Programming made easy – loops (ii)

With the basics of for loops, let’s look at an example of an actual program which calculates the Harmonic series, which is an infinite series of the form:

h(n) = 1 + 1/2 + 1/3 + … + 1/n

The code for the program in Fortran, Ada, Julia and C is shown below. The loop is highlighted in blue.  For interest sake, the loops are presented in reverse, i.e. 1/n + 1/(n-1) + … + 1, as it illustrates clearly how each language deals with the simple issue of a decreasing index. In each case the starting value of the index variable i is n, and the ending value is 1. Here it is the algorithm for the Harmonic series depicted visually, clearly showing the role of the loop:

Fortran

program harmonic
   integer :: n, i
   real :: h

   read (*,*) n
   h = 0
   do i = n,1,-1
      h = h + 1.0/i
   end do
   write(*,*) h
end program harmonic

Here the third item (the modifier) in the Fortran loop denotes the type of change to the loop index, in this case, a decrease by 1. In a  normal loop incrementing by 1, the modifier can be omitted.

C

#include <stdio.h>

int main(void){
   int i, n;
   float h;

   scanf("%d", &n);
   printf("%d\n", n);
   h = 0.0;
   for (i=n; i>=1; i=i-1)
      h = h + 1.0/i;
   printf("%lf\n", h);
   return 0;
}

In the C version, the loop index is decremented using the statement i=i–1. For more than one statement after the for loop definition, the statements would have to be encapsulated in { and }.

Ada

with ada.Float_Text_IO; use Ada.Float_Text_IO;
with ada.Integer_Text_IO; use Ada.Integer_Text_IO;

procedure harmonic is
   n : integer;
   h : float;
begin
   get(n);
   h := 0.0;
   for i in reverse 1..n loop
      h := h + 1.0/float(i);
   end loop;
   put(h);
end harmonic;

In Ada, the keyword reverse is used to specify a loop will be decreasing in value.

Julia

n = parse(Int64, chomp(readline()))
println(n)
h = 0
for i = n:-1:1
   h = h + 1.0/i
end
println(h)

Here the index modifier is placed in the centre, n:-1:1, implying i has the values n to 1, modified by -1 each loop iteration. In a  normal loop incrementing by 1, the modifier can be omitted.