How to resolve the algorithm Hamming numbers step by step in the Fortran programming language

Published on 12 May 2024 09:40 PM
#Fortran

How to resolve the algorithm Hamming numbers step by step in the Fortran programming language

Table of Contents

Problem Statement

Hamming numbers are numbers of the form   Hamming numbers   are also known as   ugly numbers   and also   5-smooth numbers   (numbers whose prime divisors are less or equal to 5).

Generate the sequence of Hamming numbers, in increasing order.   In particular:

Let's start with the solution:

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

Source code in the fortran programming language

program Hamming_Test
  use big_integer_module
  implicit none
  
  call Hamming(1,20)
  write(*,*)
  call Hamming(1691)
  write(*,*)
  call Hamming(1000000)
   
contains

subroutine Hamming(first, last)

  integer, intent(in) :: first
  integer, intent(in), optional :: last
  integer :: i, n, i2, i3, i5, lim
  type(big_integer), allocatable :: hnums(:)

  if(present(last)) then
    lim = last
  else
    lim = first
  end if

  if(first < 1 .or. lim > 2500000 ) then
    write(*,*) "Invalid input"
    return
  end if
  
  allocate(hnums(lim))
  
  i2 = 1 ;  i3 = 1 ; i5 = 1  
  hnums(1) = 1
  n = 1
  do while(n < lim)
    n = n + 1
    hnums(n) = mini(2*hnums(i2), 3*hnums(i3), 5*hnums(i5))
    if(2*hnums(i2) == hnums(n)) i2 = i2 + 1
    if(3*hnums(i3) == hnums(n)) i3 = i3 + 1
    if(5*hnums(i5) == hnums(n)) i5 = i5 + 1
  end do
  
  if(present(last)) then
    do i = first, last
      call print_big(hnums(i))
      write(*, "(a)", advance="no") " "
    end do
  else
    call print_big(hnums(first))
  end if
  
  deallocate(hnums)
end subroutine
 
function mini(a, b, c)
  type(big_integer) :: mini
  type(big_integer), intent(in) :: a, b, c
   
  if(a < b ) then 
    if(a < c) then
      mini = a
    else
      mini = c
    end if
  else if(b < c) then
    mini = b
  else
    mini = c
  end if 
end function mini 
end program

You may also check:How to resolve the algorithm Arithmetic/Integer step by step in the Nanoquery programming language
You may also check:How to resolve the algorithm Formatted numeric output step by step in the Arturo programming language
You may also check:How to resolve the algorithm 4-rings or 4-squares puzzle step by step in the Ada programming language
You may also check:How to resolve the algorithm Averages/Mode step by step in the Tcl programming language
You may also check:How to resolve the algorithm Josephus problem step by step in the Clojure programming language