110 lines
2.7 KiB
C
110 lines
2.7 KiB
C
/* Working from left-to-right if no digit is exceeded by the digit to its left it is called an increasing number; for example, 134468.
|
|
*
|
|
* Similarly if no digit is exceeded by the digit to its right it is called a decreasing number; for example, 66420.
|
|
*
|
|
* We shall call a positive integer that is neither increasing nor decreasing a "bouncy" number; for example, 155349.
|
|
*
|
|
* Clearly there cannot be any bouncy numbers below one-hundred, but just over half of the numbers below one-thousand (525) are bouncy.
|
|
* In fact, the least number for which the proportion of bouncy numbers first reaches 50% is 538.
|
|
*
|
|
* Surprisingly, bouncy numbers become more and more common and by the time we reach 21780 the proportion of bouncy numbers is equal to 90%.
|
|
*
|
|
* Find the least number for which the proportion of bouncy numbers is exactly 99%.*/
|
|
|
|
#define _POSIX_C_SOURCE 199309L
|
|
|
|
#include <stdio.h>
|
|
#include <stdlib.h>
|
|
#include <string.h>
|
|
#include <time.h>
|
|
|
|
int is_bouncy(int n);
|
|
|
|
int main(int argc, char **argv)
|
|
{
|
|
int i = 100, n_bouncy = 0;
|
|
double ratio = 0.0, elapsed;
|
|
struct timespec start, end;
|
|
|
|
clock_gettime(CLOCK_MONOTONIC, &start);
|
|
|
|
while(1)
|
|
{
|
|
if(is_bouncy(i))
|
|
{
|
|
n_bouncy++;
|
|
}
|
|
|
|
ratio = (double)n_bouncy / i;
|
|
|
|
if(ratio == 0.99)
|
|
{
|
|
break;
|
|
}
|
|
|
|
i++;
|
|
}
|
|
|
|
clock_gettime(CLOCK_MONOTONIC, &end);
|
|
|
|
elapsed = (end.tv_sec - start.tv_sec) + (double)(end.tv_nsec - start.tv_nsec) / 1000000000;
|
|
|
|
printf("Project Euler, Problem 112\n");
|
|
printf("Answer: %d\n", i);
|
|
|
|
printf("Elapsed time: %.9lf seconds\n", elapsed);
|
|
|
|
return 0;
|
|
}
|
|
|
|
/* Check if the number is bouncy.*/
|
|
int is_bouncy(int n)
|
|
{
|
|
int i = 0, l;
|
|
char n_string[100];
|
|
|
|
sprintf(n_string, "%d", n);
|
|
|
|
l = strlen(n_string);
|
|
|
|
/* Ignore consecutive equal digits.*/
|
|
while(i < l - 1 && n_string[i] == n_string[i+1])
|
|
{
|
|
i++;
|
|
}
|
|
|
|
/* If all the digits are the same, the number is not bouncy.*/
|
|
if(i == l - 1)
|
|
{
|
|
return 0;
|
|
}
|
|
|
|
/* If the first two different digits are increasing, if a successive
|
|
* digit smaller than the previous digit is found, the number is bouncy.*/
|
|
if(n_string[i] < n_string[i+1])
|
|
{
|
|
for(; i < l - 1; i++)
|
|
{
|
|
if(n_string[i] > n_string[i+1])
|
|
{
|
|
return 1;
|
|
}
|
|
}
|
|
}
|
|
|
|
/* If the first two different digits are decreasing, if a successive
|
|
* digit larger than the previous digit is found, the number is bouncy.*/
|
|
if(n_string[i] > n_string[i+1])
|
|
{
|
|
for(; i < l - 1; i++)
|
|
{
|
|
if(n_string[i] < n_string[i+1])
|
|
{
|
|
return 1;
|
|
}
|
|
}
|
|
}
|
|
|
|
return 0;
|
|
}
|