From 20df0aa1edab2daa0661cab2a3f8b9d10a715f26 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?S=C3=A1ndor=20Dar=C3=B3czi?=
 <83545679+daroczisandor@users.noreply.github.com>
Date: Tue, 23 Nov 2021 00:13:19 +0100
Subject: [PATCH] Create solution.cpp

---
 Codechef/2-D Point Meeting/solution.cpp | 263 ++++++++++++++++++++++++
 1 file changed, 263 insertions(+)
 create mode 100644 Codechef/2-D Point Meeting/solution.cpp

diff --git a/Codechef/2-D Point Meeting/solution.cpp b/Codechef/2-D Point Meeting/solution.cpp
new file mode 100644
index 0000000..559751c
--- /dev/null
+++ b/Codechef/2-D Point Meeting/solution.cpp	
@@ -0,0 +1,263 @@
+#include <iostream>
+#include <bits/stdc++.h>
+
+#define ll long long
+
+using namespace std;
+
+int root(int k) {
+    int sq = floor(sqrt((float)(1+8*k)));
+    return (1+sq)/2;
+}
+
+bool on_line(ll x1, ll y1, ll x2, ll y2, int dir) {
+    if (dir == 1) return (y1 == y2);
+    if (dir == 2) return (x1 == x2);
+    if (dir == 3) return (x2-x1 == y2-y1);
+    if (dir == 4) return (x1+y1 == x2+y2);
+}
+
+pair<ll,ll> intersection(ll x1, ll y1, int dir1, ll x2, ll y2, int dir2) {
+
+    ll p1, p2, q1, q2, r1, r2;
+
+    switch(dir1) {
+        case 1:
+            p1 = 0; q1 = 1;
+            break;
+        case 2:
+            p1 = 1; q1 = 0;
+            break;
+        case 3:
+            p1 = 1; q1 = -1;
+            break;
+        case 4:
+            p1 = 1; q1 = 1;
+    }
+
+    switch(dir2) {
+        case 1:
+            p2 = 0; q2 = 1;
+            break;
+        case 2:
+            p2 = 1; q2 = 0;
+            break;
+        case 3:
+            p2 = 1; q2 = -1;
+            break;
+        case 4:
+            p2 = 1; q2 = 1;
+    }
+
+    r1 = p1*x1 + q1*y1;
+    r2 = p2*x2 + q2*y2;
+
+    ll x = (q2*r1 - q1*r2)/(p1*q2 - p2*q1);
+    ll y = (p1*r2 - p2*r1)/(p1*q2 - p2*q1);
+
+    return {x,y};
+
+}
+
+int main()
+{
+
+    int t;
+    cin >> t;
+
+    while(t--) {
+
+        int n;
+        cin >> n;
+
+//        auto p = intersection(0,0,3,4,2,1);
+//        cout << "int: " << p.first << " " << p.second << "\n";
+
+        map<pair<pair<ll,ll>, int>, set<pair<ll,ll>>> line_to_normal_points;
+        map<pair<pair<ll,ll>, int>, set<pair<ll,ll>>> line_to_all_points;
+        map<pair<ll,ll>, int> scores;
+        set<pair<ll,ll>> points;
+        vector<pair<pair<ll,ll>, int>> lines;
+
+        ll x[n], y[n];
+        for (int i = 0; i<n; i++) {
+            int c;
+            cin >> c;
+            x[i] = 2*c;
+        }
+        for (int i = 0; i<n; i++) {
+            int c;
+            cin >> c;
+            y[i] = 2*c;
+        }
+
+        for (int i = 0; i<n; i++) {
+            scores[{x[i], y[i]}]++;
+            scores[{x[i], y[i]}]++;
+            points.insert({x[i],y[i]});
+        }
+
+        for (int i = 0; i<n; i++) {
+            for (int dir = 1; dir <= 4; dir++) {
+                ll x1 = x[i];
+                ll y1 = y[i];
+                bool ok = true;
+                for (auto line : lines) {
+                    int dir2 = line.second;
+                    auto p = line.first;
+                    ll x2 = p.first;
+                    ll y2 = p.second;
+
+                    if (dir == dir2 && on_line(x1, y1, x2, y2, dir)) {
+                        ok = false;
+                        break;
+                    }
+
+                }
+
+                if (ok) {
+                    lines.push_back({{x1,y1},dir});
+                }
+            }
+        }
+
+        int line_len = lines.size();
+//        cout << "line_len: " << line_len << "\n";
+//        for (auto line : lines) {
+//            auto p = line.first;
+//            ll x1 = p.first;
+//            ll y1 = p.second;
+//
+//            cout << "line: " << x1 << " " << y1 << " " << line.second << "\n";
+//
+//        }
+
+        for (int i = 0; i<line_len-1; i++) {
+
