How to resolve the algorithm Averages/Median step by step in the Mathematica / Wolfram Language programming language

Published on 22 June 2024 08:30 PM
#Wolfram

How to resolve the algorithm Averages/Median step by step in the Mathematica / Wolfram Language programming language

Table of Contents

Problem Statement

Write a program to find the   median   value of a vector of floating-point numbers. The program need not handle the case where the vector is empty, but must handle the case where there are an even number of elements.   In that case, return the average of the two middle values. There are several approaches to this.   One is to sort the elements, and then pick the element(s) in the middle. Sorting would take at least   O(n logn).   Another approach would be to build a priority queue from the elements, and then extract half of the elements to get to the middle element(s).   This would also take   O(n logn).   The best solution is to use the   selection algorithm   to find the median in   O(n)   time. Quickselect_algorithm

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Averages/Median step by step in the Mathematica / Wolfram Language programming language

The provided Wolfram code defines two functions for calculating the median of a given list of numbers:

1. Wolfram Built-in Median Function:

  • The first expression calculates the median of the list {1, 5, 3, 2, 4} using Wolfram's built-in Median function, which returns the middle value when the list is sorted in ascending order. In this case, the median is 3.

  • The second expression calculates the median of the list {1, 5, 3, 6, 4, 2} using the Median function. This time, the median is 4.

2. Custom mymedian Function:

  • The mymedian function is a custom function defined using the Module construct. It takes a list x as input and returns the median.

  • Inside the function:

    • t is a sorted copy of the input list, obtained using Sort[x].
    • L is the length of the input list, obtained using Length[x].
    • There is a conditional statement using If.
      • If the length of the list (L) is even (divisible by 2), it calculates the median as the average of the two middle values (t[[L/2]] and t[[L/2+1]]) and divides it by 2.
      • If the length of the list is odd, it simply returns the middle value (t[[(L+1)/2]]).

  • The final two expressions demonstrate the usage of the mymedian function for the same two lists as the Median function. It returns the same result as the built-in function for both lists.

Source code in the wolfram programming language

Median[{1, 5, 3, 2, 4}]
Median[{1, 5, 3, 6, 4, 2}]


mymedian[x_List]:=Module[{t=Sort[x],L=Length[x]},
 If[Mod[L,2]==0,
  (t[[L/2]]+t[[L/2+1]])/2
 ,
  t[[(L+1)/2]]
 ]
]


mymedian[{1, 5, 3, 2, 4}]
mymedian[{1, 5, 3, 6, 4, 2}]

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