From 367c0bef37a7b46168829197c19e9d3cb2ea8be7 Mon Sep 17 00:00:00 2001
From: subcrip <contact@subc.rip>
Date: Sat, 9 Nov 2024 18:58:46 +0800
Subject: [PATCH] Add geometry/convex_hull.cc

Signed-off-by: subcrip <contact@subc.rip>
---
 geometry/convex_hull.cc | 38 ++++++++++++++++++++++++++++++++++++++
 1 file changed, 38 insertions(+)
 create mode 100644 geometry/convex_hull.cc

diff --git a/geometry/convex_hull.cc b/geometry/convex_hull.cc
new file mode 100644
index 0000000..dffc9c8
--- /dev/null
+++ b/geometry/convex_hull.cc
@@ -0,0 +1,38 @@
+struct convex_hull {
+    int n, m;
+    vector<int> on_hull;
+    // WARN: counter-clockwise
+    vector<int> hull;
+
+    // WARN: sort the points before initializing
+    template <typename T>
+    convex_hull(const vector<point<T>>& a) : n(a.size()), on_hull(n) {
+        for (int i = 0; i < n; ++i) {
+            int m = hull.size();
+            // WARN: keeping the points that are on edges
+            while (m > 1 and (a[hull[m - 1]] - a[hull[m - 2]]) * (a[i] - a[hull[m - 2]]) < 0) {
+                on_hull[hull[m - 1]] -= 1;
+                hull.pop_back();
+                m -= 1;
+            }
+            on_hull[i] += 1;
+            hull.emplace_back(i);
+        }
+        int low = hull.size();
+
+        for (int i = n - 2; ~i; --i) {
+            int m = hull.size();
+            while (m > low and (a[hull[m - 1]] - a[hull[m - 2]]) * (a[i] - a[hull[m - 2]]) < 0) {
+                on_hull[hull[m - 1]] -= 1;
+                hull.pop_back();
+                m -= 1;
+            }
+            on_hull[i] += 1;
+            hull.emplace_back(i);
+        }
+        if (n > 1) {
+            hull.pop_back();
+        }
+        m = hull.size();
+    }
+};