Closest-pair problem/C
<lang C>#include <stdio.h>
- include <stdlib.h>
- include <values.h>
- include <math.h>
- include <string.h>
typedef struct { double x, y; } point_t, *point;
inline double dist(point a, point b) {
double dx = a->x - b->x, dy = a->y - b->y; return dx * dx + dy * dy;
}
inline int cmp_dbl(double a, double b) {
return a < b ? -1 : a > b ? 1 : 0;
}
int cmp_x(const void *a, const void *b) {
return cmp_dbl( (*(const point*)a)->x, (*(const point*)b)->x );
}
int cmp_y(const void *a, const void *b) {
return cmp_dbl( (*(const point*)a)->y, (*(const point*)b)->y );
}
double brute_force(point* pts, int max_n, point *a, point *b) {
int i, j; double d, min_d = MAXDOUBLE;
for (i = 0; i < max_n; i++) { for (j = i + 1; j < max_n; j++) { d = dist(pts[i], pts[j]); if (d >= min_d ) continue; *a = pts[i]; *b = pts[j]; min_d = d; } } return min_d;
}
double closest(point* sx, int nx, point* sy, int ny, point *a, point *b) {
int left, right, i; double d, min_d, x0, x1, mid, x; point a1, b1; point *s_yy;
if (nx <= 8) return brute_force(sx, nx, a, b);
s_yy = malloc(sizeof(point) * ny); mid = sx[nx/2]->x;
/* adding points to the y-sorted list; if a point's x is less than mid, add to the begining; if more, add to the end backwards, hence the need to reverse it */ left = -1; right = ny; for (i = 0; i < ny; i++) if (sy[i]->x < mid) s_yy[++left] = sy[i]; else s_yy[--right]= sy[i];
/* reverse the higher part of the list */ for (i = ny - 1; right < i; right ++, i--) { a1 = s_yy[right]; s_yy[right] = s_yy[i]; s_yy[i] = a1; }
min_d = closest(sx, nx/2, s_yy, left + 1, a, b); d = closest(sx + nx/2, nx - nx/2, s_yy + left + 1, ny - left - 1, &a1, &b1);
if (d < min_d) { min_d = d; *a = a1; *b = b1; } d = sqrt(min_d);
/* get all the points within distance d of the center line */ left = -1; right = ny; for (i = 0; i < ny; i++) { x = sy[i]->x - mid; if (x <= -d || x >= d) continue;
if (x < 0) s_yy[++left] = sy[i]; else s_yy[--right] = sy[i]; }
/* compare each left point to right point */ while (left >= 0) { x0 = s_yy[left]->y + d;
while (right < ny && s_yy[right]->y > x0) right ++; if (right >= ny) break;
x1 = s_yy[left]->y - d; for (i = right; i < ny && s_yy[i]->y > x1; i++) if ((x = dist(s_yy[left], s_yy[i])) < min_d) { min_d = x; d = sqrt(min_d); *a = s_yy[left]; *b = s_yy[i]; }
left --; }
free(s_yy); return min_d;
}
- define NP 1000000
int main() {
int i; point a, b;
point pts = malloc(sizeof(point_t) * NP); point* s_x = malloc(sizeof(point) * NP); point* s_y = malloc(sizeof(point) * NP);
for(i = 0; i < NP; i++) { s_x[i] = pts + i; pts[i].x = 100 * (double) rand()/RAND_MAX; pts[i].y = 100 * (double) rand()/RAND_MAX; }
/* printf("brute force: %g, ", sqrt(brute_force(s_x, NP, &a, &b)));
printf("between (%f,%f) and (%f,%f)\n", a->x, a->y, b->x, b->y); */
memcpy(s_y, s_x, sizeof(point) * NP); qsort(s_x, NP, sizeof(point), cmp_x); qsort(s_y, NP, sizeof(point), cmp_y);
printf("min: %g; ", sqrt(closest(s_x, NP, s_y, NP, &a, &b))); printf("point (%f,%f) and (%f,%f)\n", a->x, a->y, b->x, b->y);
/* not freeing the memory, let OS deal with it. Habit. */ return 0;
}</lang>Compile and run (1000000 points, bruteforce method not shown because it takes forever):<lang> % gcc -Wall -lm -O2 test.c % time ./a.out min: 5.6321e-05; point (19.657247,79.900855) and (19.657303,79.900862) ./a.out 7.16s user 0.08s system 96% cpu 7.480 total </lang>