# Write a program to rearrange a given 'r * c' (r - rows, c - columns) matrix as follows:

# - each row is sorted in increasing order

# - each column is sorted in increasing order

#--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Requirements:

# You will perform the required sorted output of the matrix by two methods:

Method 1:

# Take all the 'r*c' elements in an array, sort it, then output row-wise (column-wise will also work!) as a 'r*c' matrix.

Method 2:

# Sort each row separately one-by-one.

# Then, sort each column separately one-by-one.

# Output this matrix.

Sorting Method:

# Use QuickSort.

# Your program must have the following functions clearly identified and implemented:

1. The Comparison functions (three functions) - to compare an element to another element:

# - EQ(a, b) : if (a == b) return true, else return false.

# - LT(a, b) : if (a < b) return true, else return false.

# - GT(a, b) : if (a > b) return true, else return false.

# Note that other operators (!=, >=, <=) can be computed by combining the NOT operator with the above three.

# Each of the above three functions must increment a [global] counter 'comparison_count' (this will be needed for output).

# Obviously, one of your goals is to minimize the total number of element comparisons.

# Absolutely no element comparisons outside these functions.

2. The Assignment function:

# - ASSIGN(a, b): assigns a = b, or, a <- b.

# This function must increment a [global] counter 'assignment_count' (this will be needed for output).

# Note that a swap can be done by calling the assignment function three times.

# Obviously, one of your goals is to minimize the total number of element assignments.

# Absolutely no element assignments outside this function.

3. The PARTITION function.

# The partitioning must be done In-Place.

# For element comparisons and element assignments, you must use the above functions.

# Integer comparisons (like i < n), assignments (like i = 0), or arithmetic (like i++), need not be counted and can be done directly.

# In addition, the Partition method written by you must make exactly:

# ( - 1) (i.e., (right - left) in the variables used in lecture notes)

# element comparisons per call, for the actual partitioning.

# Comparisons and Assignments you make for choosing a better pivot (like median of 3 elements) are extra (note that they should also be counted by 'comparison_count' and 'assignment_count').

The program should output the sorted matrix and output the total number of element comparisons and element assignments taken for each of the methods.

#--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

# # Specifications

# Program Compiles, Runs, Correct Output, No major issues, for both methods:

# EQ, GT, LT, and ASSIGN methods correctly

# PARTITION makes (right-left) comparisons

#----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------#

INPUT:

# You can assume the elements will be of type 'double'.

# Read the input matrix from a file named "input.txt".

# This file will have the matrix elements separated ONLY by "space" and "end of line (newline)" characters.

# The first line will have the number of rows and columns (separated by space).

# Thereafter, each line will contain the elements of a row (separated by space).

# You can assume each element value will be between 0.00 and 999.99 (rounded to two decimal places, so that you can format the output correctly).

# For example:

# 5 by 7 example

# 14 51.3 17 28.77 31 1 2

# 2 2 2 2 2.0 2 2

# 8 5 0.00 2 1 18.32 19

# 1 200.36 0 4 5.21 6.6 7

# 9 8 7 6.6 0.0 4 3

# Test your program with matrix of size ~ 100-by-100.

# No other characters will be present in the file.

# Note that your program must NOT take command line inputs.

OUTPUT(S):

# Your program will generate 2 output files:

# _1.txt:

# output the matrix for method 1 (keep same format as the input)

# output the total number of comparisons and assignments taken

# _2.txt:

# output the matrix for method 2 (keep same format as the input)

# output the total number of comparisons and assignments taken

#-------------------------------------------------------------------------------------------

write in python or c++