) + T(n-1-i)). Give Dual recurrence equations expressing T(

Use the quicksort algorithm to sort vector v. During each pass, list all exchanges of a pair of elements in the lower and upper sublist. List the ordering of the elements after each pass.
int arr[] = {790, 175, 284, 581, 374, 799, 852, 685, 486, 333};
int arrSize = sizeof(arr)/sizeof(int);
vectorv(arr, arr+arrSize);

Describe the worst case scenario for quick sort algorithm. Any ideas to improve the worst case? Comment on the improvement in running time vs. increase in code complexity.

We have considered the following sorting algorithms in this book:
Heap, Insertion, Merge, Quicksort, Radix, Selection
For each sort, give the average and worst case running time and the space requirements, and make some additional comments about the efficiency of the algorithm. The additional comments may specify how proba

Please see attached file for full problem description.
The revenue derived from the production of x units of a particular commodity is million dollars. What level of production results in maximum revenue? What is the maximum revenue?
a. a. Maximum at x = 8 and maximum revenue is R(8) = 32 (million dollars)
b. b. Maxi

Sometimes a slight change in a problem can significantly alter the form of its solution. For example, find a simple algorithm for solving the following problem and classify it using big-theta notation:
Divide a group of people into two disjoint subgroups (of arbitrary size) such that the difference in the total ages of the m