Step by Step solution about How to resolve the algorithm Floyd's triangle step by step in the C programming language

The provided C code generates right-aligned triangles of numbers. These triangles follow a specific pattern, where the numbers in each row increase by 1 and start from 1. The triangles are right-aligned, meaning the numbers are positioned at the far right of the available space. It includes two functions: t() and main().

1. t() Function:

   • Parameters: The t() function takes an integer n as a parameter, representing the number of rows in the triangle.

   • Function Body:

     • It calculates the total number of elements in the triangle using i = n * (n - 1) / 2.
     • It determines the maximum length (len) of the numbers printed by finding the number of digits in i.
     • It calculates c, which represents the column where the width of the numbers starts to change (becoming shorter). c is initially set to 1.
     • It defines a macro SPEED_MATTERS. This macro is used to optimize the printing process for large triangles.

   • Printing: The printing process depends on the value of SPEED_MATTERS:

     • If SPEED_MATTERS is defined as 0 (NO_IT_DOESN'T), the code uses the following approach:
       • It initializes an integer variable num to 1.
       • For each row i up to n:
         • For each column j up to i:
           • It prints num right-aligned with a width of len minus j < c, which determines whether the number should be shortened due to the varying width.
           • If j is not the last column, it prints a space.
           • Otherwise (last column), it prints a newline character.
           • It increments num by 1.
     • If SPEED_MATTERS is defined as 1, the code uses a faster approach:
       • It declares a temporary buffer tmp and a string s.
       • It initializes tmp with a leading zero and a width of len.
       • It defines an inline function inc_numstr() to increment the number stored in tmp.
       • It loops through the rows i up to n:
         • For each column j up to i:
           • It calls inc_numstr() to increment the number.
           • It copies a portion of tmp into s, starting from the rightmost digit and ending just before j < c, which determines whether the number should be shortened.
           • It prints a space if j is not the last column.
           • Otherwise (last column), it prints a newline character.
           • It checks if the buffer s has reached its maximum capacity. If so, it flushes the contents of s to the standard output and resets s.
       • Finally, it flushes the remaining contents of s to the standard output.

2. main() Function:

   • Function Body:
     • It calls the t() function with different parameters to generate two triangles.
     • The first triangle has 5 rows, and the second triangle has 14 rows.
     • It also uncomments a call to generate a triangle with 10,000 rows, but this is marked as "maybe not" because it can be computationally expensive.
     • The program returns 0, indicating successful execution.

#include <stdio.h>

void t(int n)
{
	int i, j, c, len;

	i = n * (n - 1) / 2;
	for (len = c = 1; c < i; c *= 10, len++);
	c -= i; // c is the col where width changes

#define SPEED_MATTERS 0
#if SPEED_MATTERS	// in case we really, really wanted to print huge triangles often
	char tmp[32], s[4096], *p;

	sprintf(tmp, "%*d", len, 0);

	inline void inc_numstr(void) {
		int k = len;

	redo:	if (!k--) return;

		if (tmp[k] == '9') {
			tmp[k] = '0';
			goto redo;
		}

		if (++tmp[k] == '!')
			tmp[k] = '1';
	}

	for (p = s, i = 1; i <= n; i++) {
		for (j = 1; j <= i; j++) {
			inc_numstr();
			__builtin_memcpy(p, tmp + 1 - (j >= c), len - (j < c));
			p += len - (j < c);

			*(p++) = (i - j)? ' ' : '\n';

			if (p - s + len >= 4096) {
				fwrite(s, 1, p - s, stdout);
				p = s;
			}
		}
	}

	fwrite(s, 1, p - s, stdout);
#else // NO_IT_DOESN'T
	int num;
	for (num = i = 1; i <= n; i++)
		for (j = 1; j <= i; j++)
			printf("%*d%c",	len - (j < c), num++, i - j ? ' ':'\n');
#endif
}

int main(void)
{
	t(5), t(14);

	// maybe not 
	// t(10000);
	return 0;
}