P2163 [SHOI2007] 园丁的烦恼 题解

题目链接：园丁的烦恼

挺经典的题目，转化成二维数点去做

这玩意和常规的偏序计数问题有区别：

转化为求 \(a \le x \le b \ \&\& \ c \le y \le d\) 的数量，这种就别想着拆来拆去了，这种权值类带偏序计数类问题，是经典的可差性问题，我们计：\(ans(x,l,r)\) 表示 \(t\le x,l\le y\le r\) 的数量，那么原问题就可以差分了：\(=ans(b,c,d)-ans(a-1,c,d)\)，这玩意可能你一开始会想直接 \(cdq\) 分治，因为统计的 \(l\le y \le r\) 也可以看做可差性问题，\(pre[r]-pre[l-1]\)，\(pre[x]\ 为 \le x\ 的权值数量\)。这个直接权值树状数组就行，所以只需要 \(cdq\) 保证 \(x\) 的序与 \(y\) 的插入序即可，注意离散化。当然这个复杂度是 \(O(n\log^2{(n+m)})\)，而且中间离散化需要包括了 \(x\) 和 \(y\)，实质上应该为 \(2 \times n+4\times m\) 个需要离散化点，常数大：

cdq分治 参照代码

#include <bits/stdc++.h>

// #pragma GCC optimize(2)
// #pragma GCC optimize("Ofast,no-stack-protector,unroll-loops,fast-math")
// #pragma GCC target("sse,sse2,sse3,ssse3,sse4.1,sse4.2,avx,avx2,popcnt,tune=native")

#define isPbdsFile

#ifdef isPbdsFile

#include <bits/extc++.h>

#else

#include <ext/pb_ds/priority_queue.hpp>
#include <ext/pb_ds/hash_policy.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#include <ext/pb_ds/trie_policy.hpp>
#include <ext/pb_ds/tag_and_trait.hpp>
#include <ext/pb_ds/hash_policy.hpp>
#include <ext/pb_ds/list_update_policy.hpp>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/exception.hpp>
#include <ext/rope>

#endif

using namespace std;
using namespace __gnu_cxx;
using namespace __gnu_pbds;
typedef long long ll;
typedef long double ld;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef tuple<int, int, int> tii;
typedef tuple<ll, ll, ll> tll;
typedef unsigned int ui;
typedef unsigned long long ull;
typedef __int128 i128;
#define hash1 unordered_map
#define hash2 gp_hash_table
#define hash3 cc_hash_table
#define stdHeap std::priority_queue
#define pbdsHeap __gnu_pbds::priority_queue
#define sortArr(a, n) sort(a+1,a+n+1)
#define all(v) v.begin(),v.end()
#define yes cout<<"YES"
#define no cout<<"NO"
#define Spider ios_base::sync_with_stdio(false);cin.tie(nullptr);cout.tie(nullptr);
#define MyFile freopen("..\\input.txt", "r", stdin),freopen("..\\output.txt", "w", stdout);
#define forn(i, a, b) for(int i = a; i <= b; i++)
#define forv(i, a, b) for(int i=a;i>=b;i--)
#define ls(x) (x<<1)
#define rs(x) (x<<1|1)
#define endl '\n'
//用于Miller-Rabin
[[maybe_unused]] static int Prime_Number[13] = {0, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37};

template <typename T>
int disc(T* a, int n)
{
    return unique(a + 1, a + n + 1) - (a + 1);
}

template <typename T>
T lowBit(T x)
{
    return x & -x;
}

template <typename T>
T Rand(T l, T r)
{
    static mt19937 Rand(time(nullptr));
    uniform_int_distribution<T> dis(l, r);
    return dis(Rand);
}

template <typename T1, typename T2>
T1 modt(T1 a, T2 b)
{
    return (a % b + b) % b;
}

template <typename T1, typename T2, typename T3>
T1 qPow(T1 a, T2 b, T3 c)
{
    a %= c;
    T1 ans = 1;
    for (; b; b >>= 1, (a *= a) %= c)if (b & 1)(ans *= a) %= c;
    return modt(ans, c);
}

template <typename T>
void read(T& x)
{
    x = 0;
    T sign = 1;
    char ch = getchar();
    while (!isdigit(ch))
    {
        if (ch == '-')sign = -1;
        ch = getchar();
    }
    while (isdigit(ch))
    {
        x = (x << 3) + (x << 1) + (ch ^ 48);
        ch = getchar();
    }
    x *= sign;
}

