// competitive-verifier: PROBLEM https://yukicoder.me/problems/no/2909
// competitive-verifier: ERROR 1e-5
#include "DataStructure/kd_tree.hpp"
#include <bits/stdc++.h>
using namespace std;
int main()
{
int N, M, K;
cin >> N >> M >> K;
long double P, Q;
cin >> P >> Q;
vector<array<long double, 2>> stations(N);
for (int i = 0; i < N; i++)
{
cin >> stations[i][0] >> stations[i][1];
}
vector<array<long double, 2>> targets(K);
for (int i = 0; i < K; i++)
{
cin >> targets[i][0] >> targets[i][1];
}
long double V;
cin >> V;
vector<array<int, 2>> ST(M);
for (int i = 0; i < M; i++)
{
cin >> ST[i][0] >> ST[i][1];
ST[i][0]--, ST[i][1]--;
}
KDTree<long double, 2> kd_tree(stations);
long double ans = 0;
for (auto target : targets)
{
// 直接目的地に行く
long double dist1 = hypotl(P - target[0], Q - target[1]);
// 駅を使って移動する
long double sub_dis1;
auto point1 = kd_tree.nearest({P, Q}).value();
long double sub_dist1 = hypotl(P - point1.point[0], Q - point1.point[1]);
auto point2 = kd_tree.nearest(target).value();
long double sub_dist2 = hypotl(target[0] - point2.point[0], target[1] - point2.point[1]);
long double dist2 = sub_dist1 + sub_dist2;
ans += min(dist1, dist2) * 2;
}
cout << fixed << setprecision(15) << ans << endl;
return 0;
}
#line 1 "test/DataStructure/kd-tree/yukicoder-2909.cpp"
// competitive-verifier: PROBLEM https://yukicoder.me/problems/no/2909
// competitive-verifier: ERROR 1e-5
#line 1 "DataStructure/kd_tree.hpp"
#include <bits/stdc++.h>
using namespace std;
template <typename T, size_t K>
class KDTree
{
public:
// 座標と id をまとめた構造体
struct PointWithID
{
array<T, K> point;
size_t id;
};
// ノードは PointWithID の情報を持つ
struct Node
{
PointWithID data;
Node *left;
Node *right;
Node(const PointWithID &pwid)
: data(pwid), left(nullptr), right(nullptr) {}
};
// コンストラクタ: 点群から kd 木を構築
KDTree(const vector<array<T, K>> &points)
{
vector<PointWithID> pts;
pts.reserve(points.size());
for (size_t i = 0; i < points.size(); ++i)
{
pts.push_back({points[i], i});
}
root = build(pts.begin(), pts.end(), 0);
}
~KDTree()
{
free_tree(root);
}
optional<PointWithID> nearest(const array<T, K> &target,
function<bool(int)> check) const
{
Node *best = nullptr;
T bestDist = numeric_limits<T>::max();
nearest_search(root, target, 0, best, bestDist, check);
if (best)
return best->data;
else
return nullopt;
}
optional<PointWithID> nearest(const array<T, K> &target) const
{
return nearest(target, [](int)
{ return true; });
}
vector<PointWithID> range_search(const array<T, K> &lower, const array<T, K> &upper,
function<bool(int)> check) const
{
vector<PointWithID> results;
range_search(root, 0, lower, upper, check, results);
return results;
}
vector<PointWithID> range_search(const array<T, K> &lower, const array<T, K> &upper) const
{
return range_search(lower, upper, [](int)
{ return true; });
}
/// target から近いものを最大 k 個返す（check で絞り込み可）
vector<PointWithID> nearest_k(const array<T, K> &target, size_t k, function<bool(int)> check) const
{
if (k == 0 || root == nullptr)
{
return {};
}
MaxHeap pq;
nearest_k_search(root, target, 0, k, check, pq);
vector<PointWithID> res;
res.reserve(pq.size());
while (!pq.empty())
{
res.push_back(pq.top().second->data);
pq.pop();
}
reverse(res.begin(), res.end());
return res;
}
vector<PointWithID> nearest_k(const array<T, K> &target, size_t k) const
{
return nearest_k(target, k, [](int)
{ return true; });
}
private:
using iterator = typename vector<PointWithID>::iterator;
Node *root = nullptr;
// kd木の構築 (中央値による分割)
Node *build(iterator begin, iterator end, size_t depth)
{
if (begin >= end)
return nullptr;
size_t axis = depth % K;
iterator mid = begin + distance(begin, end) / 2;
nth_element(begin, mid, end, [axis](const PointWithID &a, const PointWithID &b)
{ return a.point[axis] < b.point[axis]; });
Node *node = new Node(*mid);
node->left = build(begin, mid, depth + 1);
node->right = build(mid + 1, end, depth + 1);
