DataStructure/test/segment_tree_2d_pointaddrectsum.test.cpp

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• Last update: 2022-12-21 14:26:45+08:00
• Problem: https://judge.yosupo.jp/problem/point_add_rectangle_sum

Depends on

• DataStructure/SegTree.h
• DataStructure/SegTree2D.h
• buffered_reader.h

Code

#define PROBLEM "https://judge.yosupo.jp/problem/point_add_rectangle_sum"

#include <bits/stdc++.h>
using namespace std;

#include "../../buffered_reader.h"
#include "../SegTree2D.h"

#define REP(i, a) for (int i = 0, _##i = (a); i < _##i; ++i)

template<typename T>
struct Query {
    static const int ADD = 0;
    static const int QUERY = 1;

    int typ;  // ADD or QUERY
    int x, y;
    int x2, y2;  // for QUERY: [x1, x2-1] * [y1, y2-1]

    T weight;
};

int32_t main() {
    ios::sync_with_stdio(0); cin.tie(0);
    int n = IO::get<int>();
    int q = IO::get<int>();

    using ll = long long;
    vector<Query<ll>> queries;
    REP(i,n) {
        int x = IO::get<int>();
        int y = IO::get<int>();
        ll val = IO::get<ll>();
        queries.push_back({Query<ll>::ADD, x, y, -1, -1, val});
    }

    REP(i,q) {
        int typ = IO::get<int>();
        if (typ == 0) {
            int x = IO::get<int>();
            int y = IO::get<int>();
            ll val = IO::get<ll>();
            queries.push_back({Query<ll>::ADD, x, y, -1, -1, val});
        } else {
            int x = IO::get<int>();
            int y = IO::get<int>();
            int x2 = IO::get<int>();
            int y2 = IO::get<int>();
            queries.push_back({Query<ll>::QUERY, x, y, x2, y2, 0});
        }
    }

    using P = pair<int,int>;
    vector<P> points;
    for (auto query : queries) {
        if (query.typ == Query<ll>::ADD) {
            points.push_back({query.x, query.y});
        }
    }

    SegTree2D<ll, SumSegTreeOp::op, SumSegTreeOp::e, int> st(points);
    for (auto query : queries) {
        if (query.typ == Query<ll>::ADD) {
            P p{query.x, query.y};
            st.set(p, st.get(p) + query.weight);
        } else {
            cout << st.prod(P{query.x, query.y}, P{query.x2, query.y2}) << '\n';
        }
    }
    return 0;
}

#line 1 "DataStructure/test/segment_tree_2d_pointaddrectsum.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/point_add_rectangle_sum"

#include <bits/stdc++.h>
using namespace std;

#line 1 "buffered_reader.h"
// Buffered reader {{{
namespace IO {
    const int BUFSIZE = 1<<14;
    char buf[BUFSIZE + 1], *inp = buf;

    bool reacheof;
    char get_char() {
        if (!*inp && !reacheof) {
            memset(buf, 0, sizeof buf);
            int tmp = fread(buf, 1, BUFSIZE, stdin);
            if (tmp != BUFSIZE) reacheof = true;
            inp = buf;
        }
        return *inp++;
    }
    template<typename T>
    T get() {
        int neg = 0;
        T res = 0;
        char c = get_char();
        while (!std::isdigit(c) && c != '-' && c != '+') c = get_char();
        if (c == '+') { neg = 0; }
        else if (c == '-') { neg = 1; }
        else res = c - '0';

        c = get_char();
        while (std::isdigit(c)) {
            res = res * 10 + (c - '0');
            c = get_char();
        }
        return neg ? -res : res;
    }
};
// Helper methods
int ri() {
    return IO::get<int>();
}
// }}}
#line 1 "DataStructure/SegTree2D.h"
// 2D segment tree
#line 1 "DataStructure/SegTree.h"
// SegTree, copied from AtCoder library {{{
// AtCoder doc: https://atcoder.github.io/ac-library/master/document_en/segtree.html
//
// Notes:
// - Index of elements from 0 -> n-1
// - Range queries are [l, r-1]
//
// Tested:
// - (binary search) https://atcoder.jp/contests/practice2/tasks/practice2_j
// - https://oj.vnoi.info/problem/gss
// - https://oj.vnoi.info/problem/nklineup
// - (max_right & min_left for delete position queries) https://oj.vnoi.info/problem/segtree_itstr
// - https://judge.yosupo.jp/problem/point_add_range_sum
// - https://judge.yosupo.jp/problem/point_set_range_composite
int ceil_pow2(int n) {
    int x = 0;
    while ((1U << x) < (unsigned int)(n)) x++;
    return x;
}