template <typename T, typename... U>
void read(T& x, U&... y)
{
    read(x);
    read(y...);
}

template <typename T>
void write(T x)
{
    if (typeid(x) == typeid(char))return;
    if (x < 0)x = -x, putchar('-');
    if (x > 9)write(x / 10);
    putchar(x % 10 ^ 48);
}

template <typename C, typename T, typename... U>
void write(C c, T x, U... y)
{
    write(x), putchar(c);
    write(c, y...);
}


template <typename T11, typename T22, typename T33>
struct T3
{
    T11 one;
    T22 tow;
    T33 three;

    bool operator<(const T3 other) const
    {
        if (one == other.one)
        {
            if (tow == other.tow)return three < other.three;
            return tow < other.tow;
        }
        return one < other.one;
    }

    T3() { one = tow = three = 0; }

    T3(T11 one, T22 tow, T33 three) : one(one), tow(tow), three(three)
    {
    }
};

template <typename T1, typename T2>
void uMax(T1& x, T2 y)
{
    if (x < y)x = y;
}

template <typename T1, typename T2>
void uMin(T1& x, T2 y)
{
    if (x > y)x = y;
}

struct Hash
{
    static uint64_t splitmix64(uint64_t x)
    {
        x += 0x9e3779b97f4a7c15;
        x = (x ^ x >> 30) * 0xbf58476d1ce4e5b9;
        x = (x ^ x >> 27) * 0x94d049bb133111eb;
        return x ^ x >> 31;
    }

    static size_t get(const uint64_t x)
    {
        static const uint64_t FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();
        return splitmix64(x + FIXED_RANDOM);
    }

    template <typename T>
    size_t operator()(T x) const
    {
        return get(std::hash<T>()(x));
    }

    template <typename F, typename S>
    size_t operator()(pair<F, S> p) const
    {
        return get(std::hash<F>()(p.first)) ^ std::hash<S>()(p.second);
    }
};

constexpr int N = 2e6 + 10;

struct Query
{
    int x, y;
    int l, r; //如果是查找y的限制范围
    int id;
} qu[N];

inline bool cmpX(const Query& a, const Query& b)
{
    if (a.x != b.x)return a.x < b.x;
    return a.y < b.y;
}

inline bool cmpY(const Query& a, const Query& b)
{
    return a.y < b.y;
}

int ans[N];
set<int> ord;
hash2<int, int, Hash> mp;
int n, m, mx;
int bit[N];
int cnt;
int ansIdx;

inline void add(int x, const int val)
{
    while (x <= mx)bit[x] += val, x += lowBit(x);
}

inline int query(int x)
{
    int res = 0;
    for (; x; x -= lowBit(x))res += bit[x];
    return res;
}

inline int query(const int l, const int r)
{
    return query(r) - query(l - 1);
}

inline void cdq(const int L, const int R)
{
    const int mid = L + R >> 1;
    if (L == R)return;
    cdq(L, mid), cdq(mid + 1, R);
    stable_sort(qu + L, qu + mid + 1, cmpY), stable_sort(qu + mid + 1, qu + R + 1, cmpY);
    int l = L;
    forn(r, mid+1, R)
    {
        const auto [x,y,queryL,queryR,id] = qu[r];
        while (l <= mid and qu[l].y <= y)
        {
            if (!qu[l].id)add(qu[l].y, 1);
            l++;
        }
        if (id)
        {
            ans[abs(id)] += id / abs(id) * query(queryL, queryR);
        }
    }
    forn(i, L, l-1)if (!qu[i].id)add(qu[i].y, -1);
}

inline void solve()
{
    read(n, m);
    forn(i, 1, n)
    {
        int x, y;
        read(x, y), ord.insert(x), ord.insert(y);
        qu[++cnt] = Query(x, y, 0, 0, 0);
    }
    forn(i, 1, m)
    {
        int x1, y1, x2, y2;
        read(x1, y1, x2, y2);
        ord.insert(x1 - 1), ord.insert(x2);
        ord.insert(y1), ord.insert(y2);
        ++ansIdx;
        qu[++cnt] = Query(x2, y2, y1, y2, ansIdx);
        qu[++cnt] = Query(x1 - 1, y2, y1, y2, -ansIdx);
    }
    for (const auto x : ord)mp[x] = ++mx;
    forn(i, 1, cnt)
    {
        auto& [x,y,l,r,id] = qu[i];
        x = mp[x], y = mp[y];
        if (id)l = mp[l], r = mp[r];
    }
    stable_sort(qu + 1, qu + cnt + 1, cmpX);
    cdq(1, cnt);
    forn(i, 1, ansIdx)write(endl, ans[i]);
}

