Get The Treasury

http://acm.hdu.edu.cn/showproblem.php?pid=3642

Time Limit: 10000/5000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)

Problem Description

Jack knows that there is a great underground treasury
in a secret region. And he has a special device that can be used to detect
treasury under the surface of the earth. One day he got outside with the device
to ascertain the treasury. He chose many different locations on the surface of
the earth near the secret region. And at each spot he used the device to detect
treasury and got some data from it representing a region, which may contain
treasury below the surface. The data from the device at each spot is six
integers x₁, y₁, z₁, x₂,
y₂ and z₂ (x₁<x₂,
y₁<y₂, z₁<z₂). According to
the instruction of the device they represent the range of x, y and z coordinates
of the region. That is to say, the x coordinate of the region, which may contain
treasury, ranges from x₁ to x₂. So do y and z coordinates.
The origin of the coordinates is a fixed point under the ground.
Jack can’t
get the total volume of the treasury because these regions don’t always contain
treasury. Through years of experience, he discovers that if a region is detected
that may have treasury at more than two different spots, the region really exist
treasure. And now Jack only wants to know the minimum volume of the
treasury.
Now Jack entrusts the problem to you.

Input

The first line of the input file contains a single
integer t, the number of test cases, followed by the input data for each test
case.
Each test case is given in some lines. In the first line there is an
integer n (1 ≤ n ≤ 1000), the number of spots on the surface of the earth that
he had detected. Then n lines follow, every line contains six integers
x₁, y₁, z₁, x₂, y₂ and
z₂, separated by a space. The absolute value of x and y coordinates
of the vertices is no more than 10⁶, and that of z coordinate is no
more than 500.

Output

For each test case, you should output “Case a: b” in a
single line. a is the case number, and b is the minimum volume of treasury. The
case number is counted from one.

Sample Input

2
1
0 0 0 5 6 4
3
0 0 0 5 5 5
3 3 3 9 10 11
3 3 3 13 20 45

Sample Output

Case 1: 0
Case 2: 8

Source

2010
Asia Regional Hangzhou Site —— Online Contest

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题意：求n个长方体至少相交3次的体积和

z这一维只有500，所以枚举z轴，然后就相当于二维的扫描线

线段树维护区间完全覆盖1、2、3次的长度

#include<cstring>
#include<algorithm>
#include<cstdio>
using namespace std;
#define N 1001
#define lc k<<1,l,mid
#define rc k<<1|1,mid+1,r
struct node
{
    int l,r,h,f;
    bool operator < (node p)const
    {
        return h<p.h;
    }
}a[N<<1];
struct edge
{
    int x,xx,y,yy,z,zz;
}b[N];
int sum1[N<<3],sum2[N<<3],sum3[N<<3],f[N<<3],has[N<<1],has2[N<<1];
long long ans;
int n,cnt,opl,opr,w;
void up(int k,int l,int r)
{
    if(f[k]>=3) sum3[k]=has2[r+1]-has2[l];
    else if(f[k]==2)
    {
        sum3[k]=sum1[k<<1]+sum1[k<<1|1];
        sum2[k]=has2[r+1]-has2[l];
    }
    else if(f[k]==1)
    {
        sum3[k]=sum2[k<<1]+sum2[k<<1|1];
        sum2[k]=sum1[k<<1]+sum1[k<<1|1];
        sum1[k]=has2[r+1]-has2[l];
    }
    else
    {
        sum3[k]=sum3[k<<1]+sum3[k<<1|1];
        sum2[k]=sum2[k<<1]+sum2[k<<1|1];
        sum1[k]=sum1[k<<1]+sum1[k<<1|1];
    }
}
void change(int k,int l,int r)
{
    if(opl<=l && r<=opr)
    {
        f[k]+=w;
        up(k,l,r);
        return;
    }
    int mid=l+r>>1;
    if(opl<=mid) change(lc);
    if(opr>mid) change(rc);
    up(k,l,r);
}
int main()
{
    int T;
    scanf("%d",&T);
    for(int t=1;t<=T;t++)
    {
        ans=0;
        cnt=0;
        scanf("%d",&n);
        for(int i=1;i<=n;i++)
        {
            scanf("%d%d%d%d%d%d",&b[i].x,&b[i].y,&b[i].z,&b[i].xx,&b[i].yy,&b[i].zz);
            has[i*2-1]=b[i].z; has[i*2]=b[i].zz;
        }
        sort(has+1,has+2*n+1);
        cnt=unique(has+1,has+2*n+1)-(has+1);
        for(int i=1;i<cnt;i++)
        {
            int sz=0;
            for(int j=1;j<=n;j++)
             if(b[j].z<=has[i] && b[j].zz>=has[i+1])
             {
                 a[++sz].l=b[j].x; a[sz].r=b[j].xx; a[sz].h=b[j].y; a[sz].f=1;
                 a[++sz].l=b[j].x; a[sz].r=b[j].xx; a[sz].h=b[j].yy; a[sz].f=-1;
                 has2[sz-1]=b[j].x; has2[sz]=b[j].xx;
             }
            sort(has2+1,has2+sz+1);
            int m=unique(has2+1,has2+sz+1)-(has2+1);
            sort(a+1,a+sz+1);
            memset(sum1,0,sizeof(sum1));
            memset(sum2,0,sizeof(sum2));
            memset(sum3,0,sizeof(sum3));
            for(int j=1;j<=sz;j++)
            {
                opl=lower_bound(has2+1,has2+m+1,a[j].l)-has2;
                opr=lower_bound(has2+1,has2+m+1,a[j].r)-has2-1;
                w=a[j].f;
                change(1,1,m);
                ans+=1ll*sum3[1]*(a[j+1].h-a[j].h)*(has[i+1]-has[i]);
            }
        }
        printf("Case %d: %I64d\n",t,ans);
    }
}