Problem description: solve the following problems:

$1.$ generate a histogram of $20,000$ randomly generated integer numbers according to a normal distribution with a user$-$specified mean and standard deviation.

$2.$ generate a histogram of $20,000$ randomly generated floating$-$point numbers according to a uniform distribution with a user$-$specified range.

$3.$ implement an almost generic randomized$-$QuickSort algorithm to sort an array of TokenFreq objects by a given sorting criterion. To realize this, you will use

function templates

function objects, Lambda expressions, or a pointer to functions

$4.$ implement an almost generic algorithm $($the randomized version$)$ to find the k$-$th ranked object in an array without first sorting this array. Same as above, you will use. function templates and function objects.

Deliverables:

Please follow the problem solving process and submit the following steps in one document :

A design$-$doc that describes the problem$-$solving process for all the above problems. For each problem, include the following aspects:

input and output of the problem

your algorithm in pseudo code with comments

worst$-$case time complexity analysis

your choice of data structures with a brief justification in the final coding stage $($e$.$g$.,"$We declared a user$-$defined struct for $...$ because $...")$

Your program files. You are required to solve all the problems in one CPP project, similar to what we did in Coding Lab $3.$

A header file:

the function prototype to generate x uniformly distributed random numbers

the function prototype to generate x random numbers following a specified normal distribution

the function prototype to calculate the underlying data of a histogram, given a collection of numbers

the function prototype to print out a histogram using a user$-$specified symbol $($e$.$g$.,*)$

the function prototype of the partition subroutine that's shared by the quickSort and k$-$th ranked object algorithms

the function prototype of the almost generic quicksort algorithm

the function prototype of the almost generic k$-$th ranked algorithm

your CPP file with comments

define the above functions

a header file consisting of your unit tests:

at least two unit tests per function

a separate cpp file containing the main$()$ function