How to resolve the algorithm Quickselect algorithm step by step in the Fortran programming language

Published on 12 May 2024 09:40 PM

How to resolve the algorithm Quickselect algorithm step by step in the Fortran programming language

Table of Contents

Problem Statement

Use the quickselect algorithm on the vector To show the first, second, third, ... up to the tenth largest member of the vector, in order, here on this page.

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Quickselect algorithm step by step in the Fortran programming language

Source code in the fortran programming language

      INTEGER FUNCTION FINDELEMENT(K,A,N)	!I know I can.
Chase an order statistic: FindElement(N/2,A,N) leads to the median, with some odd/even caution.
Careful! The array is shuffled: for i < K, A(i) <= A(K); for i > K, A(i) >= A(K).
Charles Anthony Richard Hoare devised this method, as related to his famous QuickSort.
       INTEGER K,N		!Find the K'th element in order of an array of N elements, not necessarily in order.
       INTEGER A(N),HOPE,PESTY	!The array, and like associates.
       INTEGER L,R,L2,R2	!Fingers.
        L = 1			!Here we go.
        R = N			!The bounds of the work area within which the K'th element lurks.
        DO WHILE (L .LT. R)	!So, keep going until it is clamped.
          HOPE = A(K)		!If array A is sorted, this will be rewarded.
          L2 = L		!But it probably isn't sorted.
          R2 = R		!So prepare a scan.
          DO WHILE (L2 .LE. R2)	!Keep squeezing until the inner teeth meet.
            DO WHILE (A(L2) .LT. HOPE)	!Pass elements less than HOPE.
              L2 = L2 + 1		!Note that at least element A(K) equals HOPE.
            END DO			!Raising the lower jaw.
            DO WHILE (HOPE .LT. A(R2))	!Elements higher than HOPE
              R2 = R2 - 1		!Are in the desired place.
            END DO			!And so we speed past them.
            IF (L2 - R2) 1,2,3	!How have the teeth paused?
    1       PESTY = A(L2)		!On grit. A(L2) > HOPE and A(R2) < HOPE.
            A(L2) = A(R2)		!So swap the two troublemakers.
            A(R2) = PESTY		!To be as if they had been in the desired order all along.
    2       L2 = L2 + 1		!Advance my teeth.
            R2 = R2 - 1		!As if they hadn't paused on this pest.
    3     END DO		!And resume the squeeze, hopefully closing in K.
          IF (R2 .LT. K) L = L2	!The end point gives the order position of value HOPE.
          IF (K .LT. L2) R = R2	!But we want the value of order position K.
        END DO			!Have my teeth met yet?
        FINDELEMENT = A(K)	!Yes. A(K) now has the K'th element in order.
      END FUNCTION FINDELEMENT	!Remember! Array A has likely had some elements moved!

      PROGRAM POKE
      INTEGER FINDELEMENT	!Not the default type for F.
      INTEGER N			!The number of elements.
      PARAMETER (N = 10)	!Fixed for the test problem.
      INTEGER A(66)		!An array of integers.
      DATA A(1:N)/9, 8, 7, 6, 5, 0, 1, 2, 3, 4/	!The specified values.

      WRITE (6,1) A(1:N)	!Announce, and add a heading.
    1 FORMAT ("Selection of the i'th element in order from an array.",/
     1 "The array need not be in order, and may be reordered.",/
     2 "  i Val:Array elements...",/,8X,666I2)

      DO I = 1,N	!One by one,
        WRITE (6,2) I,FINDELEMENT(I,A,N),A(1:N)	!Request the i'th element.
    2   FORMAT (I3,I4,":",666I2)	!Match FORMAT 1.
      END DO		!On to the next trial.

      END	!That was easy.


  

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