62 lines
2.0 KiB
C++
62 lines
2.0 KiB
C++
#include <algorithm>
|
|
#include <vector>
|
|
|
|
/**
|
|
* 587. Erect the Fence
|
|
* You are given an array trees where trees[i] = [xi, yi] represents the location of a tree in the garden.
|
|
* You are asked to fence the entire garden using the minimum length of rope as it is expensive. The garden is well fenced only if all the trees are enclosed.
|
|
* Return the coordinates of trees that are exactly located on the fence perimeter.
|
|
*
|
|
* Note: it is all about computing the convex hull.
|
|
*/
|
|
|
|
class Solution {
|
|
public:
|
|
static std::vector<std::vector<int>> outerTrees(std::vector<std::vector<int>>& trees) {
|
|
std::sort(trees.begin(), trees.end(), [](const std::vector<int>& x, const std::vector<int>& y) { return x[0] == y[0] ? x[1] < y[1] : x[0] < y[0]; });
|
|
int n = trees.size();
|
|
std::vector<std::vector<int>> top, bottom;
|
|
|
|
auto CrossProduct = [](const std::pair<int, int>& x, const std::pair<int, int>& y) {
|
|
// x, y are vectors
|
|
return x.first * y.second - x.second * y.first;
|
|
};
|
|
|
|
std::for_each(trees.cbegin(), trees.cend(), [&](const std::vector<int>& p) {
|
|
while (bottom.size() > 1 && [&](){
|
|
int n = bottom.size();
|
|
const auto& b1 = bottom[n - 1];
|
|
const auto& b2 = bottom[n - 2];
|
|
return CrossProduct({b1[0] - b2[0], b1[1] - b2[1]}, {p[0] - b1[0], p[1] - b1[1]}) < 0;
|
|
}()) bottom.pop_back();
|
|
bottom.push_back(p);
|
|
});
|
|
|
|
std::for_each(trees.crbegin(), trees.crend(), [&](const std::vector<int>& p) {
|
|
while (top.size() > 1 && [&](){
|
|
int n = top.size();
|
|
const auto& b1 = top[n - 1];
|
|
const auto& b2 = top[n - 2];
|
|
return CrossProduct({b1[0] - b2[0], b1[1] - b2[1]}, {p[0] - b1[0], p[1] - b1[1]}) < 0;
|
|
}()) top.pop_back();
|
|
top.push_back(p);
|
|
});
|
|
|
|
std::vector<std::vector<int>> ret;
|
|
bool x[65536]{};
|
|
for (const auto& p : top) {
|
|
if (x[(p[0] << 8) | p[1]])
|
|
continue;
|
|
x[(p[0] << 8) | p[1]] = true;
|
|
ret.push_back(p);
|
|
}
|
|
for (const auto& p : bottom) {
|
|
if (x[(p[0] << 8) | p[1]])
|
|
continue;
|
|
x[(p[0] << 8) | p[1]] = true;
|
|
ret.push_back(p);
|
|
}
|
|
return ret;
|
|
}
|
|
};
|