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K-d tree: Difference between revisions

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K-d tree (view source)

Revision as of 12:38, 6 May 2015

625 bytes added ,  9 years ago
m
Made the code compilable on gcc and g++ versions 4.8, the thisn is a bit ugly though.
m ({{out}})
m (Made the code compilable on gcc and g++ versions 4.8, the thisn is a bit ugly though.)
Line 31:
=={{header|C}}==
Using a Quickselectesque median algorithm. Compared to unbalanced trees (random insertion), it takes slightly longer (maybe half a second or so) to construct a million-node tree, though average look up visits about 1/3 fewer nodes.
<lang c>#include <stdio.h>
 
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
Line 39 ⟶ 41:
#define MAX_DIM 3
struct kd_node_t{
double x[MAX_DIM];
struct kd_node_t *left, *right;
};
 
inline double
dist(struct kd_node_t *a, struct kd_node_t *b, int dim)
{
double t, d = 0;
while (dim--) {
t = a->x[dim] - b->x[dim];
d += t * t;
}
}▼
return d;
}
inline void swap(struct kd_node_t *x, struct kd_node_t *y) {
double tmp[MAX_DIM];
memcpy(tmp, x->x, sizeof(tmp));▼
memcpy(x->x, y->x, sizeof(tmp));▼
memcpy(y->x, tmp, sizeof(tmp));▼
}
 
 
/* see quickselect method */
struct kd_node_t*
find_median(struct kd_node_t *start, struct kd_node_t *end, int idx)
{
if (end <= start) return NULL;
if (end == start + 1)
return start;
 
inline void swap( struct kd_node_t *xp, struct kd_node_t*store, *ymd = start + (end - start) {/ 2;
double tmp[MAX_DIM]pivot;
while (1) {▼
▲ memcpy(tmp, x->x, sizeof(tmp));
pivot = md->x[idx];▼
▲ memcpy(x->x, y->x, sizeof(tmp));
▲ memcpy(y->x, tmp, sizeof(tmp));
}
 
struct kd_node_t *p, *store, *md = start + swap(md, end - start1) / 2;
for (store = p = start; p < end; p++) {▼
double pivot;
if (p->x[idx] < pivot) {▼
▲ while (1) {
if (p != store)▼
▲ pivot = md->x[idx];
swap(p, store);▼
store++;
}
}
swap(store, end - 1);▼
 
/* median has duplicate values */▼
swap(md, end - 1);
if (store->x[idx] == md->x[idx])▼
▲ for (store = p = start; p < end; p++) {
return md;▼
▲ if (p->x[idx] < pivot) {
▲ if (p != store)
▲ swap(p, store);
store++;
}
}
▲ swap(store, end - 1);
 
if (store > md) end = store;▼
▲ /* median has duplicate values */
else start = store;▼
▲ if (store->x[idx] == md->x[idx])
}
▲ return md;
 
▲ if (store > md) end = store;
▲ else start = store;
}
}
 
struct kd_node_t*
make_tree(struct kd_node_t *t, int len, int i, int dim)
{
struct kd_node_t *n;
 
if (!len) return 0;
 
if ((n = find_median(t, t + len, i))) {
i = (i + 1) % dim;
n->left = make_tree(t, n - t, i, dim);
n->right = make_tree(n + 1, t + len - (n + 1), i, dim);
}
}
return n;
}
 
Line 112 ⟶ 114:
 
void nearest(struct kd_node_t *root, struct kd_node_t *nd, int i, int dim,
struct kd_node_t **best, double *best_dist)
{
double d, dx, dx2;
 
if (!root) return;
d = dist(root, nd, dim);
dx = root->x[i] - nd->x[i];
dx2 = dx * dx;
 
visited ++;
 
if (!*best || d < *best_dist) {
*best_dist = d;
*best = root;
}
}
 
/* if chance of exact match is high */
if (!*best_dist) return;
 
if (++i >= dim) i = 0;
 
nearest(dx > 0 ? root->left : root->right, nd, i, dim, best, best_dist);
if (dx2 >= *best_dist) return;
nearest(dx > 0 ? root->right : root->left, nd, i, dim, best, best_dist);
}
 
#define N 1000000
#define rand1() (rand() / (double)RAND_MAX)
#define rand_pt(v) { v.x[0] = rand1(); v.x[1] = rand1(); v.x[2] = rand1(); }
int main(void)
{
int i;
struct kd_node_t wp[] = {
{{2, 3}}, {{5, 4}}, {{9, 6}}, {{4, 7}}, {{8, 1}}, {{7, 2}}
};
struct kd_node_t thisthisn = {{9, 2}};
struct kd_node_t *root, *found, *million;
double best_dist;
 
root = make_tree(wp, sizeof(wp) / sizeof(wp[1]), 0, 2);
 
visited = 0;
found = 0;
nearest(root, &thisthisn, 0, 2, &found, &best_dist);
 
printf(">> WP tree\nsearching for (%g, %g)\n"
"found (%g, %g) dist %g\nseen %d nodes\n\n",
this thisn.x[0], thisthisn.x[1],
found->x[0], found->x[1], sqrt(best_dist), visited);
 
million =(struct kd_node_t*) calloc(N, sizeof(struct kd_node_t));
srand(time(0));
for (i = 0; i < N; i++) rand_pt(million[i]);
 
root = make_tree(million, N, 0, 3);
rand_pt(thisthisn);
 
visited = 0;
found = 0;
nearest(root, &thisthisn, 0, 3, &found, &best_dist);
 
printf(">> Million tree\nsearching for (%g, %g, %g)\n"
"found (%g, %g, %g) dist %g\nseen %d nodes\n",
this thisn.x[0], thisthisn.x[1], thisthisn.x[2],
found->x[0], found->x[1], found->x[2],
sqrt(best_dist), visited);
 
/* search many random points in million tree to see average behavior.
tree size vs avg nodes visited:
10 ~ 7
100 ~ 16.5
1000 ~ 25.5
10000 ~ 32.8
100000 ~ 38.3
1000000 ~ 42.6
10000000 ~ 46.7 */
int sum = 0, test_runs = 100000;
for (i = 0; i < test_runs; i++) {
found = 0;
visited = 0;
rand_pt(thisthisn);
nearest(root, &thisthisn, 0, 3, &found, &best_dist);
sum += visited;
}
}
printf("\n>> Million tree\n"
"visited %d nodes for %d random findings (%f per lookup)\n",
sum, test_runs, sum/(double)test_runs);
 
// free(million);
 
return 0;
▲ }
}</lang>
{{out}}
<pre>>> WP tree
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