return node;
}
// 再帰的な最近傍探索
void nearest_search(Node *node, const array<T, K> &target, size_t depth,
Node *&best, T &bestDist, function<bool(int)> check) const
{
if (node == nullptr)
return;
size_t axis = depth % K;
T d = distance_squared(node->data.point, target);
if (d < bestDist && check(static_cast<int>(node->data.id)))
{
bestDist = d;
best = node;
}
T diff = target[axis] - node->data.point[axis];
Node *nearChild = (diff < 0) ? node->left : node->right;
Node *farChild = (diff < 0) ? node->right : node->left;
nearest_search(nearChild, target, depth + 1, best, bestDist, check);
if (diff * diff < bestDist)
nearest_search(farChild, target, depth + 1, best, bestDist, check);
}
// 再帰的な範囲探索
void range_search(Node *node, size_t depth,
const array<T, K> &lower, const array<T, K> &upper,
function<bool(int)> check, vector<PointWithID> &results) const
{
if (node == nullptr)
return;
bool inside = true;
for (size_t i = 0; i < K; i++)
{
if (node->data.point[i] < lower[i] || node->data.point[i] > upper[i])
{
inside = false;
break;
}
}
if (inside && check(static_cast<int>(node->data.id)))
results.push_back(node->data);
size_t axis = depth % K;
if (lower[axis] <= node->data.point[axis])
range_search(node->left, depth + 1, lower, upper, check, results);
if (upper[axis] >= node->data.point[axis])
range_search(node->right, depth + 1, lower, upper, check, results);
}
using QElem = std::pair<T, const Node *>;
struct WorseFirst
{
bool operator()(const QElem &lhs, const QElem &rhs) const
{
return lhs.first < rhs.first;
}
};
using MaxHeap = priority_queue<QElem, vector<QElem>, WorseFirst>;
void nearest_k_search(
const Node *node, const array<T, K> &target,
size_t depth, size_t k,
const function<bool(int)> &check, MaxHeap &pq) const
{
if (node == nullptr)
return;
size_t axis = depth % K;
T dist2 = distance_squared(node->data.point, target);
if (check(static_cast<int>(node->data.id)))
{
if (pq.size() < k)
{
pq.emplace(dist2, node);
}
else if (dist2 < pq.top().first)
{
pq.pop();
pq.emplace(dist2, node);
}
}
T diff = target[axis] - node->data.point[axis];
const Node *nearChild = (diff < 0) ? node->left : node->right;
const Node *farChild = (diff < 0) ? node->right : node->left;
nearest_k_search(nearChild, target, depth + 1, k, check, pq);
if (pq.size() < k || diff * diff < pq.top().first)
{
nearest_k_search(farChild, target, depth + 1, k, check, pq);
}
}
// 2点間の二乗距離を計算
T distance_squared(const array<T, K> &a, const array<T, K> &b) const
{
T dist = 0;
for (size_t i = 0; i < K; i++)
{
T d = a[i] - b[i];
dist += d * d;
}
return dist;
}
// kd木のメモリ解放
void free_tree(Node *node)
{
if (node == nullptr)
return;
free_tree(node->left);
free_tree(node->right);
delete node;
}
};
#line 6 "test/DataStructure/kd-tree/yukicoder-2909.cpp"
using namespace std;
int main()
{
int N, M, K;
cin >> N >> M >> K;
long double P, Q;
cin >> P >> Q;
vector<array<long double, 2>> stations(N);
for (int i = 0; i < N; i++)
{
cin >> stations[i][0] >> stations[i][1];
}
vector<array<long double, 2>> targets(K);
for (int i = 0; i < K; i++)
{
cin >> targets[i][0] >> targets[i][1];
}
long double V;
cin >> V;
vector<array<int, 2>> ST(M);
for (int i = 0; i < M; i++)
{
cin >> ST[i][0] >> ST[i][1];
ST[i][0]--, ST[i][1]--;
}
KDTree<long double, 2> kd_tree(stations);
long double ans = 0;
for (auto target : targets)
{
// 直接目的地に行く
long double dist1 = hypotl(P - target[0], Q - target[1]);
// 駅を使って移動する
long double sub_dis1;
auto point1 = kd_tree.nearest({P, Q}).value();
long double sub_dist1 = hypotl(P - point1.point[0], Q - point1.point[1]);
auto point2 = kd_tree.nearest(target).value();
long double sub_dist2 = hypotl(target[0] - point2.point[0], target[1] - point2.point[1]);
long double dist2 = sub_dist1 + sub_dist2;
ans += min(dist1, dist2) * 2;
}
cout << fixed << setprecision(15) << ans << endl;
return 0;
}
test/DataStructure/kd-tree/yukicoder-2909.cpp