#!/usr/bin/perl -w
# turn on strict forcing definition of variables and subs/functions
  use strict;
#
# Declare Function/Sub Routines
sub Mean ; #Given input array return the mean, that is sum of
# elements divided by number of elements.
#
sub Median ; #Given input array return the Median, that is the value
# which has 50 percent of the elements above and 50 percent below.
#
sub Mode; #Given input array return the value that occurs most
# frequently or return NONE if no duplicates.
#
sub Sample_standard_dev; #Given Input of Mean and Sum_of the differences of the 
# Mean Squared, return the Sample Standard Deviation.
# Sample Standard Deviation = SQRT( (Sum_of( X - Mean)**2) / (N - 1) )
# Note, divide by N - 1 for the Bessel Correction for a finite sample.
#
sub Sum_of; #Given an input Array and the Mean, calculate the total 
# sum of (X - Mean)**2 for each value in the Array. 
# This returns the Total value of the difference of the Squares.
#
#Sub Routine / Function Section
sub Mean # Returns  Arithmetic mean sum of Elements/num of elements
         # Input is an array
 {
  my $Mean_value = 0;
  my $knum = 0; #Number of elements in Array.
  my $j = 0;  #iteration loop scalar counter
  my $result = 0 ;     # initialize sum for array 
  my  @input_array = @_;
  $knum = scalar@input_array; #Get number of elements  in array.  
  if ( $knum < 2 ){
      printf " Must have an input array with at least two elements ";
      exit;
    }
  # Note we must subtract -1 from $knum so we do not go past the 
  # end of the search array. 
     for ( $j = 0; $j <= ($knum -1 ); $j++)
     {
     $result +=   $input_array[$j];
     }
     $Mean_value = $result/$knum ;
     $Mean_value = sprintf ("%.2f", $Mean_value) ; # Trim of the floating point stuff after two decimal points.
     return $Mean_value; # 
 }  # End sub Mean
#
sub Sum_of # Returns a Value for the sum of the mean squared differences
# Input is a Mean Value followed by an Array.

{
  my $knum = 0; #Number of elements in Array.
  my $j = 0;  #iteration loop scalar counter
  my $result = 0 ;     # initialize sum of mean squared differences 
                       # for array 
  my $sum_squared_diff = 0;
  my  ($Average, @input_ar  ) = @_ ;
  $knum = scalar@input_ar; #Get number of elements  in array.  
  if ( $knum < 2)  {
      printf " Must have an input array with at least two elements ";
      exit;
    }
  # Note we must subtract -1 from $knum so we do not go past the 
  # end of the search array. 
     for ( $j = 0; $j <= ($knum -1 ); $j++)
     {
     $result +=   ($input_ar[$j] - $Average ) **2;
     }
     $sum_squared_diff = $result; 
     return $sum_squared_diff;  

} # End sub Sum_of
#
sub Sample_standard_dev
{
my $result = 0;
my $Sample_dev  = 0;
my ($Sum_squared_diff, $num_of_elements ) = @_  ; # Input Sum Squared differences
                                                  # Number of elements in Array
if ($num_of_elements < 2 ) {
   printf "Array must have at least two elements, exiting now! \n";
   exit;
   }
$result = sqrt ($Sum_squared_diff / ($num_of_elements - 1 ) );
$result = sprintf ("%.2f", $result) ; # Trim of the floating point stuff after two decimal points.
return $Sample_dev = $result;

} # End Sample_standard_dev
#
#
sub Median
{
  my @array_in = @_;
  my @sorted_array = ();
  my $knum = 0; #Number of elements in Array.
  my $median = 0;
  my $j = 0;  #iteration loop scalar counter
  my $result = 0 ;     # initialize median element
  @sorted_array  = sort { $a <=> $b } @array_in ;  # numerical sort
  # force numeric sort here, note $a and $b or special variables and do not have to initialized!
  printf " This is the Sorted Array:   @sorted_array \n";
  $knum = scalar@sorted_array; #Get number of elements  in array.  
  if ( $knum < 2)  {
      printf " Must have an input array with at least two elements ";
      exit;
    }
     $knum-- ; # Decrement it because otherwise we go beyond the array
     # remember $knum = 0 is first element;
     $j = int (($knum/2) + 0.5); #Force rounding up of index with int function
     $result =   $sorted_array[$j]  ;
     $median = $result; 
     return $median ;  

