templates/convex-hull-andrew.cpp
compilable
$cat templates/convex-hull-andrew
Convex Hull (Andrew's)
Andrew's monotone chain algorithm for convex hull in O(n log n).
#convex-hull#geometry#monotone-chain#andrew
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$cat source_code/
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#include <bits/stdc++.h>
using namespace std;
using ll = long long;
struct Point {
ll x, y;
Point(ll x = 0, ll y = 0) : x(x), y(y) {}
Point operator-(const Point &p) const { return {x - p.x, y - p.y}; }
ll cross(const Point &p) const { return x * p.y - y * p.x; }
ll dist(const Point &p) const { return (x-p.x)*(x-p.x) + (y-p.y)*(y-p.y); }
bool operator<(const Point &p) const { return x < p.x || (x == p.x && y < p.y); }
friend istream &operator>>(istream &in, Point &p) { return in >> p.x >> p.y; }
};
vector<Point> convexHull(vector<Point> pts, bool includeCollinear = false) {
int n = pts.size();
if (n < 2) return pts;
sort(pts.begin(), pts.end());
pts.erase(unique(pts.begin(), pts.end(), [](const Point &a, const Point &b) {
return a.x == b.x && a.y == b.y;
}), pts.end());
n = pts.size();
if (n < 2) return pts;
vector<Point> hull;
auto check = [&](const Point &p) -> bool {
ll cr = (hull.back() - hull[hull.size()-2]).cross(p - hull.back());
return includeCollinear ? cr < 0 : cr <= 0;
};
for (int i = 0; i < n; i++) {
while (hull.size() >= 2 && check(pts[i])) hull.pop_back();
hull.push_back(pts[i]);
}
int lower = hull.size();
for (int i = n - 2; i >= 0; i--) {
while ((int)hull.size() > lower && check(pts[i])) hull.pop_back();
hull.push_back(pts[i]);
}
hull.pop_back();
return hull;
}42 linesutf-8
$cat explanation_notes.md
notes_viewer --renderedmarkdown (math enabled)
Convex Hull — Andrew's Monotone Chain
Compute the convex hull of a set of 2D points in .
How It Works
Orientation Test
The cross product determines turn direction:
When to Use
Notes
includeCollinear = true to keep collinear points on the hull boundary