Analysis of Algorithms Class Problem Statement
Sort (in ascending order) the items in a file of size 2x KIB using limited memory.
Note that x is a unsigned integer where x > 0.
(a) Rules:
i. The file is located in disk (not in memory)
ii. Memory is limited to 2 input buffers and 1 output buffer (4KIB each) Total memory capacity 12 KIB
iii. Assume that the contents of the file are unsigned integers separated by a comma delimiter. (i. e 3,1,3,100,99...)
iv. The unsigned integers are not sorted
v. The file can contain duplicated integers
vi. When in a file, a digit from an integer is 1 byte (datatype is char). When in a buffer, an integer is 4 bytes (data type is integer).
vii. Pass number 0 can only use the output buffer. All the remaining passes can use all the available buffers in memory
viii. All the buffers in memory support ±4 bytes of additional memory allocation.
ix. The merging process must be done using Merge Sort algorithm.
x. Temporary files, in disk, can only hold a max size of ((#pass + 1) ∗ 4)KIB
(b) Input and Output
i. Input: A file containing unsorted unsigned integers in the range of 0 and 100 (both inclusive). For example: 100,67,99,99,1,1,3,24,88,96,37,10,1 0,88,100,99,99
ii. Output: A file containing the sorted integers from the input file. For example: 1,1,3,10,10,24,37,67,88,88,96,99,99 ,99,99,100,100
Describe the algorithm to solve the problem for a given file of size 2^5 and 2^x (any given x). Note that x is a unsigned integer where x > 0. You can use tables, diagrams, pics, paragraph description to describe the algorithm. Be as clear as possible, and define clearly each step taken during the process.