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Split point.hpp
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6 files changed

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‎cp-algo/geometry/all

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#ifndef CP_ALGO_GEOMETRY_ALL
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#define CP_ALGO_GEOMETRY_ALL
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#include "point.hpp"
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#include "convex_hull.hpp"
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#include "closest_pair.hpp"
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#endif // CP_ALGO_GEOMETRY_ALL

‎cp-algo/geometry/closest_pair.hpp

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#ifndef CP_ALGO_GEOMETRY_CLOSEST_PAIR_HPP
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#define CP_ALGO_GEOMETRY_CLOSEST_PAIR_HPP
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#include "../random/rng.hpp"
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#include "point.hpp"
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#include <vector>
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#include <map>
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namespace cp_algo::geometry {
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// Rabin & Lipton
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template<typename ftype>
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auto closest_pair(std::vector<point_t<ftype>> const& r) {
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using point = point_t<ftype>;
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size_t n = size(r);
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int64_t md = 1e18;
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for(size_t i = 0; i < n / 100; i++) {
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auto A = random::rng() % n;
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auto B = random::rng() % n;
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if(A != B) {
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md = std::min(md, norm(r[A] - r[B]));
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if(md == 0) {
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return std::pair{A, B};
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}
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}
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}
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std::map<point, std::vector<int>> neigs;
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md = ceil(sqrtl(md));
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for(size_t i = 0; i < n; i++) {
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neigs[r[i] / md].push_back(i);
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}
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size_t a = 0, b = 1;
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md = norm(r[a] - r[b]);
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for(auto &[p, id]: neigs) {
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for(int dx: {-1, 0, 1}) {
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for(int dy: {-1, 0, 1}) {
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auto pp = p + point{dx, dy};
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if(!neigs.count(pp)) {
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continue;
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}
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for(size_t i: neigs[p + point{dx, dy}]) {
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for(size_t j: id) {
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if(j == i) {
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break;
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}
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int64_t cur = norm(r[i] - r[j]);
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if(cur < md) {
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md = cur;
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a = i;
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b = j;
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}
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}
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}
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}
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}
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}
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return std::pair{a, b};
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}
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}
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#endif // CP_ALGO_GEOMETRY_CLOSEST_PAIR_HPP

‎cp-algo/geometry/convex_hull.hpp

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#ifndef CP_ALGO_GEOMETRY_CONVEX_HULL_HPP
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#define CP_ALGO_GEOMETRY_CONVEX_HULL_HPP
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#include "point.hpp"
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#include <algorithm>
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#include <utility>
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#include <vector>
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#include <ranges>
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namespace cp_algo::geometry {
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template<typename ftype>
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std::vector<point_t<ftype>> convex_hull(std::vector<point_t<ftype>> r) {
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using point = point_t<ftype>;
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std::ranges::sort(r);
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if(size(r) <= 1 || r[0] == r.back()) {
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return empty(r) ? r : std::vector{r[0]};
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}
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std::vector<point> hull = {r[0]};
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for(int half: {0, 1}) {
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size_t base = size(hull);
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for(auto it: std::views::drop(r, 1)) {
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while(size(hull) >= base + 1) {
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point a = hull.back();
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if(point::ccw(it - a, *(end(hull) - 2) - a)) {
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break;
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} else {
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hull.pop_back();
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}
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}
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hull.push_back(it);
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}
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std::ranges::reverse(r);
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std::ignore = half;
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}
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hull.pop_back();
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return hull;
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}
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}
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#endif // CP_ALGO_GEOMETRY_CONVEX_HULL_HPP

‎cp-algo/geometry/point.hpp

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#ifndef CP_ALGO_GEOMETRY_POINT_HPP
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#define CP_ALGO_GEOMETRY_POINT_HPP
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#include "../random/rng.hpp"
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#include <algorithm>
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#include <iostream>
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#include <complex>
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#include <utility>
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#include <vector>
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#include <ranges>
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#include <map>
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namespace cp_algo::geometry {
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template<typename ftype>
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struct point_t: public std::complex<ftype> {
@@ -49,80 +44,5 @@ namespace cp_algo::geometry {
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std::cout << x() << ' ' << y() << "\n";
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}
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};
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template<typename point>
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std::vector<point> convex_hull(std::vector<point> r) {
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std::ranges::sort(r);
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if(size(r) <= 1 || r[0] == r.back()) {
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return empty(r) ? r : std::vector{r[0]};
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}
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std::vector<point> hull = {r[0]};
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for(int half: {0, 1}) {
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size_t base = size(hull);
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for(auto it: std::views::drop(r, 1)) {
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while(size(hull) >= base + 1) {
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point a = hull.back();
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if(point::ccw(it - a, *(end(hull) - 2) - a)) {
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break;
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} else {
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hull.pop_back();
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}
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}
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hull.push_back(it);
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}
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std::ranges::reverse(r);
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std::ignore = half;
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}
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hull.pop_back();
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return hull;
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}
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// Rabin & Lipton
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template<typename point>
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auto closest_pair(std::vector<point> const& r) {
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size_t n = size(r);
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int64_t md = 1e18;
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for(size_t i = 0; i < n; i++) {
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auto A = random::rng() % n;
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auto B = random::rng() % n;
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if(A != B) {
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md = std::min(md, norm(r[A] - r[B]));
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if(md == 0) {
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return std::pair{A, B};
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}
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}
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}
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std::map<point, std::vector<int>> neigs;
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md = ceil(sqrtl(md));
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for(size_t i = 0; i < n; i++) {
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neigs[r[i] / md].push_back(i);
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}
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size_t a = 0, b = 1;
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md = norm(r[a] - r[b]);
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for(auto &[p, id]: neigs) {
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for(int dx: {-1, 0, 1}) {
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for(int dy: {-1, 0, 1}) {
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auto pp = p + point{dx, dy};
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if(!neigs.count(pp)) {
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continue;
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}
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for(size_t i: neigs[p + point{dx, dy}]) {
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for(size_t j: id) {
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if(j == i) {
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break;
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}
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int64_t cur = norm(r[i] - r[j]);
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if(cur < md) {
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md = cur;
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a = i;
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b = j;
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}
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}
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}
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}
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}
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}
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return std::pair{a, b};
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}
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}
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#endif // CP_ALGO_GEOMETRY_POINT_HPP

‎verify/geometry/closest_pair.test.cpp

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// @brief Closest Pair of Points
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#define PROBLEM "https://judge.yosupo.jp/problem/closest_pair"
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#pragma GCC optimize("Ofast,unroll-loops")
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#include "cp-algo/geometry/point.hpp"
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#include "cp-algo/geometry/closest_pair.hpp"
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#include <bits/stdc++.h>
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using namespace std;

‎verify/geometry/hull.test.cpp

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#define PROBLEM "https://judge.yosupo.jp/problem/static_convex_hull"
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#pragma GCC optimize("Ofast,unroll-loops")
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#pragma GCC target("tune=native")
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#include "cp-algo/geometry/point.hpp"
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#include "cp-algo/geometry/convex_hull.hpp"
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#include <bits/stdc++.h>
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using namespace std;

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