closest pair of points
时间: 2023-04-17 20:04:33 浏览: 68
最近点对问题是计算平面上最近的两个点之间的距离的问题。这个问题在计算几何学和计算机科学中都非常重要,有许多有效的算法可以解决它。其中最常用的算法是分治法,它可以在O(nlogn)的时间内解决这个问题。
相关问题
一维最近点对——C语言代码
以下是一维最近点对的C语言代码:
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
struct point {
int x;
int y;
};
int compare(const void *a, const void *b) {
return ((struct point *)a)->x - ((struct point *)b)->x;
}
float distance(struct point a, struct point b) {
return sqrt(pow(a.x - b.x, 2) + pow(a.y - b.y, 2));
}
float closest_pair(struct point *points, int n) {
if (n <= 1) {
return INFINITY;
}
qsort(points, n, sizeof(struct point), compare);
float min_distance = INFINITY;
for (int i = 0; i < n - 1; i++) {
float d = distance(points[i], points[i + 1]);
if (d < min_distance) {
min_distance = d;
}
}
return min_distance;
}
int main() {
int n;
printf("Enter the number of points: ");
scanf("%d", &n);
struct point *points = malloc(n * sizeof(struct point));
for (int i = 0; i < n; i++) {
printf("Enter x and y coordinates of point %d: ", i + 1);
scanf("%d %d", &points[i].x, &points[i].y);
}
float min_distance = closest_pair(points, n);
printf("The closest pair of points has distance: %.2f\n", min_distance);
free(points);
return 0;
}
用matlab写chan算法
由于您没有给出chan算法的具体内容和问题,我无法为您提供完整的代码。但是,我可以为您提供一些关于如何在MATLAB中实现chan算法的指导。
Chan算法是一种用于计算最近邻点对的快速算法,其基本思路是分治法。它将n个点分成两个集合,然后递归地计算每个集合内的最近邻点对,最后再计算跨集合的最近邻点对。
以下是一个基本的MATLAB函数,用于计算给定点集中的最近邻点对:
```
function [d, p1, p2] = chan_algorithm(points)
% points: a matrix of size n x 2, where each row contains the x and y coordinates of a point
% d: the Euclidean distance between the closest pair of points
% p1, p2: the indices of the closest pair of points
n = size(points, 1);
% If there are only two points, return their distance and indices
if n == 2
d = norm(points(1,:) - points(2,:));
p1 = 1;
p2 = 2;
return;
end
% If there are three points, compute their distances and return the closest pair
if n == 3
d12 = norm(points(1,:) - points(2,:));
d13 = norm(points(1,:) - points(3,:));
d23 = norm(points(2,:) - points(3,:));
if d12 <= d13 && d12 <= d23
d = d12;
p1 = 1;
p2 = 2;
elseif d13 <= d12 && d13 <= d23
d = d13;
p1 = 1;
p2 = 3;
else
d = d23;
p1 = 2;
p2 = 3;
end
return;
end
% Otherwise, divide the points into two sets and recursively compute their closest pairs
mid = ceil(n/2);
[d1, p1_1, p2_1] = chan_algorithm(points(1:mid,:));
[d2, p1_2, p2_2] = chan_algorithm(points(mid+1:end,:));
% Determine the closer of the two closest pairs
if d1 <= d2
d = d1;
p1 = p1_1;
p2 = p2_1;
else
d = d2;
p1 = p1_2 + mid;
p2 = p2_2 + mid;
end
% Compute the closest pair that crosses the midpoint
strip = points(abs(points(:,1)-points(mid,1)) < d,:);
strip_size = size(strip, 1);
for i = 1:strip_size-1
for j = i+1:min(i+7,strip_size)
dij = norm(strip(i,:) - strip(j,:));
if dij < d
d = dij;
p1 = find(ismember(points,strip(i,:),'rows'));
p2 = find(ismember(points,strip(j,:),'rows'));
end
end
end
end
```
该函数首先检查点集中的点数,如果只有两个点,则直接返回它们之间的距离和索引。如果有三个点,则计算它们之间的距离并返回最近的一对点。
对于大于三个点的情况,该函数将点集分成两组,并递归地调用自身以计算每个组内的最近邻点对。然后,该函数将计算跨越分组的最近邻点对(即位于两个不同组中的点),并返回距离最近的点对。
请注意,此函数假定点集中没有重复的点。如果存在重复的点,则可能需要对此进行检查和处理。
希望这可以帮助您来实现chan算法。