84 lines
1.6 KiB
C
84 lines
1.6 KiB
C
/* The 5-digit number, 16807=7^5, is also a fifth power. Similarly, the 9-digit number, 134217728=8^9, is a ninth power.
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*
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* How many n-digit positive integers exist which are also an nth power?*/
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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 <gmp.h>
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int count_digits(mpz_t n);
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int main(int argc, char **argv)
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{
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int i, j, count = 0, finished = 0;
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double elapsed;
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struct timespec start, end;
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mpz_t p;
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mpz_init(p);
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clock_gettime(CLOCK_MONOTONIC, &start);
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i = 1;
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while(!finished)
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{
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/* When j=10, j^i will have i+1 digits (e.g if i=3, 10^3=1000).*/
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for(j = 1; j < 10; j++)
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{
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mpz_ui_pow_ui(p, j, i);
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if(count_digits(p) == i)
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{
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count++;
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}
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}
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/* When 9^i has less than i digits, all the numbers have been found.*/
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if(count_digits(p) < i)
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{
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finished = 1;
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}
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i++;
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}
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mpz_clear(p);
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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 63\n");
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printf("Answer: %d\n", count);
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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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int count_digits(mpz_t n)
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{
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int count = 0;
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mpz_t tmp;
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if(mpz_cmp_ui(n, 0) == 0)
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{
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return 1;
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}
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mpz_init_set(tmp, n);
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while(mpz_cmp_ui(tmp, 0))
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{
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mpz_tdiv_q_ui(tmp, tmp, 10);
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count++;
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}
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return count;
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}
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