mirror of
https://github.com/TheAlgorithms/C
synced 2024-11-25 06:49:36 +03:00
43 lines
1.0 KiB
C
43 lines
1.0 KiB
C
/**
|
|
* \file
|
|
* \brief [Problem 9](https://projecteuler.net/problem=9) solution
|
|
* \author [Krishna Vedala](https://github.com/kvedala)
|
|
*
|
|
Problem Statement:
|
|
A Pythagorean triplet is a set of three natural numbers, \f$a < b < c\f$,
|
|
for which, \f$a^2 + b^2 = c^2\f$. For example, \f$3^2 + 4^2 = 9 + 16 = 25 =
|
|
5^2\f$. There exists exactly one Pythagorean triplet for which \f$a + b + c =
|
|
1000\f$. Find the product abc.
|
|
|
|
|
|
Given \f$a^2 + b^2 = c^2\f$ and \f$a+b+c = n\f$, we can write:
|
|
\f{eqnarray*}{
|
|
b &=& \frac{n^2 - 2an}{2n - 2a}\\
|
|
c &=& n - a - b
|
|
\f}
|
|
*/
|
|
#include <stdio.h>
|
|
#include <stdlib.h>
|
|
|
|
/** Main function */
|
|
int main(void)
|
|
{
|
|
int N = 1000;
|
|
|
|
for (int a = 1; a < 300; a++)
|
|
{
|
|
long tmp1 = N * N - 2 * a * N;
|
|
long tmp2 = 2 * (N - a);
|
|
div_t tmp3 = div(tmp1, tmp2);
|
|
int b = tmp3.quot;
|
|
int c = N - a - b;
|
|
|
|
if (a * a + b * b == c * c)
|
|
{
|
|
printf("%d x %d x %d = %ld\n", a, b, c, (long int)a * b * c);
|
|
return 0;
|
|
}
|
|
}
|
|
|
|
return 0;
|
|
} |