signed int main()
{
    // MyFile
    Spider
    //------------------------------------------------------
    // clock_t start = clock();
    int test = 1;
    //    read(test);
    // cin >> test;
    forn(i, 1, test)solve();
    //    while (cin >> n, n)solve();
    //    while (cin >> test)solve();
    // clock_t end = clock();
    // cerr << "time = " << double(end - start) / CLOCKS_PER_SEC << "s" << endl;
}

归并排序合并优化 cdq分治

#include <bits/stdc++.h>

// #pragma GCC optimize(2)
// #pragma GCC optimize("Ofast,no-stack-protector,unroll-loops,fast-math")
// #pragma GCC target("sse,sse2,sse3,ssse3,sse4.1,sse4.2,avx,avx2,popcnt,tune=native")

#define isPbdsFile

#ifdef isPbdsFile

#include <bits/extc++.h>

#else

#include <ext/pb_ds/priority_queue.hpp>
#include <ext/pb_ds/hash_policy.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#include <ext/pb_ds/trie_policy.hpp>
#include <ext/pb_ds/tag_and_trait.hpp>
#include <ext/pb_ds/hash_policy.hpp>
#include <ext/pb_ds/list_update_policy.hpp>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/exception.hpp>
#include <ext/rope>

#endif

using namespace std;
using namespace __gnu_cxx;
using namespace __gnu_pbds;
typedef long long ll;
typedef long double ld;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef tuple<int, int, int> tii;
typedef tuple<ll, ll, ll> tll;
typedef unsigned int ui;
typedef unsigned long long ull;
typedef __int128 i128;
#define hash1 unordered_map
#define hash2 gp_hash_table
#define hash3 cc_hash_table
#define stdHeap std::priority_queue
#define pbdsHeap __gnu_pbds::priority_queue
#define sortArr(a, n) sort(a+1,a+n+1)
#define all(v) v.begin(),v.end()
#define yes cout<<"YES"
#define no cout<<"NO"
#define Spider ios_base::sync_with_stdio(false);cin.tie(nullptr);cout.tie(nullptr);
#define MyFile freopen("..\\input.txt", "r", stdin),freopen("..\\output.txt", "w", stdout);
#define forn(i, a, b) for(int i = a; i <= b; i++)
#define forv(i, a, b) for(int i=a;i>=b;i--)
#define ls(x) (x<<1)
#define rs(x) (x<<1|1)
#define endl '\n'
//用于Miller-Rabin
[[maybe_unused]] static int Prime_Number[13] = {0, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37};

template <typename T>
int disc(T* a, int n)
{
    return unique(a + 1, a + n + 1) - (a + 1);
}

template <typename T>
T lowBit(T x)
{
    return x & -x;
}

template <typename T>
T Rand(T l, T r)
{
    static mt19937 Rand(time(nullptr));
    uniform_int_distribution<T> dis(l, r);
    return dis(Rand);
}

template <typename T1, typename T2>
T1 modt(T1 a, T2 b)
{
    return (a % b + b) % b;
}

template <typename T1, typename T2, typename T3>
T1 qPow(T1 a, T2 b, T3 c)
{
    a %= c;
    T1 ans = 1;
    for (; b; b >>= 1, (a *= a) %= c)if (b & 1)(ans *= a) %= c;
    return modt(ans, c);
}

template <typename T>
void read(T& x)
{
    x = 0;
    T sign = 1;
    char ch = getchar();
    while (!isdigit(ch))
    {
        if (ch == '-')sign = -1;
        ch = getchar();
    }
    while (isdigit(ch))
    {
        x = (x << 3) + (x << 1) + (ch ^ 48);
        ch = getchar();
    }
    x *= sign;
}

template <typename T, typename... U>
void read(T& x, U&... y)
{
    read(x);
    read(y...);
}

template <typename T>
void write(T x)
{
    if (typeid(x) == typeid(char))return;
    if (x < 0)x = -x, putchar('-');
    if (x > 9)write(x / 10);
    putchar(x % 10 ^ 48);
}

template <typename C, typename T, typename... U>
void write(C c, T x, U... y)
{
    write(x), putchar(c);
    write(c, y...);
}


template <typename T11, typename T22, typename T33>
struct T3
{
    T11 one;
    T22 tow;
    T33 three;

    bool operator<(const T3 other) const
    {
        if (one == other.one)
        {
            if (tow == other.tow)return three < other.three;
            return tow < other.tow;
        }
        return one < other.one;
    }