template<
    class T,  // data type for nodes
    T (*op) (T, T),  // operator to combine 2 nodes
    T (*e)() // identity element
>
struct SegTree {
    SegTree() : SegTree(0) {}
    explicit SegTree(int n) : SegTree(vector<T> (n, e())) {}
    explicit SegTree(const vector<T>& v) : _n((int) v.size()) {
        log = ceil_pow2(_n);
        size = 1<<log;
        d = vector<T> (2*size, e());

        for (int i = 0; i < _n; i++) d[size+i] = v[i];
        for (int i = size - 1; i >= 1; i--) {
            update(i);
        }
    }

    // 0 <= p < n
    void set(int p, T x) {
        assert(0 <= p && p < _n);
        p += size;
        d[p] = x;
        for (int i = 1; i <= log; i++) update(p >> i);
    }

    // 0 <= p < n
    T get(int p) const {
        assert(0 <= p && p < _n);
        return d[p + size];
    }

    // Get product in range [l, r-1]
    // 0 <= l <= r <= n
    // For empty segment (l == r) -> return e()
    T prod(int l, int r) const {
        assert(0 <= l && l <= r && r <= _n);
        T sml = e(), smr = e();
        l += size;
        r += size;
        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);
    }

    T all_prod() const {
        return d[1];
    }

    // Binary search on SegTree to find largest r:
    //    f(op(a[l] .. a[r-1])) = true   (assuming empty array is always true)
    //    f(op(a[l] .. a[r])) = false    (assuming op(..., a[n]), which is out of bound, is always false)
    template <bool (*f)(T)> int max_right(int l) const {
        return max_right(l, [](T x) { return f(x); });
    }
    template <class F> int max_right(int l, F f) const {
        assert(0 <= l && l <= _n);
        assert(f(e()));
        if (l == _n) return _n;
        l += size;
        T sm = e();
        do {
            while (l % 2 == 0) l >>= 1;
            if (!f(op(sm, d[l]))) {
                while (l < size) {
                    l = (2 * l);
                    if (f(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;
    }

    // Binary search on SegTree to find smallest l:
    //    f(op(a[l] .. a[r-1])) = true      (assuming empty array is always true)
    //    f(op(a[l-1] .. a[r-1])) = false   (assuming op(a[-1], ..), which is out of bound, is always false)
    template <bool (*f)(T)> int min_left(int r) const {
        return min_left(r, [](T x) { return f(x); });
    }
    template <class F> int min_left(int r, F f) const {
        assert(0 <= r && r <= _n);
        assert(f(e()));
        if (r == 0) return 0;
        r += size;
        T sm = e();
        do {
            r--;
            while (r > 1 && (r % 2)) r >>= 1;
            if (!f(op(d[r], sm))) {
                while (r < size) {
                    r = (2 * r + 1);
                    if (f(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;
    }

private:
    int _n, size, log;
    vector<T> d;

    void update(int k) {
        d[k] = op(d[2*k], d[2*k+1]);
    }
};
// }}}

// SegTree examples {{{
// Examples: Commonly used SegTree ops: max / min / sum
struct MaxSegTreeOp {
    static int op(int x, int y) {
        return max(x, y);
    }
    static int e() {
        return INT_MIN;
    }
};

struct MinSegTreeOp {
    static int op(int x, int y) {
        return min(x, y);
    }
    static int e() {
        return INT_MAX;
    }
};

struct SumSegTreeOp {
    static long long op(long long x, long long y) {
        return x + y;
    }
    static long long e() {
        return 0;
    }
};

// using STMax = SegTree<int, MaxSegTreeOp::op, MaxSegTreeOp::e>;
// using STMin = SegTree<int, MinSegTreeOp::op, MinSegTreeOp::e>;
// using STSum = SegTree<int, SumSegTreeOp::op, SumSegTreeOp::e>;
// }}}
#line 3 "DataStructure/SegTree2D.h"
template<
    class S,        // aggregate data type
    S (*op) (S, S), // combine aggregate data
    S (*e) (),      // empty element
    class Coord     // for x and y coordinates
> struct SegTree2D {
    using P = pair<Coord, Coord>;

    // _points must contains all add queries
    SegTree2D(const vector<P>& _points) : points(_points) {
        sort(points.begin(), points.end());
        points.erase(unique(points.begin(), points.end()), points.end());
        n = points.size();

