有一个数组,元素为线段,将数组内处于相交状态的线段放入迭代器,用分治算法实现
时间: 2024-03-20 20:43:55 浏览: 51
好的,下面是使用分治算法实现该功能的代码。
```cpp
#include <iostream>
#include <vector>
#include <algorithm>
using namespace std;
struct LineSegment {
int x1, y1, x2, y2;
};
bool isIntersecting(LineSegment a, LineSegment b) {
int x1 = a.x1, y1 = a.y1, x2 = a.x2, y2 = a.y2;
int x3 = b.x1, y3 = b.y1, x4 = b.x2, y4 = b.y2;
int d = (y2 - y1) * (x4 - x3) - (x2 - x1) * (y4 - y3);
if (d == 0) {
return false;
}
double t = ((x3 - x1) * (y4 - y3) - (y3 - y1) * (x4 - x3)) / (double)d;
double u = ((x2 - x1) * (y3 - y1) - (y2 - y1) * (x3 - x1)) / (double)d;
if (t >= 0 && t <= 1 && u >= 0 && u <= 1) {
return true;
}
return false;
}
vector<LineSegment> merge(vector<LineSegment>& left, vector<LineSegment>& right) {
vector<LineSegment> result;
int i = 0, j = 0;
while (i < left.size() && j < right.size()) {
if (left[i].x2 < right[j].x1) {
i++;
} else if (right[j].x2 < left[i].x1) {
j++;
} else {
if (isIntersecting(left[i], right[j])) {
result.push_back(left[i]);
result.push_back(right[j]);
}
if (left[i].x2 < right[j].x2) {
i++;
} else {
j++;
}
}
}
return result;
}
vector<LineSegment> findIntersectingSegments(vector<LineSegment>& segments) {
if (segments.size() <= 1) {
return {};
}
int mid = segments.size() / 2;
vector<LineSegment> left(segments.begin(), segments.begin() + mid);
vector<LineSegment> right(segments.begin() + mid, segments.end());
vector<LineSegment> leftIntersecting = findIntersectingSegments(left);
vector<LineSegment> rightIntersecting = findIntersectingSegments(right);
vector<LineSegment> intersecting = merge(left, right);
intersecting.insert(intersecting.end(), leftIntersecting.begin(), leftIntersecting.end());
intersecting.insert(intersecting.end(), rightIntersecting.begin(), rightIntersecting.end());
return intersecting;
}
int main() {
vector<LineSegment> segments = {{0, 0, 1, 1}, {1, 0, 0, 1}, {0, 0, 0, 1}, {0, 1, 1, 1}};
vector<LineSegment> intersectingSegments = findIntersectingSegments(segments);
cout << "Intersecting segments:" << endl;
for (auto segment : intersectingSegments) {
cout << "(" << segment.x1 << "," << segment.y1 << ") - (" << segment.x2 << "," << segment.y2 << ")" << endl;
}
return 0;
}
```
该函数使用递归的方式实现分治算法。在每一次递归中,将线段数组分成两部分,分别递归求解,并将两部分的结果合并。合并时,先将两个子问题的结果合并,并对跨越两个子问题的线段进行相交检查。具体的实现中,merge 函数用于合并两个有序线段数组,并进行相交检查。findIntersectingSegments 函数用于递归求解。当线段数组大小小于等于 1 时,直接返回空数组。
该算法的时间复杂度为 $O(n \log^2 n)$,其中 $n$ 是线段的数量。
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