Algorithms_in_C 1.0.0
Set of algorithms implemented in C.
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sol2.c File Reference

Problem 9 solution More...

#include <stdio.h>
#include <stdlib.h>
Include dependency graph for sol2.c:

Functions

int main (void)
 Main function. More...
 

Detailed Description

Problem 9 solution

Author
Krishna Vedala

Problem Statement: A Pythagorean triplet is a set of three natural numbers, \(a < b < c\), for which, \(a^2 + b^2 = c^2\). For example, \(3^2 + 4^2 = 9 + 16 = 25 = 5^2\). There exists exactly one Pythagorean triplet for which \(a + b + c = 1000\). Find the product abc.

Given \(a^2 + b^2 = c^2\) and \(a+b+c = n\), we can write:

\begin{eqnarray*} b &=& \frac{n^2 - 2an}{2n - 2a}\\ c &=& n - a - b \end{eqnarray*}

Function Documentation

◆ main()

int main ( void  )

Main function.

24{
25 int N = 1000;
26
27 for (int a = 1; a < 300; a++)
28 {
29 long tmp1 = N * N - 2 * a * N;
30 long tmp2 = 2 * (N - a);
31 div_t tmp3 = div(tmp1, tmp2);
32 int b = tmp3.quot;
33 int c = N - a - b;
34
35 if (a * a + b * b == c * c)
36 {
37 printf("%d x %d x %d = %ld\n", a, b, c, (long int)a * b * c);
38 return 0;
39 }
40 }
41
42 return 0;
43}