SPOJ IITWPC4F - Gopu and the Grid Problem （双线段树区间修改 区间查询）

Posted 2020-09-01 贱人方

Gopu and the Grid Problem

Gopu is interested in the integer co-ordinates of the X-Y plane (0<=x,y<=100000). Each integer coordinate contain a lamp, initially all the lamps are in off mode. Flipping a lamp means switching it on if it is in off mode and vice versa. Maggu will ask gopu 3 type of queries.

 

Type 1:  x l r,  meaning: flip all the lamps whose x-coordinate are between l and r (both inclusive) irrespective of the y coordinate.

 

Type 2:  y l r, meaning: flip all the lamps whose y-coordinate are between l and r (both inclusive) irrespective of the x coordinate.

 

Type 3: q x y X Y, meaning: count the number of lamps which are in ‘on mode’(say this number be A) and ‘off mode’ (say this number  be B) in the region where x-coordinate is between x and X(both inclusive) and y-coordinate is between y and Y(both inclusive).

Input

First line contains Q-number of queries that maggu will ask to gopu. (Q <= 10^5)

Then there will be Q lines each containing a query of one of the three type described above.

Output

For each query of 3rd type you need to output a line containing one integer A.

Example

Input:

3

x 0 1

y 1 2

q 0 0 2 2

 Output: 

 4
一开始想的是直接二维线段树或者二维树状数组搞一下，然后一看数据范围，GG。实在没办法看了网上的题解，用两个线段树分别处理行和列，然后查询的时候，再综合一下。
减去重叠的部分。

#include <iostream>
#include <cstring>
#include <cstdio>
#include <algorithm>
#include <cmath>
#include <string>
#include <map>
#include <stack>
#include <queue>
#include <vector>
#define inf 0x3f3f3f3f
#define met(a,b) memset(a,b,sizeof a)
#define pb push_back
typedef long long ll;
using namespace std;
const int N = 1e5+5;
const int M = 24005;
typedef long long LL;

int q;
struct Seg {
    int Tree[N << 2]; // 标记的行数/列数
    bool lazy[N << 2];
    void init() {
        memset(Tree, 0, sizeof(Tree));
        memset(lazy, 0, sizeof(lazy));
    }
    inline void pushup(int rt) { Tree[rt] = Tree[rt << 1] + Tree[rt << 1 | 1]; }
    inline void pushdown(int pos,int len)
    {
        if(lazy[pos])
        {
            Tree[pos<<1]=len-len/2-Tree[pos<<1];
            Tree[pos<<1|1]=len/2-Tree[pos<<1|1];
            lazy[pos<<1]^=1;
            lazy[pos<<1|1]^=1;
            lazy[pos]=0;
        }
        return;
    }
    void update(int L,int R,int l,int r,int pos)
    {
        if(l>=L&&r<=R)
        {
            Tree[pos]=(r-l+1)-Tree[pos];
            lazy[pos]^=1;
            return;
        }
        int mid=(l+r)>>1;
        pushdown(pos,r-l+1);
        if(L<=mid) update(L,R,l,mid,pos<<1);
        if(mid<R)update(L,R,mid+1,r,pos<<1|1);
        pushup(pos);
    }
    int query(int L,int R,int l,int r,int pos)
    {
        if(L<=l&&r<=R)return Tree[pos];
        int mid=(l+r)>>1;
        pushdown(pos,r-l+1);
        int ans=0;
        if(L<=mid) ans+=query(L,R,l,mid,pos<<1);
        if(R>mid) ans+=query(L,R,mid+1,r,pos<<1|1);
        return ans;
    }
}row,col;

int main() {
    char op[5];
    int n = N;
    row.init();
    col.init();
    int l,r,val;
    int lx,ly,rx,ry;
    char sign[20];
    int m;
    scanf("%d",&m);
    while(m--)
    {
        scanf("%s",sign);
        if(sign[0]==‘x‘)
        {
            scanf("%d%d",&l,&r);
            ++l,++r;
            row.update(l,r,1,n,1);
        }
        else if(sign[0]==‘y‘){
            scanf("%d%d",&l,&r);
            ++l,++r;
            col.update(l,r,1,n,1);
        }
        else
        {
            scanf("%d%d%d%d",&lx,&ly,&rx,&ry);
            ++lx,++ly,++rx,++ry;
            int nx=row.query(lx,rx,1,n,1);
            int ny=col.query(ly,ry,1,n,1);
            ll ans=(ll)(rx-lx+1)*ny+(ll)(ry-ly+1)*nx-(ll)2*nx*ny;
            printf("%lld\n",ans);
        }
    }
}