Program to Generate Floyd's Triangle in C | C Program

Here's a C program to generate Floyd's triangle using nested for loops with output and proper explanation.

What's a Floyd Triangle? Floyd's triangle is a right-angled triangular array of natural numbers, used in computer science education. It is named after Robert Floyd. It is defined by filling the rows of the triangle with consecutive numbers, starting with a 1 in the top left corner

Floyd's Triangle

# include <stdio.h>
# include <conio.h>
void main() 
{ 
 int r, i, j, c = 1 ; 
 clrscr() ; 
 printf("Enter the number of rows : ") ; 
 scanf("%d", &r) ; 
 printf("\nFloyd's triangle is : \n\n") ; 
 for(i = 0 ; i < r ; i++) 
 { 
  for(j = 0 ; j <= i ; j++) 
  { 
   printf("%-6d", c) ; 
   c++ ; 
  } 
  printf("\n\n") ; 
 } 
 getch() ; 
} 

Output of above program is

Enter the number of rows : 5

Floyd's triangle is :

1

2     3

4     5     6

7     8     9     10

11    12    13    14    15


Explanation of above program

The program first asks the user to enter number of rows that he/she wants to print. After that the program uses two for loops or nested for loops to draw Floyd's Triangle.

Lets see how these two loops work with an example -

Suppose r = 5. So the outer loop will run for i = 0 to 4 while the inner loop depends on the value of i (outer loop).

Outer loop i = 0, c = 1

• In this case, inner loop executes for j = 0 to i i.e. 0. So inner loop executes only one time for i = 0.
• Inside inner loop, first the value of variable c is printed in a formatted way. Currently c = 1 so 1 is outputted (first line of output). Value of c and j are incremented by 1.
• Inner loop terminates as now j = 1 so j is not less than or equal to 0. Now, outer for loop executes with i = 1.

Outer loop i = 1, c = 2

• In this case, inner loop executes for j = 0 to i i.e. 1. So inner loop executes two times for i = 1.
• Inside inner loop, first the value of variable c is printed in a formatted way. Currently c = 2 so 2 is outputted. Value of c and j are incremented by 1.
• The inner loop executes again with j = 1 and c = 3.
• Again the value of c  is printed. And value of c and j are again incremented. (Second line of output is printed at this step)
  
• Inner loop terminates as now j = 2 so j is not less than or equal to 1. Now, outer for loop executes with i = 2.

Outer loop i = 2, c = 4

• In this case, inner loop executes for j = 0 to i i.e. 2. So inner loop executes three times for i = 2.
• Inside inner loop, first the value of variable c is printed in a formatted way. Currently c = 4 so 4 is outputted. Value of c and j are incremented by 1.
• The inner loop executes two more times printing c = 5 and c = 6 i.e. third line of output. Also j is incremented each time.
• Inner loop terminates as now j = 3 so j is not less than or equal to 2. Now, outer for loop executes with i = 3.

Outer loop i = 3, c = 7

• In this case, inner loop executes for j = 0 to i i.e. 3. So inner loop executes only four time for i = 3.
• Inside inner loop, first the value of variable c is printed in a formatted way. Currently c = 7 so 7 is outputted. Value of c and j are incremented by 1.
• The inner loop executes three more times printing c = 8, c = 9 and c = 10 i.e. fourth line of output. Also j is incremented each time.
  
• Inner loop terminates as now j = 4 so j is not less than or equal to 3. Now, outer for loop executes with i = 4.

Outer loop i = 4, c = 11

• In this case, inner loop executes for j = 0 to i i.e. 4. So inner loop executes only five time for i = 4.
• Inside inner loop, first the value of variable c is printed in a formatted way. Currently c = 11 so 11 is outputted. Value of c and j are incremented by 1.
• The inner loop executes four more times printing c = 12, c = 13, c = 14 and c = 15 i.e. last line of output. Also j is incremented each time.
  
• Inner loop terminates as now j = 5 so j is not less than or equal to 3. Now, outer for loop executes with i = 5 making the looping condition false so the outer loop is also terminated.