} # End Sub Median
#
sub Mode 
#Input is an Array
# This will  print out as part of calling the Function the 
# Mode (Key Value pair) , stating the value which occurs and 
# and its frequency.
{
#   Storage initialization
    my $do_while = "TRUE";
    my $freq = "999";
    my $store_freq = "999";             
    my @values = ();
    my $result = "NADA";
    my $j = 0;  # number of value key pairs in Hash list
    my @Max_mode_values; # used to store mode values that occur more than once
    my @array = @_ ;
    my $num_of_hash_pairs = scalar@array;
    my %hash_count = qw ( ) ;
    # Previous intializes the hash list, which will be a value , followed by
    # the number of occurences.
    my $key_val = "NONE"; # Assume nothing will be found for now.
#   Note, $a and $b are special Perl variables, used in 
#   sorting hashes so we do not have to define them!
    
    # we store the values and their frequency in a hash
    map{ $hash_count{$_}++ } @array;
    # sort the hash by values
    # Using the special variables $a and $b built in , compare with the
    # <=> (numerical compare operator) any two consecutive values in the 
    # hash list sorting ascending, it would $b and $a if you were doing
    # descending...
    # and sort them, you keep doing this to generate a sorted hash list.
    # Don't worry about the details, Perl takes care of it for you.
    #
    for $key_val ( sort {$hash_count{$a} <=> $hash_count{$b}} keys %hash_count )    {
        
        if ($hash_count{$key_val} > int(1) ) {
#                push @AoH, { husband => "fred", wife => "wilma", daughter => "pebbles" };
        push ( @Max_mode_values,   "$key_val ,  $hash_count{$key_val}" ) ;
        $j++ ;# To get a count of how many values you pushed into push array 
#        push ( @Max_mode_values,  " $key_val occurs $hash_count{$key_val} times \n" ) ;
        }
    } 
#    printf " @Max_mode_values \n";
#    uncomment previous to prove algorithm works, to print all modes.
   # Do first pop , this will always be done!
        $result = pop (@Max_mode_values);
        @values = split(',', $result);
        $freq  = $values[1];
#        printf " This is the frequency:  $freq \n";
        printf " $values[0] occurs $freq times \n";
        $store_freq = $freq; # save frequency
   
    while ($do_while eq "TRUE")
   {
        $result = pop (@Max_mode_values);
        @values = split(',', $result);
        $freq  = $values[1];
        if ($store_freq !=  $freq) {
            $do_while = "FALSE";
            next  ;     # This will terminate the while loop!
        }
        # otherwise we still have more frequencies to print that are at
        # the maximum value.
#        printf " This is the frequency:  $freq \n";
        printf " $values[0] occurs $freq times \n";
#        printf " This is store_freq: $store_freq and this is frequency: $freq \n";
        $store_freq = $freq; # store the frequency we just got and printed.
        }
     return; # break out of called routine for safety, you should never get
     # here;
    
}
# End Sub Mode 
#
# Main Section
# my @input_array_values = ( 1, 2, 5, 9, 2, 8, 3);
# Use a randomly generated array
    my $i = 0; # array index 0.. $array_num_of_elements - 1
    my $range = 100; # This says what  will be the maximum value we can get
    my $min_value = 1; # similarly this is the minimum value we can get
    my $array_num_of_elements = 300;
    my @random_number = ();
    for ($i = 0; $i < $array_num_of_elements  ; $i++)
    {
#    Note, rand will return 0 so we add a 1 to it to force it to
#    be that minimum value.
     $random_number[$i] = int( $min_value + rand($range));
    }
my @input_array_values = @random_number;
my $num_of_array_elements = scalar@input_array_values ;
my $Mean_is = 0;
my $Median_is = 0;
my $Sum_squared_diff_is = 0;
my $Sample_dev = 0;
printf "\n Note, all calculations are done to two decimal places.   \n" ;
printf "\n This is the orginal array:  @input_array_values  \n" ;
$Mean_is  = Mean( @input_array_values);
$Median_is = Median( @input_array_values) ; 
printf " The mean is $Mean_is  and the Median is $Median_is  \n";
printf " The Greatest Mode Values are:   \n";
Mode(@input_array_values);
# Previous will return the Mode saying what it is and how many times
# it occurs.
$Sum_squared_diff_is  = Sum_of($Mean_is, @input_array_values   );
printf " \n The Sum Squared differences value is:  $Sum_squared_diff_is \n" ;
$Sample_dev = Sample_standard_dev( $Sum_squared_diff_is, $num_of_array_elements);
printf " The Sample Standard Deviations is:  $Sample_dev \n" ;
exit;