yukicoder No.96

yukicoder96.cpp

#include <iostream>
#include <iomanip>
#include <vector>
#include <algorithm>
#include <numeric>
#include <functional>
#include <cmath>
#include <queue>
#include <stack>
#include <map>

#define repd(i,a,b) for (int i=(a);i<(b);i++)
#define rep(i,n) repd(i,0,n)
typedef long long ll;

using namespace std;


int inputValue(){
    int a;
    cin >> a;
    return a;
}

void inputArray(int * p, int a){
    rep(i, a){
        cin >> p[i];
    }
}

void inputVector(vector<int> * p, int a){
    rep(i, a){
        int input;
        cin >> input;
        p -> push_back(input);
    }
}

template <typename T>
void output(T a, int precision) {
    if(precision > 0){
        cout << fixed << setprecision(precision)  << a << "\n";
    }
    else{
        cout << a << "\n";
    }
}

// 正なら反時計回り，負なら時計回り
int det(pair<int, int> a, pair<int, int> b){
    return a.first * b.second - a.second * b.first;
}

// v = q - p
pair<int, int> vec(pair<int, int> p, pair<int, int> q){
    return make_pair(q.first - p.first, q.second - p.second);
}

bool isCCW(pair<int, int> a1, pair<int, int> a2, pair<int, int> a3){
    pair<int, int> v1 = vec(a2, a1);
    pair<int, int> v2 = vec(a2, a3);
    
    if (det(v1, v2) >= 0) {
        return true;
    }
    return false;
}

vector<pair<int, int> > convex_hull(vector<pair<int, int> > v){
    if (v.size() < 3) {
        return v;
    }
    
    sort(v.begin(), v.end());
    
    // vh: 上部の凸 vl: 下部の凸
    vector<pair<int, int> > vh, vl;
    // x座標の昇順に2つvhに追加 降順に2つvlに追加
    vh.push_back(v[0]);
    vh.push_back(v[1]);
    vl.push_back(v[v.size() - 1]);
    vl.push_back(v[v.size() - 2]);
    
    // vh
    repd(i, 2, v.size()){
        for (int n = (int)vh.size(); n >= 2 && isCCW(vh[n - 2], vh[n - 1], v[i]); n--) {
            vh.pop_back();
        }
        vh.push_back(v[i]);
    }
    
    // vl
    for (int i = (int)v.size() - 3; i >= 0; i--) {
        for (int n = (int)vl.size(); n >= 2 && isCCW(vl[n - 2], vl[n - 1], v[i]); n--) {
            vl.pop_back();
        }
        vl.push_back(v[i]);
    }
    
    reverse(vl.begin(), vl.end());
    for (int i = (int)vh.size() - 2; i >= 1; i--) {
        vl.push_back(vh[i]);
    }
    
    return vl;
}

vector<int> parent, rnk;

int root(int x){
    if (parent[x] == x) {
        return x;
    }
    else{
        return root(parent[x]);
    }
}

void unite(int x, int y){
    x = root(x);
    y = root(y);
    if (x == y) {
        return;
    }
    if (rnk[x] < rnk[y]) {
        parent[x] = y;
    }
    else{
        parent[y] = x;
        if (rnk[x] == rnk[y]) {
            rnk[x]++;
        }
    }
}

// L2ノルムの2乗
int L2(pair<int, int> a, pair<int, int> b){
    return (a.first - b.first) * (a.first - b.first) + (a.second - b.second) * (a.second - b.second);
}

vector<int> V[2001][2001]; // 4000000


int main(int argc, const char * argv[]) {
    
    // source code
    
    
    int N = inputValue();
    vector<pair<int, int> > A(N);
    
    // 縦横10の区画に入れる
    rep(i, N){
        A[i] = make_pair(inputValue(), inputValue()); //(x, y)
        V[(A[i].first + 10000) / 10][(A[i].second + 10000) / 10].push_back(i);
    }
    
    // 0個のときは1
    if (N == 0) {
        output(1, 0);
        return 0;
    }
    
    // union find init
    parent.resize(N);
    rnk.resize(N);
    rep(i, N){
        parent[i] = i;
        rnk[i] = 0;
    }
    
    // unite 自分と周り8区画を見る
    rep(i, N){
        int x = (A[i].first + 10000) / 10;
        int y = (A[i].second + 10000) / 10;
        for (int dx = -1; dx <= 1; dx++) {
            if (x + dx < 0 || x + dx > 2000) continue;
            for (int dy = -1; dy <= 1; dy++) {
                if (y + dy < 0 || y + dy > 2000) continue;
                rep(j, V[x + dx][y + dy].size()){
                    if (i == V[x + dx][y + dy][j]) continue;
                    if (L2(A[i], A[V[x + dx][y + dy][j]]) <= 100) {
                        unite(i, V[x + dx][y + dy][j]);
                    }
                }
            }
        }
    }
    
    map<int, vector<int> > clst;
    rep(i, N){
        clst[root(i)].push_back(i);
    }
    
    int maxDist = 0;
    
    rep(i, clst.size()) {
        if (clst[i].size() == 0) {
            continue;
        }
        vector<pair<int, int> > points;
        rep(j, clst[i].size()){
            points.push_back(A[clst[i][j]]);
        }
        vector<pair<int, int> > ch = convex_hull(points);
        
        rep(p, ch.size()){
            rep(q, ch.size()){
                if (p == q) continue;
                maxDist = max(maxDist, L2(ch[p], ch[q]));
            }
        }
        
    }

    output(sqrt((double)maxDist) + 2.0, 16);
    
    
    return 0;
}