How to resolve the algorithm Humble numbers step by step in the Action! programming language

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

How to resolve the algorithm Humble numbers step by step in the Action! programming language

Table of Contents

Problem Statement

Humble numbers are positive integers which have   no   prime factors   >   7.

Humble numbers are also called   7-smooth numbers,   and sometimes called   highly composite, although this conflicts with another meaning of   highly composite numbers.

Another way to express the above is:

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Humble numbers step by step in the Action! programming language

Source code in the action! programming language

;;; Find some humble numbers - numbers with no prime factors above 7

PROC humbleStat( CARD s, d ) ;;; displays a statistic about humble numbers
  Print( "There are " )
  IF s <  10 THEN Put(' ) FI
  IF s < 100 THEN Put(' ) FI
  PrintC( s )Print( " humble numbers with " )PrintC( d )Print( " digit" )
  IF d > 1 THEN Put('s) FI
  PutE()
RETURN

PROC Main() ;;; find and print humble numbers

  DEFINE MAX_HUMBLE = "400"

  CARD ARRAY H( MAX_HUMBLE )
  CARD h1, h2, h3, h4, h5, h6, hPos, m
  CARD p2, p3, p5, p7
  CARD last2, last3, last5, last7

  ; 1 is the first humble number
  H( 0 ) = 1
  h1    = 0 h2    = 0 h3    = 0 h4    = 0 h5 = 0 h6 = 0
  last2 = 0 last3 = 0 last5 = 0 last7 = 0
  p2    = 2 p3    = 3 p5    = 5 p7    = 7

  FOR hPos = 1 TO MAX_HUMBLE - 1 DO
    ; the next humble number is the lowest of the
    ; next multiples of 2, 3, 5, 7
    IF p2 < p3 THEN m = p2 ELSE m = p3 FI
    IF p5 < m  THEN m = p5 FI
    IF p7 < m  THEN m = p7 FI
    H( hPos ) = m
    IF m = p2 THEN last2 = last2 + 1  p2 = 2 * H( last2 ) FI
    IF m = p3 THEN last3 = last3 + 1  p3 = 3 * H( last3 ) FI
    IF m = p5 THEN last5 = last5 + 1  p5 = 5 * H( last5 ) FI
    IF m = p7 THEN last7 = last7 + 1  p7 = 7 * H( last7 ) FI
  OD

  FOR hPos = 0 TO 49 DO
    Put(' )PrintC( H( hPos ) )
  OD
  PutE()

  FOR hPos = 0 TO MAX_HUMBLE - 1 DO
    m = H( hPos )
    IF     m <    10 THEN h1 = h1 + 1
    ELSEIF m <   100 THEN h2 = h2 + 1
    ELSEIF m <  1000 THEN h3 = h3 + 1
    ELSEIF m < 10000 THEN h4 = h4 + 1
    FI
  OD

  humbleStat( h1, 1 )
  humbleStat( h2, 2 )
  humbleStat( h3, 3 )
  humbleStat( h4, 4 )

RETURN

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