python/TangDou/AcWing/BinarySearch/ZhengTiErFen/P3332.cpp

#include <algorithm>
#include <iostream>
#include <cstring>

using namespace std;
typedef long long LL;

//快读
LL read() {
    LL x = 0, f = 1;
    char ch = getchar();
    while (ch < '0' || ch > '9') {
        if (ch == '-') f = -1;
        ch = getchar();
    }
    while (ch >= '0' && ch <= '9') {
        x = (x << 3) + (x << 1) + (ch ^ 48);
        ch = getchar();
    }
    return x * f;
}
const int N = 200010;

LL ans[N]; //每个询问的答案
int n, m;  //原始n个数字，共m个操作

//线段树结构体
#define ls u << 1
#define rs u << 1 | 1
struct Node {
    int l, r; //区间范围
    LL lazy;  //区间修改懒标记
    LL sum;   //区间和
} tr[N << 2];

//向上更新统计信息:区间和
void pushup(int u) {
    tr[u].sum = tr[ls].sum + tr[rs].sum;
}

//向下传递区间修改标记
void pushdown(int u) {
    //如果懒标记为0,没有可以传递
    if (!tr[u].lazy) return;

    //向下传递lazy标志
    tr[ls].lazy += tr[u].lazy, tr[rs].lazy += tr[u].lazy; //加法有叠加性

    //用lazy通过计算，更新左右儿子的sum值
    int l = tr[u].l, r = tr[u].r;
    int mid = (l + r) >> 1;
    tr[ls].sum += tr[u].lazy * (mid - l + 1);
    tr[rs].sum += tr[u].lazy * (r - mid);

    // lazy标记清零
    tr[u].lazy = 0;
}

//构建线段树
void build(int u, int l, int r) {
    tr[u] = {l, r, 0, 0};
    if (l == r) return;
    int mid = (l + r) >> 1;
    build(ls, l, mid), build(rs, mid + 1, r);
}

//区间更新
//之所以参数起名为[ql,qr]因为这是查询区间，而不是构建区间
void modify(int u, int ql, int qr, LL c) {
    int l = tr[u].l, r = tr[u].r;     //将变量名l,r保留下来给tr[u].l,tr[u].r
    if (ql <= l && qr >= r) {         // u结点的管辖范围[tr[u].l~tr[u].r]完整命中
        tr[u].lazy += c;              //区间修改加上lazy标记,这样就不用现在就逐层下传了
        tr[u].sum += c * (r - l + 1); //对统计信息进行更新,完成本层的统计信息更新
        return;
    }

    //下面要进行分裂，分裂前需要pushdown
    pushdown(u);

    int mid = (l + r) >> 1;
    if (ql <= mid) modify(ls, ql, qr, c); //与左儿子区间有交集，递归左儿子
    if (mid < qr) modify(rs, ql, qr, c);  //与右儿子区间有交集，递归右儿子

    //向上更新统计信息
    pushup(u);
}

//查询区间sum和
LL query(int u, int ql, int qr) {
    int l = tr[u].l, r = tr[u].r;
    if (ql <= l && r <= qr) return tr[u].sum; //完整命中，返回区间和

    LL res = 0;
    //分裂前需要pushdown
    pushdown(u);
    int mid = (l + r) >> 1;
    if (ql <= mid) res += query(ls, ql, qr); //与左儿子区间有交集，递归左儿子
    if (mid < qr) res += query(rs, ql, qr);  //与右儿子区间有交集，递归右儿子
    return res;
}

//整体二分的查询结构体
struct Q {
    int op, l, r;
    LL k;
    int id;
} q[N], q1[N], q2[N];

//整体二分
void solve(int l, int r, int ql, int qr) {
    if (ql > qr) return; //无效查询区间，防RE

    if (l == r) {
        for (int i = ql; i <= qr; i++)
            if (q[i].op == 2) ans[q[i].id] = l; //二分标识答案
        return;
    }

    int mid = (l + r) >> 1;
    int nl = 0, nr = 0;
    for (int i = ql; i <= qr; i++) {
        if (q[i].op == 1) { //增加
            if (q[i].k > mid) {
                modify(1, q[i].l, q[i].r, 1); //用线段树指定区全都+1
                q1[++nl] = q[i];           //加入左增加操作
            } else
                q2[++nr] = q[i]; //加入右增加操作
        } else {                 //查询
            LL t = query(1, q[i].l, q[i].r);
            if (t >= q[i].k)
                q1[++nl] = q[i];
            else {
                q[i].k -= t;
                q2[++nr] = q[i];
            }
        }
    }
    //有加就有减
    for (int i = ql; i <= qr; i++)
        if (q[i].op == 1)
            if (q[i].k > mid) modify(1, q[i].l, q[i].r, -1);

    //合并到q数组
    for (int i = ql; i < ql + nl; i++) q[i] = q1[i - ql + 1];
    for (int i = ql + nl; i <= qr; i++) q[i] = q2[i - ql - nl + 1];

    //递归左右
    solve(mid + 1, r, ql, ql + nl - 1), solve(l, mid, ql + nl, qr);
}
int main() {
    //原序列n个数字，共m个操作
    n = read(), m = read();

    //构建线段树
    build(1, 1, n);

    int qc = 0; //查询的个数
    for (int i = 1; i <= m; i++) {
        int op = read(), l = read(), r = read(), k = read();
        if (op == 2) //查询操作
            q[i] = {op, l, r, k, ++qc};
        else // 增加操作 op=1
             // 1 l r k : op=1 增加，[l,r]:增加k
            q[i] = {op, l, r, k};
    }

    //整体二分
    solve(-1e9, 1e9, 1, m);

    //输出
    for (int i = 1; i <= qc; i++) printf("%lld\n", ans[i]);

    return 0;
}