bzoj4066

Posted 2020-10-15 123456

KD-tree

强制在线就不能愉快的做这道题了。

我们用KD-tree维护平面上的点，这样建出来的树高大概是log,复杂度过得去，但是插入过多会使树深很深，这样就能卡死，那么我们每个10000次插入就重构一次。

#include<bits/stdc++.h>
using namespace std;
const int N = 2e5 + 5;
int n, root, cnt, m = 10000, d, last;
struct data {
    int x, y, mx_x, mn_x, mx_y, mn_y, lc, rc, sum, val;
    bool friend operator < (const data &a, const data &b) {
        if(d == 0) return a.x == b.x ? a.y < b.y : a.x < b.x;
        if(d == 1) return a.y == b.y ? a.x < b.x : a.y < b.y;
    }
    bool friend operator == (const data &a, const data &b) {
        return a.x == b.x && a.y == b.y;
    }
} a[N], b[N];
inline void read(int &x)
{
    x = 0;
    int f = 1; char c = getchar();
    while(c < ‘0‘ || c > ‘9‘) { if(c == ‘-‘) f = -1; c = getchar(); }
    while(c >= ‘0‘ && c <= ‘9‘) { x = (x << 1) + (x << 3) + c - ‘0‘; c = getchar(); }
    x *= f;
}
bool in(int x1, int y1, int x2, int y2, int X1, int Y1, int X2, int Y2)
{
    return X1 >= x1 && Y1 >= y1 && x2 >= X2 && y2 >= Y2;
}
bool out(int x1, int y1, int x2, int y2, int X1, int Y1, int X2, int Y2)
{
    return x1 > X2 || x2 < X1 || y1 > Y2 || y2 < Y1;
}
void update(int x)
{
    a[x].mn_x = min(a[x].x, min(a[a[x].lc].mn_x, a[a[x].rc].mn_x));
    a[x].mx_x = max(a[x].x, max(a[a[x].lc].mx_x, a[a[x].rc].mx_x));
    a[x].mn_y = min(a[x].y, min(a[a[x].lc].mn_y, a[a[x].rc].mn_y));
    a[x].mx_y = max(a[x].y, max(a[a[x].lc].mx_y, a[a[x].rc].mx_y));
    a[x].sum = a[x].val + a[a[x].lc].sum + a[a[x].rc].sum; 
}  
int build(int l, int r, int D)
{
    if(l > r) return 0;
    d = D;
    int mid = (l + r) >> 1;
    nth_element(b + l, b + mid, b + r + 1);
    a[mid] = b[mid];
    a[mid].lc = build(l, mid - 1, D ^ 1);
    a[mid].rc = build(mid + 1, r, D ^ 1);
    update(mid);
    return mid;
}
void insert(int &x, const data &tmp, int D)
{
    d = D;
    if(!x) 
    {
        x = ++cnt;
        a[x].x = a[x].mn_x = a[x].mx_x = tmp.x;
        a[x].y = a[x].mn_y = a[x].mx_y = tmp.y;
        a[x].sum = a[x].val = tmp.val;
        return;
    }
    if(a[x] == tmp) 
    {
        a[x].val += tmp.val;
        a[x].sum += tmp.val;
        return;
    }
    if(tmp < a[x]) insert(a[x].lc, tmp, D ^ 1);
    else insert(a[x].rc, tmp, D ^ 1);
    update(x);
}
int query(int x, int x1, int y1, int x2, int y2)
{
    if(!x) return 0;
    int ret = 0;
    if(in(x1, y1, x2, y2, a[x].mn_x, a[x].mn_y, a[x].mx_x, a[x].mx_y)) return a[x].sum; 
    if(out(x1, y1, x2, y2, a[x].mn_x, a[x].mn_y, a[x].mx_x, a[x].mx_y)) return 0;
    if(in(x1, y1, x2, y2, a[x].x, a[x].y, a[x].x, a[x].y)) ret += a[x].val;
    ret += query(a[x].lc, x1, y1, x2, y2) + query(a[x].rc, x1, y1, x2, y2);
    return ret;
}
int main()
{
//  freopen("bzoj_4066.in", "r", stdin);
//  freopen("bzoj_4066.out", "w", stdout);
    a[0].mn_x = 1e9;
    a[0].mx_x = -1e9;
    a[0].mn_y = 1e9;
    a[0].mx_y = -1e9;
    b[0].mn_x = 1e9;
    b[0].mx_x = -1e9;
    b[0].mn_y = 1e9;
    b[0].mx_y = -1e9;
    read(n);
    while(1)
    {
        int opt, x1, y1, x2, y2;
        data tmp;
        read(opt);
        if(opt == 1) 
        {
            read(tmp.x);
            read(tmp.y);
            read(tmp.val);
            tmp.x ^= last;
            tmp.y ^= last;
            tmp.val ^= last;
            insert(root, tmp, 0);
            if(cnt == m)
            {
                for(int i = 1; i <= cnt; ++i) b[i] = a[i];
                root = build(1, cnt, 0); 
                m += 10000;
            }
        }
        if(opt == 2) 
        {
            read(x1);
            read(y1);
            read(x2);
            read(y2);
            x1 ^= last;
            x2 ^= last;
            y1 ^= last;
            y2 ^= last;
            printf("%d\n", last = query(root, x1, y1, x2, y2));
        }
        if(opt == 3) break;
    }
//  fclose(stdin);
//  fclose(stdout);
    return 0;
}

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