How to resolve the algorithm Averages/Median step by step in the Action! programming language

Published on 12 May 2024 09:40 PM
#Action!

How to resolve the algorithm Averages/Median step by step in the Action! 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 Action! programming language

Source code in the action! programming language

INCLUDE "H6:REALMATH.ACT"

DEFINE PTR="CARD"

PROC Sort(PTR ARRAY a INT count)
  INT i,j,minpos
  REAL POINTER tmp

  FOR i=0 TO count-2
  DO
    minpos=i
    FOR j=i+1 TO count-1
    DO
      IF RealGreaterOrEqual(a(minpos),a(j)) THEN
        minpos=j
      FI
    OD
    
    IF minpos#i THEN
      tmp=a(i)
      a(i)=a(minpos)
      a(minpos)=tmp
    FI
  OD
RETURN

PROC Median(PTR ARRAY a INT count REAL POINTER res)
  IF count=0 THEN Break() FI
  Sort(a,count)
  IF (count&1)=0 THEN
    RealAdd(a(count RSH 1-1),a(count RSH 1),res)
    RealMult(res,half,res)
  ELSE
    RealAssign(a(count RSH 1),res)
  FI
RETURN

PROC Test(PTR ARRAY a INT count)
  INT i
  REAL res

  FOR i=0 TO count-1
  DO
    PrintR(a(i)) Put(32)
  OD
  Median(a,count,res)
  Print("-> ")
  PrintRE(res)
RETURN

PROC Main()
  PTR ARRAY a(8)
  REAL r1,r2,r3,r4,r5,r6,r7,r8
  BYTE i
  
  Put(125) PutE() ;clear the screen
  MathInit()
  ValR("3.2",r1)  ValR("-4.1",r2)
  ValR("0.6",r3)  ValR("9.8",r4)
  ValR("5.1",r5)  ValR("-1.4",r6)
  ValR("0.3",r7) ValR("2.2",r8)
  FOR i=1 TO 8
  DO
    a(0)=r1 a(1)=r2 a(2)=r3 a(3)=r4
    a(4)=r5 a(5)=r6 a(6)=r7 a(7)=r8
    Test(a,i)
  OD
RETURN

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