From 574a7c3471a72845fb43edf124ce3531e6ceb833 Mon Sep 17 00:00:00 2001
From: arnabuchiha <arnabkeya04@gmail.com>
Date: Mon, 5 Oct 2020 14:18:07 +0530
Subject: [PATCH] Fixes: #{413} Implemented Convex Hull using Graham Scan

---
 Geometry/ConvexHullGraham.js | 82 ++++++++++++++++++++++++++++++++++++
 package.json                 |  4 +-
 2 files changed, 85 insertions(+), 1 deletion(-)
 create mode 100644 Geometry/ConvexHullGraham.js

diff --git a/Geometry/ConvexHullGraham.js b/Geometry/ConvexHullGraham.js
new file mode 100644
index 000000000..304166347
--- /dev/null
+++ b/Geometry/ConvexHullGraham.js
@@ -0,0 +1,82 @@
+/**
+ * Author: Arnab Ray
+ * ConvexHull using Graham Scan
+ * Wikipedia: https://en.wikipedia.org/wiki/Graham_scan
+ * Given a set of points in the plane. The Convex hull of the set is the smallest convex polygon that contains all the points of it.
+ */
+
+function compare (a, b) {
+  // Compare Function to Sort the points, a and b are points to compare
+  if (a.x < b.x) return -1
+  if (a.x === b.x && a.y < b.y) return -1
+  return 1
+}
+function orientation (a, b, c) {
+  // Check orientation of Line(a,b) and Line(b,c)
+  const alpha = (b.y - a.y) / (b.x - a.x)
+  const beta = (c.y - b.y) / (c.x - b.x)
+
+  // Clockwise
+  if (alpha > beta) return 1
+  // Anticlockwise
+  else if (beta > alpha) return -1
+  // Colinear
+  return 0
+}
+
+function convexHull (points) {
+  const pointsLen = points.length
+  if (pointsLen <= 2) {
+    console.log('Minimum of 3 points is required to form closed polygon!')
+  }
+
+  points.sort(compare)
+  const p1 = points[0]; const p2 = points[pointsLen - 1]
+
+  // Divide Hull in two halfs
+  const upperPoints = []; const lowerPoints = []
+
+  upperPoints.push(p1)
+  lowerPoints.push(p1)
+
+  for (let i = 1; i < pointsLen; i++) {
+    if (i === pointsLen - 1 || orientation(p1, points[i], p2) !== -1) {
+      let upLen = upperPoints.length
+
+      while (upLen >= 2 && orientation(upperPoints[upLen - 2], upperPoints[upLen - 1], points[i]) === -1) {
+        upperPoints.pop()
+        upLen = upperPoints.length
+      }
+      upperPoints.push(points[i])
+    }
+    if (i === pointsLen - 1 || orientation(p1, points[i], p2) !== 1) {
+      let lowLen = lowerPoints.length
+      while (lowLen >= 2 && orientation(lowerPoints[lowLen - 2], lowerPoints[lowLen - 1], points[i]) === 1) {
+        lowerPoints.pop()
+        lowLen = lowerPoints.length
+      }
+      lowerPoints.push(points[i])
+    }
+  }
+  const hull = []
+  for (let i = 1; i < upperPoints.length - 1; i++) {
+    hull.push(upperPoints[i])
+  }
+  for (let i = lowerPoints.length - 1; i >= 0; i--) {
+    hull.push(lowerPoints[i])
+  }
+  console.log('The Convex Hull found is: \n')
+  console.log(hull)
+}
+
+const points = [
+  { x: 0, y: 3 },
+  { x: 1, y: 1 },
+  { x: 2, y: 2 },
+  { x: 4, y: 4 },
+  { x: 0, y: 0 },
+  { x: 1, y: 2 },
+  { x: 3, y: 1 },
+  { x: 3, y: 3 }]
+
+convexHull(points)
diff --git a/package.json b/package.json
index eea349d1b..450a58349 100644
--- a/package.json
+++ b/package.json
@@ -16,7 +16,9 @@
     "node-fetch": "2.6.1"
   },
   "standard": {
-    "env": [ "jest" ]
+    "env": [
+      "jest"
+    ]
   },
   "devDependencies": {
     "babel-jest": "^26.3.0",