test/library_checker/data_structure/area_of_union_of_rectangles.test.cpp

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• Last update: 2025-01-09 22:07:23+09:00
• Problem: https://judge.yosupo.jp/problem/area_of_union_of_rectangles

Depends on

• lib/data_structure/lazy_segment_tree.hpp
• Compression (座標圧縮) (lib/others/compression.hpp)

Code

#define PROBLEM "https://judge.yosupo.jp/problem/area_of_union_of_rectangles"
#include <bits/stdc++.h>
using namespace std;

#include "../../../lib/data_structure/lazy_segment_tree.hpp"
#include "../../../lib/others/compression.hpp"

const long long INF = 0x1fffffffffffffff;

struct S{
    long long len, mn;
};

struct F{
    long long add;
};

F ID = {0};

S op(S l, S r){
    if(l.mn < r.mn){
        return l;
    }
    if(l.mn > r.mn){
        return r;
    }
    return S{l.len + r.len, l.mn};
}

S e(){
    return S{0, INF};
}

S mapping(F f, S x){
    return S{x.len, x.mn + f.add};
}

F composition(F f, F g){
    return F{f.add + g.add};
}

F id(){
    return ID;
}

int main(){
    ios::sync_with_stdio(false);
    cin.tie(nullptr);

    int n; cin >> n;
    vector<long long> l(n), d(n), r(n), u(n);
    vector<long long> x, y;
    for(int i = 0; i < n; i++){
        cin >> l[i] >> d[i] >> r[i] >> u[i];
        x.push_back(l[i]);
        x.push_back(r[i]);
        y.push_back(d[i]);
        y.push_back(u[i]);
    }
    compress<long long> xc(x), yc(y);
    int xs = xc.size(), ys = yc.size();
    LazySegTree<S, op, e, F, mapping, composition, id> seg(xs - 1);
    for(int i = 0; i < xs - 1; i++){
        seg.update(i, {xc.inv(i + 1) - xc.inv(i), 0});
    }
    vector<vector<tuple<int, int, int>>> q(ys);
    for(int i = 0; i < n; i++){
        int l_ = xc.compressed[2 * i], r_ = xc.compressed[2 * i + 1];
        q[yc.compressed[2 * i]].emplace_back(l_, r_, 1);
        q[yc.compressed[2 * i + 1]].emplace_back(l_, r_, -1);
    }
    long long ans = 0;
    long long xlen = xc.inv(xs - 1) - xc.inv(0);
    for(int i = 0; i < ys - 1; i++){
        for(auto [l_, r_, w] : q[i]){
            seg.apply(l_, r_, F{w});
        }
        S res = seg.all_query();
        long long t = (res.mn == 0) ? (xlen - res.len) : (xlen); 
        ans += t * (yc.inv(i + 1) - yc.inv(i));
    }
    cout << ans << "\n";
}

#line 1 "test/library_checker/data_structure/area_of_union_of_rectangles.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/area_of_union_of_rectangles"
#include <bits/stdc++.h>
using namespace std;

#line 2 "lib/data_structure/lazy_segment_tree.hpp"

template <class S,
    S(*op)(S, S),
    S(*e)(),
    class F,
    S(*mapping)(F, S),
    F(*composition)(F, F),
    F(*id)()>
struct LazySegTree{
private:
    int _n, size, log;
    vector<S> d;
    vector<F> lz;

    void pull(int k){ d[k] = op(d[2 * k], d[2 * k + 1]); }
    void all_apply(int k, F f){
        d[k] = mapping(f, d[k]);
        if(k < size) lz[k] = composition(f, lz[k]);
    }
    void push(int k){
        all_apply(2 * k, lz[k]);
        all_apply(2 * k + 1, lz[k]);
        lz[k] = id();
    }

public:
    LazySegTree() : LazySegTree(0){}
    LazySegTree(int n) : LazySegTree(vector<S>(n, e())){}
    LazySegTree(const vector<S> &v) : _n(int(v.size())){
        log = 0;
        size = 1;
        while(size < _n) size <<= 1, log++;
        d = vector<S>(2 * size, e());
        lz = vector<F>(size, id());
        for(int i = 0; i < _n; i++) d[size + i] = v[i];
        for(int i = size - 1; i >= 1; i--){
            pull(i);
        }
    }

    void update(int p, S x){
        assert(0 <= p && p < _n);
        p += size;
        for(int i = log; i >= 1; i--) push(p >> i);
        d[p] = x;
        for(int i = 1; i <= log; i++) pull(p >> i);
    }

    S get(int p){
        assert(0 <= p && p < _n);
        p += size;
        for(int i = log; i >= 1; i--) push(p >> i);
        return d[p];
    }

    S query(int l, int r){
        assert(0 <= l && l <= r && r <= _n);
        if(l == r) return e();

        l += size;
        r += size;

        for(int i = log; i >= 1; i--){
            if(((l >> i) << i) != l) push(l >> i);
            if(((r >> i) << i) != r) push(r >> i);
        }

        S sml = e(), smr = e();
        while(l < r){
            if(l & 1) sml = op(sml, d[l++]);
            if(r & 1) smr = op(d[--r], smr);
            l >>= 1;
            r >>= 1;
        }

        return op(sml, smr);
    }

    S all_query(){ return d[1]; }

    void apply(int p, F f){
        assert(0 <= p && p < _n);
        p += size;
        for(int i = log; i >= 1; i--) push(p >> i);
        d[p] = mapping(f, d[p]);
        for(int i = 1; i <= log; i++) pull(p >> i);
    }
    void apply(int l, int r, F f){
        assert(0 <= l && l <= r && r <= _n);
        if(l == r) return;

        l += size;
        r += size;

        for(int i = log; i >= 1; i--){
            if(((l >> i) << i) != l) push(l >> i);
            if(((r >> i) << i) != r) push((r - 1) >> i);
        }

