5.1.1 - Fencing the Cows.cpp

/*
ID: nathan.18
TASK: fc
LANG: C++
*/

#include <iostream>
#include <string>
#include <utility>
#include <sstream>
#include <algorithm>
#include <stack>
#include <vector>
#include <queue>
#include <map>
#include <set>
#include <bitset>
#include <cmath>
#include <cstring>
#include <iomanip>
#include <fstream>
#include <cassert>
#include <unordered_set>
#include <ctime>
#include <list>

using namespace std;

template<class T> using min_heap = priority_queue<T, vector<T>, greater<T>>;

#define FOR(i, a, b) for (int i=a; i<(b); i++)
#define F0R(i, a) for (int i=0; i<(a); i++)
#define F0R1(i, a) for (int i=1; i<=(a); i++)
#define FORd(i, a, b) for (int i = (b)-1; i >= a; i--)
#define F0Rd(i, a) for (int i = (a)-1; i >= 0; i--)
#define F0Rd1(i, a) for (int i=a; i>0; i--)
#define SORT(vec) sort(vec.begin(), vec.end())
#define MIN(a, b) a = min(a, b)
#define MAX(a, b) a = max(a, b)

#define INF 1000000010
#define LL_INF 4500000000000000000
#define LSOne(S) (S & (-S))
#define EPS 1e-9
#define pA first
#define pB second
#define mp make_pair
#define pb push_back
#define PI acos(-1.0)
#define ll long long
#define MOD (int)(2e+9+11)
#define SET(vec, val, size) for (int i = 0; i < size; i++) vec[i] = val;
#define SET2D(arr, val, dim1, dim2) F0R(i, dim1) F0R(j, dim2) arr[i][j] = val;
#define SET3D(arr, val, dim1, dim2, dim3) F0R(i, dim1) F0R(j, dim2) F0R(k, dim3) arr[i][j][k] = val;
#define SET4D(arr, val, dim1, dim2, dim3, dim4) F0R(i, dim1) F0R(j, dim2) F0R(k, dim3) F0R(l, dim4) arr[i][j][k][l] = val;
#define READGRID(arr, dim) F0R(i, dim) F0R(j, dim) cin >> arr[i][j];
#define all(x) (x).begin(), (x).end()

typedef pair<int, int> ii;
typedef pair<int, ii> iii;
typedef pair<ll, ll> pll;
typedef vector<int> vi;
typedef vector<ii> vii;
typedef vector<iii> viii;
typedef vector<ll> vl;

void setupIO(const string &PROB) {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    ifstream infile(PROB + ".in");
    if (infile.good()) {
        freopen((PROB + ".in").c_str(), "r", stdin);
        freopen((PROB + ".out").c_str(), "w", stdout);
    }
}

/* ============================ */

struct point { double x, y;   // only used if more precision is needed
    point() { x = y = 0.0; }                      // default constructor
    point(double _x, double _y) : x(_x), y(_y) {}        // user-defined
    bool operator == (point other) const {
        return (fabs(x - other.x) < EPS && (fabs(y - other.y) < EPS)); } };

struct vec { double x, y;  // name: `vec' is different from STL vector
    vec(double _x, double _y) : x(_x), y(_y) {} };

vec toVec(point a, point b) {       // convert 2 points to vector a->b
    return vec(b.x - a.x, b.y - a.y); }

double cross(vec a, vec b) { return a.x * b.y - a.y * b.x; }

double dist(point p1, point p2) {                // Euclidean distance
    return hypot(p1.x - p2.x, p1.y - p2.y); }           // return double

// returns true if point r is on the same line as the line pq
bool collinear(point p, point q, point r) {
    return fabs(cross(toVec(p, q), toVec(p, r))) < EPS; }

point pivot;
bool angleCmp(point a, point b) {                 // angle-sorting function
    if (collinear(pivot, a, b))                               // special case
        return dist(pivot, a) < dist(pivot, b);    // check which one is closer
    double d1x = a.x - pivot.x, d1y = a.y - pivot.y;
    double d2x = b.x - pivot.x, d2y = b.y - pivot.y;
    return (atan2(d1y, d1x) - atan2(d2y, d2x)) < 0; }   // compare two angles

// note: to accept collinear points, we have to change the `> 0'
// returns true if point r is on the left side of line pq
bool ccw(point p, point q, point r) {
    return cross(toVec(p, q), toVec(p, r)) > 0; }

vector<point> CH(vector<point> P) {   // the content of P may be reshuffled
    int i, j, n = (int)P.size();
    if (n <= 3) {
        if (!(P[0] == P[n-1])) P.push_back(P[0]); // safeguard from corner case
        return P;                           // special case, the CH is P itself
    }

    // first, find P0 = point with lowest Y and if tie: rightmost X
    int P0 = 0;
    for (i = 1; i < n; i++)
        if (P[i].y < P[P0].y || (P[i].y == P[P0].y && P[i].x > P[P0].x))
            P0 = i;

    point temp = P[0]; P[0] = P[P0]; P[P0] = temp;    // swap P[P0] with P[0]

    // second, sort points by angle w.r.t. pivot P0
    pivot = P[0];                    // use this global variable as reference
    sort(++P.begin(), P.end(), angleCmp);              // we do not sort P[0]

    // third, the ccw tests
    vector<point> S;
    S.push_back(P[n-1]); S.push_back(P[0]); S.push_back(P[1]);   // initial S
    i = 2;                                         // then, we check the rest
    while (i < n) {           // note: N must be >= 3 for this method to work
        j = (int)S.size()-1;
        if (ccw(S[j-1], S[j], P[i])) S.push_back(P[i++]);  // left turn, accept
        else S.pop_back(); }   // or pop the top of S until we have a left turn
    return S; }                                          // return the result

int main() {
    setupIO("fc");

    int n; cin >> n;
    vector<point> A;
    F0R(i, n) {
        double a, b; cin >> a >> b;
        A.pb(point(a, b));
    }
    vector<point> hull = CH(A);
    double ans = 0;

    point prevPoint = hull[0];
    FOR(i, 1, hull.size()) {
        ans += dist(hull[i], prevPoint);
        prevPoint = hull[i];
    }

    cout << fixed << setprecision(2);
    cout << ans << endl;

    return 0;
}