53 lines
1.6 KiB
C
53 lines
1.6 KiB
C
/* By counting carefully it can be seen that a rectangular grid measuring 3 by 2 contains eighteen rectangles.
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*
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* Although there exists no rectangular grid that contains exactly two million rectangles, find the area of the grid with the nearest solution.*/
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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 <limits.h>
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int main(int argc, char **argv)
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{
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int i, j, n, diff, min_diff = INT_MAX, area;
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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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for(i = 1; i < 100; i++)
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{
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for(j = 1; j <= i; j++)
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{
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/* In a 2x3 grid, we can take rectangles of height 2 in 3 ways
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* (two rectangles of height one and one of height 2). For the
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* width, can take 6 rectangles (3 of width 1, 2 of width 2 and
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* 1 of width 3). The total is 6x3=18 rectagles.
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* Extending to mxn, we can take (m+m-1+m-2+...+1)x(n+n-1+n-2+...+1)=
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* m(m+1)/2*n(n+1)/2=m(m+1)*n(n+1)/4 rectangles.*/
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n = ( i * (i + 1) * j * (j + 1)) / 4;
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diff = abs(2000000 - n);
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if(diff < min_diff)
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{
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min_diff = diff;
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area = i * j;
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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 85\n");
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printf("Answer: %d\n", area);
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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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