78 lines
1.9 KiB
C
78 lines
1.9 KiB
C
/* A Pythagorean triplet is a set of three natural numbers, a < b < c, for which,
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*
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* a2 + b2 = c2
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*
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* For example, 32 + 42 = 9 + 16 = 25 = 52.
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*
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* There exists exactly one Pythagorean triplet for which a + b + c = 1000.
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*
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* Find the product abc.*/
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#define _POSIX_C_SOURCE 199309L
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#include <stdio.h>
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#include <stdlib.h>
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#include <time.h>
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#include "projecteuler.h"
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int main(int argc, char **argv)
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{
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int a, b, c, tmpa, tmpb, tmpc, i, m, n, found = 0;
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double elapsed;
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struct timespec start, end;
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clock_gettime(CLOCK_MONOTONIC, &start);
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/* Brute force approach: generate all the Pythagorean triplets using
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* Euclid's formula, until the one where a+b+c=1000 is found.*/
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for(m = 2; found == 0; m++)
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{
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for(n = 1; n < m && !found; n++)
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{
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if(gcd(m, n) == 1 && ((m % 2 == 0 && n % 2 != 0) || (m % 2 != 0 && n % 2 == 0)))
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{
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a = m * m - n * n;
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b = 2 * m * n;
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c = m * m + n * n;
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if(a + b + c == 1000)
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{
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found = 1;
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break;
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}
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i = 2;
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do
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{
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tmpa = a * i;
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tmpb = b * i;
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tmpc = c * i;
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if(tmpa + tmpb + tmpc == 1000)
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{
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a = tmpa;
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b = tmpb;
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c = tmpc;
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found = 1;
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break;
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}
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i++;
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} while(tmpa + tmpb + tmpc < 1000);
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}
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}
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}
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clock_gettime(CLOCK_MONOTONIC, &end);
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elapsed = (end.tv_sec - start.tv_sec) + (double)(end.tv_nsec - start.tv_nsec) / 1000000000;
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printf("Project Euler, Problem 9\n");
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printf("Answer: %d\n", a*b*c);
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printf("Elapsed time: %.9lf seconds\n", elapsed);
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return 0;
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}
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