We’re not quite done with loops yet. There are still a few things to learn, although some can be left for later. There are certain situations where it is appropriate to use a loop inside another loop. Such a loop is called a nested loop. A nested loop is executed, essentially, from the inside out. Each loop is like a layer and has its own loop control, its own condition and its own loop body. Below is a schematic of three nested loops.

There are many different kinds of nested loops, and they are largely dependent on the underlying algorithm. Below are some examples of the types of nested loops that are possible.

We will consider how a nested loop can be used to create a times table. It basically works by iterating the inner loop 12 times for every iteration of the outer loop. So, 12 × 12 = 144 iterations. The outer loop is highlighted in blue, and the inner loop in red. Here is a sample output:

 1   2   3   4   5   6   7   8   9  10  11  12
 2   4   6   8  10  12  14  16  18  20  22  24
 3   6   9  12  15  18  21  24  27  30  33  36
 4   8  12  16  20  24  28  32  36  40  44  48
 5  10  15  20  25  30  35  40  45  50  55  60
 6  12  18  24  30  36  42  48  54  60  66  72
 7  14  21  28  35  42  49  56  63  70  77  84
 8  16  24  32  40  48  56  64  72  80  88  96
 9  18  27  36  45  54  63  72  81  90  99 108
10  20  30  40  50  60  70  80  90 100 110 120
11  22  33  44  55  66  77  88  99 110 121 132
12  24  36  48  60  72  84  96 108 120 132 144

Ada

with ada.Text_IO; use Ada.Text_IO;
with ada.Integer_Text_IO; use ada.Integer_Text_IO;
procedure nested is 
begin
   for x in 1..12 loop
      for y in 1..12 loop
         put(x*y, width=>4);
      end loop;
      new_line;
   end loop;
end nested;

Fortran

program nested
   integer :: x, y
   do x = 1, 12
      do y = 1, 12
         write(*,10,advance='no') xy
         10 format(I4)
      end do
      write(*,*)
   end do
end program nested

C

#include <stdio.h>
int main(void){
   int x, y;
   for (x=1; x<=12; x=x+1)
   {
      for (y=1; y<=12; y=y+1)
         printf("%4d", x*y);
      printf("\n");
   }
   return 0;
}

Julia

for x = 1:12
   for y = 1:12
      @printf("%4d", x*y)
   end
   println()
end
println(h)

There are of course other loops. These loops are normally used when the number of times a loop iterates isn’t known. These type of loops generally use some form of condition to control the loop. The most prominent type of loop is the while loop. A while loop checks a condition, and if true, processes the code in the loop body, otherwise it exists the loop. Unlike the for loop, which controls the values of the loop index in terms of updating its value, in the loops like while, this process must be added, i.e. the value of i is given the value 1, before the loop is activated, and its value is incremented within the loop body.

We will consider some of these loops using the same Harmonic series, this time in increasing order. The code for the program in Fortran, Ada, Julia and C is shown below. The loop is highlighted in blue.

Fortran

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

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

Here the index variable, i, must be initiated to the value 1 before the loop begins, and incremented within the loop. The condition states that the loop continues while the value of i is less than or equal to n, i.e. (i <= n) . Fortran also provides a more generic do/end do loop.

C

#include <stdio.h>

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

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

In the C version, the structure is almost the same, except that the do while of Fortran has been replace with a simple while. With the addition of the statement to increment the value of i, the loop “contents” are now enclosed within { and }. C also has another loop, the do/while() loop, that performs the loop once, then evaluates the condition at the end.

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, i : integer;
   h : float;
begin
   get(n);
   h := 0.0;
   i := 1;
   while i <= n loop
      h := h + 1.0/float(i);
      i := i + 1;
   end loop;
   put(h);
end harmonic;

In Ada, the while loop looks similar to that of the other to Fortran and C, it is just subtleties in syntax that set them apart. Here there are no parenthesis around the condition. Also note that in the for loop, the index variable, i, did not have to be declared, but here it does. Ada also provides a generic loop/end loop loop.

Julia

n = parse(Int64, chomp(readline()))
println(n)
h = 0
i = 1
while i <= n
   h = h + 1.0/i
   i = i + 1
end
println(h)

Same deal here. Similar to Ada, except the loop keyword after the condition isn’t needed. There are only two loops in Julia.

As you can see, over four languages, the only thing that fundamentally changes is the basic syntax of the loop.

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.

