55 lines
1.3 KiB
C
55 lines
1.3 KiB
C
/* Triangle, pentagonal, and hexagonal numbers are generated by the following formulae:
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*
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* Triangle T_n=n(n+1)/2 1, 3, 6, 10, 15, ...
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* Pentagonal P_n=n(3n−1)/2 1, 5, 12, 22, 35, ...
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* Hexagonal H_n=n(2n−1) 1, 6, 15, 28, 45, ...
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*
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* It can be verified that T_285 = P_165 = H_143 = 40755.
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*
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* Find the next triangle number that is also pentagonal and hexagonal.*/
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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 <math.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 found = 0;
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long int i, n;
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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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i = 143;
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while(!found)
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{
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i++;
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/* Hexagonal numbers are also triangle numbers, so it's sufficient
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* to generate hexagonal numbers (starting from H_144) and check if
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* they're also pentagonal.*/
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n = i * (2 * i - 1);
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if(is_pentagonal(n))
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{
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found = 1;
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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 45\n");
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printf("Answer: %ld\n", n);
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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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