結果

問題 No.2436 Min Diff Distance
コンテスト
ユーザー dyktr_06
提出日時 2023-08-19 00:22:14
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 510 ms / 2,000 ms
コード長 6,997 bytes
コンパイル時間 4,326 ms
コンパイル使用メモリ 276,944 KB
最終ジャッジ日時 2025-02-16 11:10:36
ジャッジサーバーID
（参考情報） 		judge3 / judge4
このコードへのチャレンジ
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ファイルパターン 結果
other AC * 23
権限があれば一括ダウンロードができます

ソースコード

diff # 

#include <bits/stdc++.h>
#include <atcoder/all>

using namespace std;
using namespace atcoder;

#define overload4(_1, _2, _3, _4, name, ...) name
#define rep1(n) for(int i = 0; i < (int)(n); ++i)
#define rep2(i, n) for(int i = 0; i < (int)(n); ++i)
#define rep3(i, a, b) for(int i = (a); i < (int)(b); ++i)
#define rep4(i, a, b, c) for(int i = (a); i < (int)(b); i += (c))
#define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__)

#define rrep(i,n) for(int i = (int)(n) - 1; i >= 0; --i)
#define ALL(a) a.begin(), a.end()
#define Sort(a) sort(a.begin(), a.end())
#define RSort(a) sort(a.rbegin(), a.rend())

typedef long long int ll;
typedef unsigned long long ul;
typedef long double ld;
typedef vector<int> vi;
typedef vector<long long> vll;
typedef vector<char> vc;
typedef vector<string> vst;
typedef vector<double> vd;
typedef vector<long double> vld;
typedef pair<long long, long long> P;

template<class T> long long sum(const T& a){ return accumulate(a.begin(), a.end(), 0LL); }
template<class T> auto min(const T& a){ return *min_element(a.begin(), a.end()); }
template<class T> auto max(const T& a){ return *max_element(a.begin(), a.end()); }

const long long MINF = 0x7fffffffffff;
const long long INF = 0x1fffffffffffffff;
const long long MOD = 998244353;
const long double EPS = 1e-9;
const long double PI = acos(-1);
 
template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; }
template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; }

template<typename T1, typename T2> istream &operator>>(istream &is, pair<T1, T2> &p){ is >> p.first >> p.second; return is; }
template<typename T1, typename T2> ostream &operator<<(ostream &os, const pair<T1, T2> &p){ os << "(" << p.first << ", " << p.second << ")"; return os; }
template<typename T> istream &operator>>(istream &is, vector<T> &v){ for(T &in : v) is >> in; return is; }
template<typename T> ostream &operator<<(ostream &os, const vector<T> &v){ for(int i = 0; i < (int) v.size(); ++i){ os << v[i] << (i + 1 != (int) v.size() ? " " : ""); } return os; }
template <typename T, typename S> ostream &operator<<(ostream &os, const map<T, S> &mp){ for(auto &[key, val] : mp){ os << key << ":" << val << " "; } return os; }
template <typename T> ostream &operator<<(ostream &os, const set<T> &st){ auto itr = st.begin(); for(int i = 0; i < (int)st.size(); ++i){ os << *itr << (i + 1 != (int)st.size() ? " " : ""); itr++; } return os; }
template <typename T> ostream &operator<<(ostream &os, const multiset<T> &st){ auto itr = st.begin(); for(int i = 0; i < (int)st.size(); ++i){ os << *itr << (i + 1 != (int)st.size() ? " " : ""); itr++; } return os; }
template <typename T> ostream &operator<<(ostream &os, queue<T> q){ while(q.size()){ os << q.front() << " "; q.pop(); } return os; }
template <typename T> ostream &operator<<(ostream &os, deque<T> q){ while(q.size()){ os << q.front() << " "; q.pop_front(); } return os; }
template <typename T> ostream &operator<<(ostream &os, stack<T> st){ while(st.size()){ os << st.top() << " "; st.pop(); } return os; }
template <class T, class Container, class Compare> ostream &operator<<(ostream &os, priority_queue<T, Container, Compare> pq){ while(pq.size()){ os << pq.top() << " "; pq.pop(); } return os; }