    T3() { one = tow = three = 0; }

    T3(T11 one, T22 tow, T33 three) : one(one), tow(tow), three(three)
    {
    }
};

template <typename T1, typename T2>
void uMax(T1& x, T2 y)
{
    if (x < y)x = y;
}

template <typename T1, typename T2>
void uMin(T1& x, T2 y)
{
    if (x > y)x = y;
}

struct Hash
{
    static uint64_t splitmix64(uint64_t x)
    {
        x += 0x9e3779b97f4a7c15;
        x = (x ^ x >> 30) * 0xbf58476d1ce4e5b9;
        x = (x ^ x >> 27) * 0x94d049bb133111eb;
        return x ^ x >> 31;
    }

    static size_t get(const uint64_t x)
    {
        static const uint64_t FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();
        return splitmix64(x + FIXED_RANDOM);
    }

    template <typename T>
    size_t operator()(T x) const
    {
        return get(std::hash<T>()(x));
    }

    template <typename F, typename S>
    size_t operator()(pair<F, S> p) const
    {
        return get(std::hash<F>()(p.first)) ^ std::hash<S>()(p.second);
    }
};

constexpr int N = 2e6 + 10;

struct Query
{
    int x, y;
    int l, r; //如果是查找y的限制范围
    int id;
} qu[N];

inline bool cmpX(const Query& a, const Query& b)
{
    if (a.x != b.x)return a.x < b.x;
    return a.y < b.y;
}

inline bool cmpY(const Query& a, const Query& b)
{
    return a.y < b.y;
}

int ans[N];
set<int> ord;
hash2<int, int, Hash> mp;
int n, m, mx;
int bit[N];
int cnt;
int ansIdx;

inline void add(int x, const int val)
{
    while (x <= mx)bit[x] += val, x += lowBit(x);
}

inline int query(int x)
{
    int res = 0;
    for (; x; x -= lowBit(x))res += bit[x];
    return res;
}

inline int query(const int l, const int r)
{
    return query(r) - query(l - 1);
}

Query tmp[N];

inline void cdq(const int L, const int R)
{
    const int mid = L + R >> 1;
    if (L == R)return;
    cdq(L, mid), cdq(mid + 1, R);
    int l = L;
    forn(r, mid+1, R)
    {
        const auto [x,y,queryL,queryR,id] = qu[r];
        while (l <= mid and qu[l].y <= y)
        {
            if (!qu[l].id)add(qu[l].y, 1);
            l++;
        }
        if (id)
        {
            ans[abs(id)] += id / abs(id) * query(queryL, queryR);
        }
    }
    forn(i, L, l-1)if (!qu[i].id)add(qu[i].y, -1);
    merge(qu + L, qu + mid + 1, qu + mid + 1, qu + R + 1, tmp + L, cmpY);
    forn(i, L, R)qu[i] = tmp[i];
}

inline void solve()
{
    read(n, m);
    forn(i, 1, n)
    {
        int x, y;
        read(x, y), ord.insert(x), ord.insert(y);
        qu[++cnt] = Query(x, y, 0, 0, 0);
    }
    forn(i, 1, m)
    {
        int x1, y1, x2, y2;
        read(x1, y1, x2, y2);
        ord.insert(x1 - 1), ord.insert(x2);
        ord.insert(y1), ord.insert(y2);
        ++ansIdx;
        qu[++cnt] = Query(x2, y2, y1, y2, ansIdx);
        qu[++cnt] = Query(x1 - 1, y2, y1, y2, -ansIdx);
    }
    for (const auto x : ord)mp[x] = ++mx;
    forn(i, 1, cnt)
    {
        auto& [x,y,l,r,id] = qu[i];
        x = mp[x], y = mp[y];
        if (id)l = mp[l], r = mp[r];
    }
    stable_sort(qu + 1, qu + cnt + 1, cmpX);
    cdq(1, cnt);
    forn(i, 1, ansIdx)write(endl, ans[i]);
}

signed int main()
{
    // MyFile
    Spider
    //------------------------------------------------------
    // clock_t start = clock();
    int test = 1;
    //    read(test);
    // cin >> test;
    forn(i, 1, test)solve();
    //    while (cin >> n, n)solve();
    //    while (cin >> test)solve();
    // clock_t end = clock();
    // cerr << "time = " << double(end - start) / CLOCKS_PER_SEC << "s" << endl;
}

