graham scan convux hull

Author: jeffin143

Math/convuxhull/grahamscan.cpp

@@ -0,0 +1,161 @@
+#include <iostream> 
+#include <stack> 
+#include <stdlib.h> 
+using namespace std; 
+  
+struct Point 
+{ 
+    int x, y; 
+}; 
+  
+// A globle point needed for  sorting points with reference 
+// to  the first point Used in compare function of qsort() 
+Point p0; 
+  
+// A utility function to find next to top in a stack 
+Point nextToTop(stack<Point> &S) 
+{ 
+    Point p = S.top(); 
+    S.pop(); 
+    Point res = S.top(); 
+    S.push(p); 
+    return res; 
+} 
+  
+// A utility function to swap two points 
+int swap(Point &p1, Point &p2) 
+{ 
+    Point temp = p1; 
+    p1 = p2; 
+    p2 = temp; 
+} 
+  
+// A utility function to return square of distance 
+// between p1 and p2 
+int distSq(Point p1, Point p2) 
+{ 
+    return (p1.x - p2.x)*(p1.x - p2.x) + 
+          (p1.y - p2.y)*(p1.y - p2.y); 
+} 
+  
+// To find orientation of ordered triplet (p, q, r). 
+// The function returns following values 
+// 0 --> p, q and r are colinear 
+// 1 --> Clockwise 
+// 2 --> Counterclockwise 
+int orientation(Point p, Point q, Point r) 
+{ 
+    int val = (q.y - p.y) * (r.x - q.x) - 
+              (q.x - p.x) * (r.y - q.y); 
+  
+    if (val == 0) return 0;  // colinear 
+    return (val > 0)? 1: 2; // clock or counterclock wise 
+} 
+  
+// A function used by library function qsort() to sort an array of 
+// points with respect to the first point 
+int compare(const void *vp1, const void *vp2) 
+{ 
+   Point *p1 = (Point *)vp1; 
+   Point *p2 = (Point *)vp2; 
+  
+   // Find orientation 
+   int o = orientation(p0, *p1, *p2); 
+   if (o == 0) 
+     return (distSq(p0, *p2) >= distSq(p0, *p1))? -1 : 1; 
+  
+   return (o == 2)? -1: 1; 
+} 
+  
+// Prints convex hull of a set of n points. 
+void convexHull(Point points[], int n) 
+{ 
+   // Find the bottommost point 
+   int ymin = points[0].y, min = 0; 
+   for (int i = 1; i < n; i++) 
+   { 
+     int y = points[i].y; 
+  
+     // Pick the bottom-most or chose the left 
+     // most point in case of tie 
+     if ((y < ymin) || (ymin == y && 
+         points[i].x < points[min].x)) 
+        ymin = points[i].y, min = i; 
+   } 
+  
+   // Place the bottom-most point at first position 
+   swap(points[0], points[min]); 
+  
+   // Sort n-1 points with respect to the first point. 
+   // A point p1 comes before p2 in sorted ouput if p2 
+   // has larger polar angle (in counterclockwise 
+   // direction) than p1 
+   p0 = points[0]; 
+   qsort(&points[1], n-1, sizeof(Point), compare); 
+  
+   // If two or more points make same angle with p0, 
+   // Remove all but the one that is farthest from p0 
+   // Remember that, in above sorting, our criteria was 
+   // to keep the farthest point at the end when more than 
+   // one points have same angle. 
+   int m = 1; // Initialize size of modified array 
+   for (int i=1; i<n; i++) 
+   { 
+       // Keep removing i while angle of i and i+1 is same 
+       // with respect to p0 
+       while (i < n-1 && orientation(p0, points[i], 
+                                    points[i+1]) == 0) 
+          i++; 
+  
+  
+       points[m] = points[i]; 
+       m++;  // Update size of modified array 
+   } 
+  
+   // If modified array of points has less than 3 points, 
+   // convex hull is not possible 
+   if (m < 3) return; 
+  
+   // Create an empty stack and push first three points 
+   // to it. 
+   stack<Point> S; 
+   S.push(points[0]); 
+   S.push(points[1]); 
+   S.push(points[2]); 
+  
+   // Process remaining n-3 points 
+   for (int i = 3; i < m; i++) 
+   { 
+      // Keep removing top while the angle formed by 
+      // points next-to-top, top, and points[i] makes 
+      // a non-left turn 
+      while (orientation(nextToTop(S), S.top(), points[i]) != 2) 
+         S.pop(); 
+      S.push(points[i]); 
+   } 
+  
+   // Now stack has the output points, print contents of stack 
+   while (!S.empty()) 
+   { 
+       Point p = S.top(); 
+       cout << "(" << p.x << ", " << p.y <<")" << endl; 
+       S.pop(); 
+   } 
+} 
+  
+int main() 
+{ 
+    Point points[] = {{0, 3}, {1, 1}, {2, 2}, {4, 4}, 
+                      {0, 0}, {1, 2}, {3, 1}, {3, 3}}; 
+    int n = sizeof(points)/sizeof(points[0]); 
+    convexHull(points, n); 
+    return 0; 
+} 
+
+/*
+(0, 3)
+(4, 4)
+(3, 1)
+(0, 0) 
+
+*/