+            auto line1 = lines[i];
+            auto p1 = line1.first;
+            ll x1 = p1.first;
+            ll y1 = p1.second;
+            int dir1 = line1.second;
+
+            for (int j = i+1; j<line_len; j++) {
+
+                auto line2 = lines[j];
+                auto p2 = line2.first;
+                ll x2 = p2.first;
+                ll y2 = p2.second;
+                int dir2 = line2.second;
+
+                if (dir1 == dir2) continue;
+                auto p = intersection(x1, y1, dir1, x2, y2, dir2);
+                ll x0 = p.first;
+                ll y0 = p.second;
+
+//                cout << "intersection: " << x0 << " " << y0 << "\n";
+//                cout << "line1: " << x1 << " " << y1 << " " << dir1 << "\n";
+//                cout << "line2: " << x2 << " " << y2 << " " << dir2 << "\n";
+
+                line_to_all_points[line1].insert({x0, y0});
+                line_to_all_points[line2].insert({x0, y0});
+
+            }
+        }
+
+        for (auto line : lines) {
+            auto p = line.first;
+            ll x1 = p.first;
+            ll y1 = p.second;
+            int dir = line.second;
+
+            for (int j = 0; j<n; j++) {
+                ll x2 = x[j];
+                ll y2 = y[j];
+
+                if (on_line(x1, y1, x2, y2, dir)) {
+                    line_to_all_points[{{x1, y1}, dir}].insert({x2, y2});
+                    line_to_normal_points[{{x1, y1}, dir}].insert({x2, y2});
+                }
+
+            }
+
+        }
+
+//        for (auto it = line_to_all_points.begin(); it != line_to_all_points.end(); ++it) {
+//
+//            auto line = (it->first);
+//            auto p = line.first;
+//            int dir = line.second;
+//            auto s = (it->second);
+//
+//            cout << "line_to_all_points: \n";
+//
+//            cout << "line: " << p.first << " " << p.second << " " << dir << "\n";
+//            cout << "points: \n";
+//            for (auto elem : s) {
+//                cout << elem.first << " " << elem.second << "\n";
+//            }
+//
+//
+//        }
+
+//        for (auto it = line_to_normal_points.begin(); it != line_to_normal_points.end(); ++it) {
+//
+//            auto line = (it->first);
+//            auto p = line.first;
+//            int dir = line.second;
+//            auto s = (it->second);
+//
+//            cout << "line_to_normal_points: \n";
+//
+//            cout << "line: " << p.first << " " << p.second << " " << dir << "\n";
+//            cout << "points: \n";
+//            for (auto elem : s) {
+//                cout << elem.first << " " << elem.second << "\n";
+//            }
+//
+//
+//        }
+
+        for (auto it = line_to_normal_points.begin(); it != line_to_normal_points.end(); ++it) {
+
+            auto line = (it->first);
+            auto s0 = (it->second);
+            int sz = s0.size();
+
+            //cout << "line: " << (line.first).first << " " << (line.first).second << " " << line.second << " size: " << sz << "\n";
+
+            auto s = line_to_all_points[line];
+            for (auto it2 = s.begin(); it2 != s.end(); ++it2) {
+
+                auto p = *it2;
+
+                scores[p] += sz;
+
+                if (points.find(p) != points.end()) {
+                    scores[p]--;
+                }
+
+//                if (p.first == 0 && p.second == 1) cout << "pair 0 1: line: " << (line.first).first << " " << (line.first).second << " " << line.second << " size: " << sz << "\n";
+
+            }
+
+        }
+
+        int mx = 0;
+        for (auto it = scores.begin(); it != scores.end(); ++it) {
+
+            int val = (it->second);
+//            cout << "point: " << (it->first).first << " " << (it->first).second << " val: " << val << "\n";
+            if (val > mx) mx = val;
+
+        }
+
+        cout << 2*n-mx << "\n";
+
+
+
+
+    }
+
+    return 0;
+}