        {
            int l2 = l, r2 = r;
            while(l < r){
                if(l & 1) all_apply(l++, f);
                if(r & 1) all_apply(--r, f);
                l >>= 1;
                r >>= 1;
            }
            l = l2;
            r = r2;
        }

        for(int i = 1; i <= log; i++){
            if(((l >> i) << i) != l) pull(l >> i);
            if(((r >> i) << i) != r) pull((r - 1) >> i);
        }
    }

    template <bool (*g)(S)>
    int max_right(int l){
        return max_right(l, [](S x){ return g(x); });
    }
    template <class G>
    int max_right(int l, G g){
        assert(0 <= l && l <= _n);
        assert(g(e()));
        if(l == _n) return _n;
        l += size;
        for(int i = log; i >= 1; i--) push(l >> i);
        S sm = e();
        do{
            while(l % 2 == 0) l >>= 1;
            if(!g(op(sm, d[l]))){
                while(l < size){
                    push(l);
                    l = (2 * l);
                    if(g(op(sm, d[l]))){
                        sm = op(sm, d[l]);
                        l++;
                    }
                }
                return l - size;
            }
            sm = op(sm, d[l]);
            l++;
        } while((l & -l) != l);
        return _n;
    }

    template <bool (*g)(S)>
    int min_left(int r){
        return min_left(r, [](S x){ return g(x); });
    }
    template <class G>
    int min_left(int r, G g){
        assert(0 <= r && r <= _n);
        assert(g(e()));
        if(r == 0) return 0;
        r += size;
        for(int i = log; i >= 1; i--) push((r - 1) >> i);
        S sm = e();
        do{
            r--;
            while(r > 1 && (r % 2)) r >>= 1;
            if(!g(op(d[r], sm))){
                while(r < size){
                    push(r);
                    r = (2 * r + 1);
                    if(g(op(d[r], sm))){
                        sm = op(d[r], sm);
                        r--;
                    }
                }
                return r + 1 - size;
            }
            sm = op(d[r], sm);
        } while((r & -r) != r);
        return 0;
    }
};
#line 2 "lib/others/compression.hpp"

/**
 * @brief Compression (座標圧縮)
 * @docs docs/others/compression.md
 */

#line 10 "lib/others/compression.hpp"

template <typename T>
struct compress{
    std::vector<T> sorted;
    std::vector<int> compressed;

    compress(const std::vector<T> &vec){
        int n = vec.size();
        compressed.resize(n);
        for(T x : vec){
            sorted.emplace_back(x);
        }
        std::sort(sorted.begin(), sorted.end());
        sorted.erase(std::unique(sorted.begin(), sorted.end()), sorted.end());
        for(int i = 0; i < n; ++i){
            compressed[i] = std::lower_bound(sorted.begin(), sorted.end(), vec[i]) - sorted.begin();
        }
    }

    int get(const T &x) const{
        return std::lower_bound(sorted.begin(), sorted.end(), x) - sorted.begin();
    }

    T inv(const int x) const{
        return sorted[x];
    }

    size_t size() const{
        return sorted.size();
    }

    std::vector<int> getCompressed() const{
        return compressed;
    }
};
#line 7 "test/library_checker/data_structure/area_of_union_of_rectangles.test.cpp"

const long long INF = 0x1fffffffffffffff;

struct S{
    long long len, mn;
};

struct F{
    long long add;
};

F ID = {0};

S op(S l, S r){
    if(l.mn < r.mn){
        return l;
    }
    if(l.mn > r.mn){
        return r;
    }
    return S{l.len + r.len, l.mn};
}

S e(){
    return S{0, INF};
}

S mapping(F f, S x){
    return S{x.len, x.mn + f.add};
}

F composition(F f, F g){
    return F{f.add + g.add};
}

F id(){
    return ID;
}

int main(){
    ios::sync_with_stdio(false);
    cin.tie(nullptr);

    int n; cin >> n;
    vector<long long> l(n), d(n), r(n), u(n);
    vector<long long> x, y;
    for(int i = 0; i < n; i++){
        cin >> l[i] >> d[i] >> r[i] >> u[i];
        x.push_back(l[i]);
        x.push_back(r[i]);
        y.push_back(d[i]);
        y.push_back(u[i]);
    }
    compress<long long> xc(x), yc(y);
    int xs = xc.size(), ys = yc.size();
    LazySegTree<S, op, e, F, mapping, composition, id> seg(xs - 1);
    for(int i = 0; i < xs - 1; i++){
        seg.update(i, {xc.inv(i + 1) - xc.inv(i), 0});
    }
    vector<vector<tuple<int, int, int>>> q(ys);
    for(int i = 0; i < n; i++){
        int l_ = xc.compressed[2 * i], r_ = xc.compressed[2 * i + 1];
        q[yc.compressed[2 * i]].emplace_back(l_, r_, 1);
        q[yc.compressed[2 * i + 1]].emplace_back(l_, r_, -1);
    }
    long long ans = 0;
    long long xlen = xc.inv(xs - 1) - xc.inv(0);
    for(int i = 0; i < ys - 1; i++){
        for(auto [l_, r_, w] : q[i]){
            seg.apply(l_, r_, F{w});
        }
        S res = seg.all_query();
        long long t = (res.mn == 0) ? (xlen - res.len) : (xlen); 
        ans += t * (yc.inv(i + 1) - yc.inv(i));
    }
    cout << ans << "\n";
}

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