如果带修，那么显然这么做很合适，但这题不带修，我们可以使用不带修更优秀的二维数点，就是离线序列扫描线。不过这里显然和值域有关，我们对 \(x\) 所在值域离线扫描线，常规的就是按照 \(x\) 挂载修改和查询，从最小的 \(x\) 访问，更新修改和查询，每次修改就是 \(y\) 的加入，查找就是 \(l\le y \le r\) 的数量，所以只需要按照 \(x\) 排序就行。然后查询按照上述说的可差性问题拆分贡献，常规离散化 \(y\) 以后跑关于 \(x\) 的序列扫描线即可，这里稍微注意下的是由于题目是 \(\le\) 非严格序，所以当修改和查询的 \(x\) 相同的时，我们需要把修改放在查询的 \(query\) 之前。当然你也可以分开做扫描线，每次先更新修改扫描线，再更新对应的查询扫描线上的挂载点。这样的复杂度显然是 \(O((n+m)\log{n})\)

离线扫描线做法

#include <bits/stdc++.h>

// #pragma GCC optimize(2)
// #pragma GCC optimize("Ofast,no-stack-protector,unroll-loops,fast-math")
// #pragma GCC target("sse,sse2,sse3,ssse3,sse4.1,sse4.2,avx,avx2,popcnt,tune=native")

#define isPbdsFile

#ifdef isPbdsFile

#include <bits/extc++.h>

#else

#include <ext/pb_ds/priority_queue.hpp>
#include <ext/pb_ds/hash_policy.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#include <ext/pb_ds/trie_policy.hpp>
#include <ext/pb_ds/tag_and_trait.hpp>
#include <ext/pb_ds/hash_policy.hpp>
#include <ext/pb_ds/list_update_policy.hpp>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/exception.hpp>
#include <ext/rope>

#endif

using namespace std;
using namespace __gnu_cxx;
using namespace __gnu_pbds;
typedef long long ll;
typedef long double ld;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef tuple<int, int, int> tii;
typedef tuple<ll, ll, ll> tll;
typedef unsigned int ui;
typedef unsigned long long ull;
typedef __int128 i128;
#define hash1 unordered_map
#define hash2 gp_hash_table
#define hash3 cc_hash_table
#define stdHeap std::priority_queue
#define pbdsHeap __gnu_pbds::priority_queue
#define sortArr(a, n) sort(a+1,a+n+1)
#define all(v) v.begin(),v.end()
#define yes cout<<"YES"
#define no cout<<"NO"
#define Spider ios_base::sync_with_stdio(false);cin.tie(nullptr);cout.tie(nullptr);
#define MyFile freopen("..\\input.txt", "r", stdin),freopen("..\\output.txt", "w", stdout);
#define forn(i, a, b) for(int i = a; i <= b; i++)
#define forv(i, a, b) for(int i=a;i>=b;i--)
#define ls(x) (x<<1)
#define rs(x) (x<<1|1)
#define endl '\n'
//用于Miller-Rabin
[[maybe_unused]] static int Prime_Number[13] = {0, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37};

template <typename T>
int disc(T* a, int n)
{
    return unique(a + 1, a + n + 1) - (a + 1);
}

template <typename T>
T lowBit(T x)
{
    return x & -x;
}

template <typename T>
T Rand(T l, T r)
{
    static mt19937 Rand(time(nullptr));
    uniform_int_distribution<T> dis(l, r);
    return dis(Rand);
}

template <typename T1, typename T2>
T1 modt(T1 a, T2 b)
{
    return (a % b + b) % b;
}

template <typename T1, typename T2, typename T3>
T1 qPow(T1 a, T2 b, T3 c)
{
    a %= c;
    T1 ans = 1;
    for (; b; b >>= 1, (a *= a) %= c)if (b & 1)(ans *= a) %= c;
    return modt(ans, c);
}

template <typename T>
void read(T& x)
{
    x = 0;
    T sign = 1;
    char ch = getchar();
    while (!isdigit(ch))
    {
        if (ch == '-')sign = -1;
        ch = getchar();
    }
    while (isdigit(ch))
    {
        x = (x << 3) + (x << 1) + (ch ^ 48);
        ch = getchar();
    }
    x *= sign;
}

