From caaaaa38905f89326c962a02f4e57c494c655df4 Mon Sep 17 00:00:00 2001
From: Kotecha Udit Hitendra <64374551+kirito-udit@users.noreply.github.com>
Date: Sat, 2 Oct 2021 20:11:17 +0530
Subject: [PATCH] Create Grahams-scan-convex-hull.cpp

---
 Algorithms/Grahams-scan-convex-hull.cpp | 44 +++++++++++++++++++++++++
 1 file changed, 44 insertions(+)
 create mode 100644 Algorithms/Grahams-scan-convex-hull.cpp

diff --git a/Algorithms/Grahams-scan-convex-hull.cpp b/Algorithms/Grahams-scan-convex-hull.cpp
new file mode 100644
index 0000000..018ef85
--- /dev/null
+++ b/Algorithms/Grahams-scan-convex-hull.cpp
@@ -0,0 +1,44 @@
+struct pt {
+    double x, y;
+};
+
+bool cmp(pt a, pt b) {
+    return a.x < b.x || (a.x == b.x && a.y < b.y);
+}
+
+bool cw(pt a, pt b, pt c) {
+    return a.x*(b.y-c.y)+b.x*(c.y-a.y)+c.x*(a.y-b.y) < 0;
+}
+
+bool ccw(pt a, pt b, pt c) {
+    return a.x*(b.y-c.y)+b.x*(c.y-a.y)+c.x*(a.y-b.y) > 0;
+}
+
+void convex_hull(vector<pt>& a) {
+    if (a.size() == 1)
+        return;
+
+    sort(a.begin(), a.end(), &cmp);
+    pt p1 = a[0], p2 = a.back();
+    vector<pt> up, down;
+    up.push_back(p1);
+    down.push_back(p1);
+    for (int i = 1; i < (int)a.size(); i++) {
+        if (i == a.size() - 1 || cw(p1, a[i], p2)) {
+            while (up.size() >= 2 && !cw(up[up.size()-2], up[up.size()-1], a[i]))
+                up.pop_back();
+            up.push_back(a[i]);
+        }
+        if (i == a.size() - 1 || ccw(p1, a[i], p2)) {
+            while(down.size() >= 2 && !ccw(down[down.size()-2], down[down.size()-1], a[i]))
+                down.pop_back();
+            down.push_back(a[i]);
+        }
+    }
+
+    a.clear();
+    for (int i = 0; i < (int)up.size(); i++)
+        a.push_back(up[i]);
+    for (int i = down.size() - 2; i > 0; i--)
+        a.push_back(down[i]);
+}