HDU - 3642 Get The Treasury（线段树求体积交）

https://cn.vjudge.net/problem/HDU-3642

题意

求立方体相交至少3次的体积。

分析

三维的呢。。首先解决至少覆盖三次的问题。则用三个标记，更新时的细节要注意。

注意到z比较小，于是枚举z一层层求，先求出在这一层的面积交，再乘上前后z的差值，就是体积了。注意离散化。

#include <iostream>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <string>
#include <algorithm>
#include <cmath>
#include <ctime>
#include <vector>
#include <queue>
#include <map>
#include <stack>
#include <set>
#include <bitset>
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
#define ms(a, b) memset(a, b, sizeof(a))
#define pb push_back
#define mp make_pair
#define pii pair<int, int>
#define eps 0.0000000001
#define IOS ios::sync_with_stdio(0);cin.tie(0);
#define random(a, b) rand()*rand()%(b-a+1)+a
#define pi acos(-1)
const ll INF = 0x3f3f3f3f3f3f3f3fll;
const int inf = 0x3f3f3f3f;
const int maxn =  + ;
const int maxm =  + ;
const int mod = ;

int n;
int z[maxn];
int y[maxn];
struct LINE{
    int x;
    int y1,y2;
    int z1,z2;
    int flag;
    bool operator <(const LINE &a)const{
        return x<a.x;
    }
}line[maxn];
struct ND{
    int l,r;
    int cover;
    bool f;
    int one;//覆盖一次以上的长度
    int two;//覆盖两次以上的长度
    int more;
}tree[maxn<<];
void build(int rt,int l,int r){
    tree[rt].l=y[l];
    tree[rt].r=y[r];
    tree[rt].cover=;
    tree[rt].one=tree[rt].two=tree[rt].more=;
    tree[rt].f=false;
    if(l+==r){
        tree[rt].f=true;
        return;
    }
    int mid = (l+r)>>;
    build(rt<<,l,mid);
    build(rt<<|,mid,r);
}

void cal(int rt){
    if(tree[rt].cover>=){
        tree[rt].more=tree[rt].r-tree[rt].l;
        tree[rt].one=tree[rt].two=;
    }else if(tree[rt].cover==){
        if(tree[rt].f){
            tree[rt].more=;
            tree[rt].two=tree[rt].r-tree[rt].l;
            tree[rt].one=;
        }else{
            tree[rt].more=tree[rt<<].one+tree[rt<<].two+tree[rt<<].more+
                          tree[rt<<|].one+tree[rt<<|].two+tree[rt<<|].more;
            tree[rt].two=tree[rt].r-tree[rt].l-tree[rt].more;
            tree[rt].one=;
        }
    }else if(tree[rt].cover==){
        if(tree[rt].f){
            tree[rt].more=;
            tree[rt].two=;
            tree[rt].one=tree[rt].r-tree[rt].l;
        }else{
            tree[rt].more=tree[rt<<].two+tree[rt<<].more+
                          tree[rt<<|].two+tree[rt<<|].more;
            tree[rt].two=tree[rt<<].one+tree[rt<<|].one;
            tree[rt].one=tree[rt].r-tree[rt].l-tree[rt].more-tree[rt].two;
        }
    }else{
        if(tree[rt].f){
            tree[rt].more=tree[rt].one=tree[rt].two=;
        }else{
            tree[rt].one=tree[rt<<].one+tree[rt<<|].one;
            tree[rt].more=tree[rt<<].more+tree[rt<<|].more;
            tree[rt].two=tree[rt<<].two+tree[rt<<|].two;
        }
    }
}
void update(int rt,double l,double r,int flag){
    if(l==tree[rt].l&&r==tree[rt].r){
        tree[rt].cover+=flag;
        cal(rt);
        return;
    }
    if(tree[rt<<].r>=r) update(rt<<,l,r,flag);
    else if(l>=tree[rt<<|].l) update(rt<<|,l,r,flag);
    else{
        update(rt<<,l,tree[rt<<].r,flag);
        update(rt<<|,tree[rt<<|].l,r,flag);
    }
    cal(rt);
}
LINE tmp[maxn];
int main() {
#ifdef LOCAL
    freopen("in.txt", "r", stdin);
//    freopen("output.txt", "w", stdout);
#endif
    int T,cas=;
    scanf("%d",&T);
    while(T--){
        scanf("%d",&n);
        int cnt=;
        int x1,x2,y1,y2,z1,z2;
        for(int i=;i<n;i++){
            scanf("%d%d%d%d%d%d",&x1,&y1,&z1,&x2,&y2,&z2);
            z[cnt]=z1;
            y[cnt]=y1;
            line[cnt].x=x1;
            line[cnt].y1=y1;
            line[cnt].y2=y2;
            line[cnt].z1=z1;
            line[cnt].z2=z2;
            line[cnt++].flag=;

            z[cnt]=z2;
            y[cnt]=y2;
            line[cnt].x=x2;
            line[cnt].y1=y1;
            line[cnt].y2=y2;
            line[cnt].z1=z1;
            line[cnt].z2=z2;
            line[cnt++].flag=-;
        }
        sort(y,y+cnt);
        sort(line,line+cnt);
        int t1=unique(y,y+cnt)-y;
        build(,,t1-);
        sort(z,z+cnt);
        int t2=unique(z,z+cnt)-z;
        ll ans=;
        ll area=;
        for(int i=;i<t2-;i++){
            int m=;
            for(int j=;j<cnt;j++){
                if(line[j].z1<=z[i]&&line[j].z2>z[i])
                    tmp[m++]=line[j];
            }
            area=;
            update(,tmp[].y1,tmp[].y2,tmp[].flag);
            for(int j=;j<m;j++){
                area+=1ll*tree[].more*(tmp[j].x-tmp[j-].x);
                update(,tmp[j].y1,tmp[j].y2,tmp[j].flag);
            }
            ans+=area*(z[i+]-z[i]);
        }
        printf("Case %d: %lld\n",cas++,ans);
    }
    return ;
}