        // init segtrees
        coords.resize(n * 2);
        for (int i = 0; i < n; i++) {
            coords[n + i] = {{points[i].second, points[i].first}};
        }
        for (int i = n-1; i > 0; i--) {
            std::merge(coords[i*2].begin(), coords[i*2].end(),
                       coords[i*2+1].begin(), coords[i*2+1].end(),
                       std::back_inserter(coords[i]));
            coords[i].erase(unique(coords[i].begin(), coords[i].end()), coords[i].end());
        }
        for (const auto& c : coords) {
            segs.emplace_back(SegTree<S, op, e>(c.size()));
        }
    }

    // Set value(p) = val
    void set(P p, S val) {
        int i = lower_bound(points.begin(), points.end(), p) - points.begin();
        assert(i < n && points[i] == p);
        for (i += n; i; i >>= 1) {
            int j = lower_bound(coords[i].begin(), coords[i].end(), P{p.second, p.first}) - coords[i].begin();
            segs[i].set(j, val);
        }
    }

    // Get value at p
    S get(P p) const {
        return prod(p, P{p.first + 1, p.second + 1});
    }

    // Get sum of points in rectangles, given bottom-left and top-right
    // [low.x, high.x - 1] * [low.y, high.y - 1]
    S prod(P low, P high) const {
        assert(low.first <= high.first);
        assert(low.second <= high.second);
        if (low.first == high.first) return e();
        if (low.second == high.second) return e();

        int l = n + (lower_bound(points.begin(), points.end(), low, cmpFirst) - points.begin());
        int r = n + (lower_bound(points.begin(), points.end(), high, cmpFirst) - points.begin());
        S res = e();
        while (l < r) {
            if (l & 1) res = op(res, prod_1d(l++, low.second, high.second));
            if (r & 1) res = op(res, prod_1d(--r, low.second, high.second));
            l >>= 1; r >>= 1;
        }
        return res;
    }

// private:
    S prod_1d(int x, Coord l, Coord r) const {
        auto il = lower_bound(coords[x].begin(), coords[x].end(), P{l, l}, cmpFirst) - coords[x].begin();
        auto ir = lower_bound(coords[x].begin(), coords[x].end(), P{r, r}, cmpFirst) - coords[x].begin();
        return segs[x].prod(il, ir);
    }

    static bool cmpFirst(const P& u, const P& v) {
        return u.first < v.first;
    }

    int n;
    vector<P> points;

    // segtrees, outer layer by x-coordinate
    vector<vector<P>> coords;  // coords[i] stores all points maintained by i-th node in ST
    vector<SegTree<S, op, e>> segs;
};
#line 8 "DataStructure/test/segment_tree_2d_pointaddrectsum.test.cpp"

#define REP(i, a) for (int i = 0, _##i = (a); i < _##i; ++i)

template<typename T>
struct Query {
    static const int ADD = 0;
    static const int QUERY = 1;

    int typ;  // ADD or QUERY
    int x, y;
    int x2, y2;  // for QUERY: [x1, x2-1] * [y1, y2-1]

    T weight;
};

int32_t main() {
    ios::sync_with_stdio(0); cin.tie(0);
    int n = IO::get<int>();
    int q = IO::get<int>();

    using ll = long long;
    vector<Query<ll>> queries;
    REP(i,n) {
        int x = IO::get<int>();
        int y = IO::get<int>();
        ll val = IO::get<ll>();
        queries.push_back({Query<ll>::ADD, x, y, -1, -1, val});
    }

    REP(i,q) {
        int typ = IO::get<int>();
        if (typ == 0) {
            int x = IO::get<int>();
            int y = IO::get<int>();
            ll val = IO::get<ll>();
            queries.push_back({Query<ll>::ADD, x, y, -1, -1, val});
        } else {
            int x = IO::get<int>();
            int y = IO::get<int>();
            int x2 = IO::get<int>();
            int y2 = IO::get<int>();
            queries.push_back({Query<ll>::QUERY, x, y, x2, y2, 0});
        }
    }

    using P = pair<int,int>;
    vector<P> points;
    for (auto query : queries) {
        if (query.typ == Query<ll>::ADD) {
            points.push_back({query.x, query.y});
        }
    }

    SegTree2D<ll, SumSegTreeOp::op, SumSegTreeOp::e, int> st(points);
    for (auto query : queries) {
        if (query.typ == Query<ll>::ADD) {
            P p{query.x, query.y};
            st.set(p, st.get(p) + query.weight);
        } else {
            cout << st.prod(P{query.x, query.y}, P{query.x2, query.y2}) << '\n';
        }
    }
    return 0;
}

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