We’re not quite done with loops yet. There are still a few things to learn, although some can be left for later. There are certain situations where it is appropriate to use a loop inside another loop. Such a loop is called a nested loop. A nested loop is executed, essentially, from the inside out. Each loop is like a layer and has its own loop control, its own condition and its own loop body. Below is a schematic of three nested loops.

There are many different kinds of nested loops, and they are largely dependent on the underlying algorithm. Below are some examples of the types of nested loops that are possible.

We will consider how a nested loop can be used to create a times table. It basically works by iterating the inner loop 12 times for every iteration of the outer loop. So, 12 × 12 = 144 iterations. The outer loop is highlighted in blue, and the inner loop in red. Here is a sample output:

 1   2   3   4   5   6   7   8   9  10  11  12
 2   4   6   8  10  12  14  16  18  20  22  24
 3   6   9  12  15  18  21  24  27  30  33  36
 4   8  12  16  20  24  28  32  36  40  44  48
 5  10  15  20  25  30  35  40  45  50  55  60
 6  12  18  24  30  36  42  48  54  60  66  72
 7  14  21  28  35  42  49  56  63  70  77  84
 8  16  24  32  40  48  56  64  72  80  88  96
 9  18  27  36  45  54  63  72  81  90  99 108
10  20  30  40  50  60  70  80  90 100 110 120
11  22  33  44  55  66  77  88  99 110 121 132
12  24  36  48  60  72  84  96 108 120 132 144

Ada

with ada.Text_IO; use Ada.Text_IO;
with ada.Integer_Text_IO; use ada.Integer_Text_IO;
procedure nested is 
begin
   for x in 1..12 loop
      for y in 1..12 loop
         put(x*y, width=>4);
      end loop;
      new_line;
   end loop;
end nested;

Fortran

program nested
   integer :: x, y
   do x = 1, 12
      do y = 1, 12
         write(*,10,advance='no') xy
         10 format(I4)
      end do
      write(*,*)
   end do
end program nested

C

#include <stdio.h>
int main(void){
   int x, y;
   for (x=1; x<=12; x=x+1)
   {
      for (y=1; y<=12; y=y+1)
         printf("%4d", x*y);
      printf("\n");
   }
   return 0;
}

Julia

for x = 1:12
   for y = 1:12
      @printf("%4d", x*y)
   end
   println()
end
println(h)

There are of course other loops. These loops are normally used when the number of times a loop iterates isn’t known. These type of loops generally use some form of condition to control the loop. The most prominent type of loop is the while loop. A while loop checks a condition, and if true, processes the code in the loop body, otherwise it exists the loop. Unlike the for loop, which controls the values of the loop index in terms of updating its value, in the loops like while, this process must be added, i.e. the value of i is given the value 1, before the loop is activated, and its value is incremented within the loop body.

We will consider some of these loops using the same Harmonic series, this time in increasing order. The code for the program in Fortran, Ada, Julia and C is shown below. The loop is highlighted in blue.

Fortran

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

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

Here the index variable, i, must be initiated to the value 1 before the loop begins, and incremented within the loop. The condition states that the loop continues while the value of i is less than or equal to n, i.e. (i <= n) . Fortran also provides a more generic do/end do loop.

C

#include <stdio.h>

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

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

In the C version, the structure is almost the same, except that the do while of Fortran has been replace with a simple while. With the addition of the statement to increment the value of i, the loop “contents” are now enclosed within { and }. C also has another loop, the do/while() loop, that performs the loop once, then evaluates the condition at the end.

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, i : integer;
   h : float;
begin
   get(n);
   h := 0.0;
   i := 1;
   while i <= n loop
      h := h + 1.0/float(i);
      i := i + 1;
   end loop;
   put(h);
end harmonic;

In Ada, the while loop looks similar to that of the other to Fortran and C, it is just subtleties in syntax that set them apart. Here there are no parenthesis around the condition. Also note that in the for loop, the index variable, i, did not have to be declared, but here it does. Ada also provides a generic loop/end loop loop.

Julia

n = parse(Int64, chomp(readline()))
println(n)
h = 0
i = 1
while i <= n
   h = h + 1.0/i
   i = i + 1
end
println(h)

Same deal here. Similar to Ada, except the loop keyword after the condition isn’t needed. There are only two loops in Julia.

As you can see, over four languages, the only thing that fundamentally changes is the basic syntax of the loop.

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.