template<class T, class U> inline T vin(T& vec, U n) { vec.resize(n); for(int i = 0; i < (int) n; ++i) cin >> vec[i]; return vec; }
template<class T> inline void vout(T vec, string s = "\n"){ for(auto x : vec) cout << x << s; }
template<class... T> void in(T&... a){ (cin >> ... >> a); }
void out(){ cout << '\n'; }
template<class T, class... Ts> void out(const T& a, const Ts&... b){ cout << a; (cout << ... << (cout << ' ', b)); cout << '\n'; }
template<class T, class U> void inGraph(vector<vector<T>>& G, U n, U m, bool directed = false){ G.resize(n); for(int i = 0; i < m; ++i){ int a, b; cin >> a >> b; a--, b--; G[a].push_back(b); if(!directed) G[b].push_back(a); } }

struct UnionFind{
    vector<int> par;
    vector<int> edg;

    UnionFind(int N) : par(N), edg(N){
        for(int i = 0; i < N; ++i){
            par[i] = -1;
            edg[i] = 0;
        }
    }

    int root(int x){
        if(par[x] < 0) return x;
        return par[x] = root(par[x]);
    }

    void unite(int x, int y){
        int rx = root(x);
        int ry = root(y);
        if(rx == ry){
            edg[rx]++;
            return;
        }
        par[ry] = par[rx] + par[ry];
        par[rx] = ry;
        edg[ry] += edg[rx] + 1;
    }

    bool same(int x, int y){
        int rx = root(x);
        int ry = root(y);
        return rx == ry;
    }

    long long size(int x){
        return -par[root(x)];
    }

    long long edge(int x){
        return edg[root(x)];
    }
};

template <typename T>
vector<pair<int, int>> manhattanMST(vector<T> x, vector<T> y){
    int n = x.size();
    vector<tuple<T, int, int>> edge;
    edge.reserve(4 * n);
    vector<int> idx(n);
    iota(idx.begin(), idx.end(), 0);
    for(int s = 0; s < 2; ++s){
        for(int t = 0; t < 2; ++t){
            sort(idx.begin(), idx.end(), [&](const int i, const int j) {
                return x[i] + y[i] < x[j] + y[j];
            });
            map<T, int, greater<>> map;
            for(const int i : idx){
                for(auto iter = map.lower_bound(y[i]); iter != map.end(); iter = map.erase(iter)){
                    const int j = iter->second;
                    const T dx = x[i] - x[j];
                    const T dy = y[i] - y[j];
                    if(dy > dx) break;
                    edge.emplace_back(dx + dy, i, j);
                }
                map[y[i]] = i;
            }
            swap(x, y);
        }
        for(int i = 0; i < n; ++i) {
            x[i] *= -1;
        }
    }
    sort(edge.begin(), edge.end());
    UnionFind dsu(n);
    vector<pair<int, int>> used;
    used.reserve(n - 1);
    for(const auto& [c, i, j] : edge){
        if(!dsu.same(i, j)){
            used.emplace_back(i, j);
            dsu.unite(i, j);
        }
    }
    return used;
}

ll n;
vll x, y;

void input(){
    in(n);
    x.resize(n);
    y.resize(n);
    rep(i, n) in(x[i], y[i]);
}


void solve(){
    vll x2(n), y2(n);
    rep(i, n){
        x2[i] = x[i] + y[i];
        y2[i] = x[i] - y[i];
    }
    ll mnx = min(x2), mxx = max(x2), mny = min(y2), mxy = max(y2);
    vector<pair<int, int>> mst = manhattanMST(x, y);
    vector<vll> G(n);
    rep(i, n - 1){
        auto [u, v] = mst[i];
        G[u].push_back(v);
        G[v].push_back(u);
    }
    ll ans = INF;
    rep(i, n){
        ll mx = max({abs(x2[i] - mnx), abs(x2[i] - mxx), abs(y2[i] - mny), abs(y2[i] - mxy)});
        ll mn = INF;
        for(auto u : G[i]){
            chmin(mn, abs(x[i] - x[u]) + abs(y[i] - y[u]));
        }
        chmin(ans, mx - mn);
    }
    out(ans);
}

int main(){
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    cout << fixed << setprecision(20);
    
    input();
    solve();
}
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