जार्विस मार्च एल्गोरिथ्म का उपयोग डेटा बिंदुओं के दिए गए सेट से उत्तल पतवार के कोने बिंदुओं का पता लगाने के लिए किया जाता है।
डेटा सेट के सबसे बाएं बिंदु से शुरू करते हुए, हम उत्तल पतवार में बिंदुओं को वामावर्त घुमाकर रखते हैं। वर्तमान बिंदु से, हम वर्तमान बिंदु से उन बिंदुओं के उन्मुखीकरण की जांच करके अगला बिंदु चुन सकते हैं। जब कोण सबसे बड़ा होता है, तो बिंदु चुना जाता है। सभी बिंदुओं को पूरा करने के बाद, जब अगला बिंदु प्रारंभ बिंदु हो, तो एल्गोरिथम को रोकें।
Input: Set of points: {(-7,8), (-4,6), (2,6), (6,4), (8,6), (7,-2), (4,-6), (8,-7),(0,0), (3,-2),(6,-10),(0,-6),(-9,-5),(-8,-2),(-8,0),(-10,3),(-2,2),(-10,4)}
Output: Boundary points of convex hull are:
(-9, -5) (6, -10) (8, -7) (8, 6) (-7, 8) (-10, 4) (-10, 3) एल्गोरिदम
findConvexHull(points, n)
इनपुट :अंक, अंकों की संख्या।
आउटपुट :उत्तल पतवार के कोने बिंदु।
Begin start := points[0] for each point i, do if points[i].x < start.x, then // get the left most point start := points[i] done current := start add start point to the result set. define colPts set to store collinear points while true, do //start an infinite loop next := points[i] for all points i except 0th point, do if points[i] = current, then skip the next part, go for next iteration val := cross product of current, next, points[i] if val > 0, then next := points[i] clear the colPts array else if cal = 0, then if next is closer to current than points[i], then add next in the colPts next := points[i] else add points[i] in the colPts done add all items in the colPts into the result if next = start, then break the loop insert next into the result current := next done return result End
उदाहरण कोड
#include<iostream>
#include<set>
#include<vector>
using namespace std;
struct point { //define points for 2d plane
int x, y;
bool operator==(point p2) {
if(x == p2.x && y == p2.y)
return 1;
return 0;
}
bool operator<(const point &p2)const { //dummy compare function used to sort in set
return true;
}
};
int crossProduct(point a, point b, point c) { //finds the place of c from ab vector
int y1 = a.y - b.y;
int y2 = a.y - c.y;
int x1 = a.x - b.x;
int x2 = a.x - c.x;
return y2*x1 - y1*x2; //if result < 0, c in the left, > 0, c in the right, = 0, a,b,c are collinear
}
int distance(point a, point b, point c) {
int y1 = a.y - b.y;
int y2 = a.y - c.y;
int x1 = a.x - b.x;
int x2 = a.x - c.x;
int item1 = (y1*y1 + x1*x1);
int item2 = (y2*y2 + x2*x2);
if(item1 == item2)
return 0; //when b and c are in same distance from a
else if(item1 < item2)
return -1; //when b is closer to a
return 1; //when c is closer to a
}
set<point> findConvexHull(point points[], int n) {
point start = points[0];
for(int i = 1; i<n; i++) { //find the left most point for starting
if(points[i].x < start.x)
start = points[i];
}
point current = start;
set<point> result; //set is used to avoid entry of duplicate points
result.insert(start);
vector<point> *collinearPoints = new vector<point>;
while(true) {
point nextTarget = points[0];
for(int i = 1; i<n; i++) {
if(points[i] == current) //when selected point is current point, ignore rest part
continue;
int val = crossProduct(current, nextTarget, points[i]);
if(val > 0) { //when ith point is on the left side
nextTarget = points[i];
collinearPoints = new vector<point>; //reset collinear points
}else if(val == 0) { //if three points are collinear
if(distance(current, nextTarget, points[i]) < 0) { //add closer one to collinear list
collinearPoints->push_back(nextTarget);
nextTarget = points[i];
}else{
collinearPoints->push_back(points[i]); //when ith point is closer or same as nextTarget
}
}
}
vector<point>::iterator it;
for(it = collinearPoints->begin(); it != collinearPoints->end(); it++) {
result.insert(*it); //add allpoints in collinear points to result set
}
if(nextTarget == start) //when next point is start it means, the area covered
break;
result.insert(nextTarget);
current = nextTarget;
}
return result;
}
int main() {
point points[] = {{-7,8},{-4,6},{2,6},{6,4},{8,6},{7,-2},{4,-6},{8,-7},{0,0},
{3,-2},{6,-10},{0,-6},{-9,-5},{-8,-2},{-8,0},{-10,3},{-2,2},{-10,4}};
int n = 18;
set<point> result;
result = findConvexHull(points, n);
cout << "Boundary points of convex hull are: "<<endl;
set<point>::iterator it;
for(it = result.begin(); it!=result.end(); it++)
cout << "(" << it->x << ", " <<it->y <<") ";
} आउटपुट
Boundary points of convex hull are: (-9, -5) (6, -10) (8, -7) (8, 6) (-7, 8) (-10, 4) (-10, 3)