# Convex Hull Monotone chain algorithm in C++

In this tutorial, we will be discussing a program to find the convex hull of a given set of points.

Convex hull is the smallest polygon convex figure containing all the given points either on the boundary on inside the figure.

## Example

Live Demo

#include <bits/stdc++.h>
#define llu long long int
using namespace std;
//structure for the given point
struct Point {
llu x, y;
bool operator<(Point p){
return x < p.x || (x == p.x && y < p.y);
}
};
//calculating the cross product of self made vectors
llu calc_crossproduct(Point O, Point A, Point B){
return (A.x - O.x) * (B.y - O.y)
- (A.y - O.y) * (B.x - O.x);
}
//calculating the points on boundary
vector<Point> convex_hull(vector<Point> A){
int n = A.size(), k = 0;
if (n <= 3)
return A;
vector<Point> ans(2 * n);
//sorting points lexicographically
sort(A.begin(), A.end());
for (int i = 0; i < n; ++i) {
while (k >= 2 && calc_crossproduct(ans[k - 2],
ans[k - 1], A[i]) <= 0)
k--;
ans[k++] = A[i];
}
//building upper hull
for (size_t i = n - 1, t = k + 1; i > 0; --i) {
while (k >= t && calc_crossproduct(ans[k - 2],
ans[k - 1], A[i - 1]) <= 0)
k--;
ans[k++] = A[i - 1];
}
//resizing the given array
ans.resize(k - 1);
return ans;
}
int main(){
vector<Point> points;
points.push_back({ 0, 3 });
points.push_back({ 2, 2 });
points.push_back({ 1, 1 });
points.push_back({ 2, 1 });
points.push_back({ 3, 0 });
points.push_back({ 0, 0 });
points.push_back({ 3, 3 });
vector<Point> ans = convex_hull(points);
for (int i = 0; i < ans.size(); i++)
cout << "(" << ans[i].x << ", "
<< ans[i].y << ")" << endl;
return 0;
}

## Output

(0, 0)
(3, 0)
(3, 3)
(0, 3)