template <typename T, typename... U>
void read(T& x, U&... y)
{
    read(x);
    read(y...);
}

template <typename T>
void write(T x)
{
    if (typeid(x) == typeid(char))return;
    if (x < 0)x = -x, putchar('-');
    if (x > 9)write(x / 10);
    putchar(x % 10 ^ 48);
}

template <typename C, typename T, typename... U>
void write(C c, T x, U... y)
{
    write(x), putchar(c);
    write(c, y...);
}


template <typename T11, typename T22, typename T33>
struct T3
{
    T11 one;
    T22 tow;
    T33 three;

    bool operator<(const T3 other) const
    {
        if (one == other.one)
        {
            if (tow == other.tow)return three < other.three;
            return tow < other.tow;
        }
        return one < other.one;
    }

    T3() { one = tow = three = 0; }

    T3(T11 one, T22 tow, T33 three) : one(one), tow(tow), three(three)
    {
    }
};

template <typename T1, typename T2>
void uMax(T1& x, T2 y)
{
    if (x < y)x = y;
}

template <typename T1, typename T2>
void uMin(T1& x, T2 y)
{
    if (x > y)x = y;
}

struct Hash
{
    static uint64_t splitmix64(uint64_t x)
    {
        x += 0x9e3779b97f4a7c15;
        x = (x ^ x >> 30) * 0xbf58476d1ce4e5b9;
        x = (x ^ x >> 27) * 0x94d049bb133111eb;
        return x ^ x >> 31;
    }

    static size_t get(const uint64_t x)
    {
        static const uint64_t FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();
        return splitmix64(x + FIXED_RANDOM);
    }

    template <typename T>
    size_t operator()(T x) const
    {
        return get(std::hash<T>()(x));
    }

    template <typename F, typename S>
    size_t operator()(pair<F, S> p) const
    {
        return get(std::hash<F>()(p.first)) ^ std::hash<S>()(p.second);
    }
};

constexpr int N = 2e6 + 10;

struct Query
{
    int x, y;
    int l, r;
    int id;

    bool operator<(const Query& other) const
    {
        if (x != other.x)return x < other.x;
        return abs(id) < abs(other.id);
    }
} node[N];

int cnt, ansCnt;
int ans[N];
set<int> ord;
hash2<int, int, Hash> mp;
int n, m, mx;
int bit[N];

inline void add(int x)
{
    for (; x <= mx; x += lowBit(x))bit[x]++;
}

inline int query(int x)
{
    int res = 0;
    for (; x; x -= lowBit(x))res += bit[x];
    return res;
}

inline int query(const int l, const int r)
{
    return query(r) - query(l - 1);
}

inline void solve()
{
    read(n, m);
    forn(i, 1, n)
    {
        int x, y;
        read(x, y);
        ord.insert(y);
        node[++cnt] = Query(x, y, 0, 0, 0);
    }
    forn(i, 1, m)
    {
        ++ansCnt;
        int x1, y1, x2, y2;
        read(x1, y1, x2, y2);
        ord.insert(y1), ord.insert(y2);
        node[++cnt] = Query(x2, 0, y1, y2, ansCnt);
        node[++cnt] = Query(x1 - 1, 0, y1, y2, -ansCnt);
    }
    for (const int x : ord)mp[x] = ++mx;
    forn(i, 1, cnt)
    {
        auto& [x,y,l,r,id] = node[i];
        if (id)l = mp[l], r = mp[r];
        else y = mp[y];
    }
    sortArr(node, cnt);
    forn(i, 1, cnt)
    {
        const auto [x,y,l,r,id] = node[i];
        if (!id)add(y);
        else
        {
            const int val = id / abs(id);
            ans[abs(id)] += val * query(l, r);
        }
    }
    forn(i, 1, ansCnt)write(endl, ans[i]);
}

signed int main()
{
    // MyFile
    Spider
    //------------------------------------------------------
    // clock_t start = clock();
    int test = 1;
    //    read(test);
    // cin >> test;
    forn(i, 1, test)solve();
    //    while (cin >> n, n)solve();
    //    while (cin >> test)solve();
    // clock_t end = clock();
    // cerr << "time = " << double(end - start) / CLOCKS_PER_SEC << "s" << endl;
}