Mayor's posters（线段树+特殊离散化）

Mayor's posters

Time Limit : 2000/1000ms (Java/Other)   Memory Limit : 131072/65536K (Java/Other)

Total Submission(s) : 53   Accepted Submission(s) : 10

Problem Description

The citizens of Bytetown, AB, could not stand that the candidates in the mayoral election campaign have been placing their electoral posters at all places at their whim. The city council has finally decided to build an electoral wall for placing the posters and introduce the following rules: 

• Every candidate can place exactly one poster on the wall. 
  
• All posters are of the same height equal to the height of the wall; the width of a poster can be any integer number of bytes (byte is the unit of length in Bytetown). 
  
• The wall is divided into segments and the width of each segment is one byte. 
  
• Each poster must completely cover a contiguous number of wall segments.

They have built a wall 10000000 bytes long (such that there is enough place for all candidates). When the electoral campaign was restarted, the candidates were placing their posters on the wall and their posters differed widely in width. Moreover, the candidates started placing their posters on wall segments already occupied by other posters. Everyone in Bytetown was curious whose posters will be visible (entirely or in part) on the last day before elections. 
Your task is to find the number of visible posters when all the posters are placed given the information about posters' size, their place and order of placement on the electoral wall. 

 

Input

The first line of input contains a number c giving the number of cases that follow. The first line of data for a single case contains number 1 <= n <= 10000. The subsequent n lines describe the posters in the order in which they were placed. The i-th line among the n lines contains two integer numbers l_i and ri which are the number of the wall segment occupied by the left end and the right end of the i-th poster, respectively. We know that for each 1 <= i <= n, 1 <= l_i <= ri <= 10000000. After the i-th poster is placed, it entirely covers all wall segments numbered l_i, l_i+1 ,... , ri.

 

Output

For each input data set print the number of visible posters after all the posters are placed. <br> <br>The picture below illustrates the case of the sample input. <br><img src=images/2528_1.jpg>

 

Sample Input

151 42 68 103 47 10

 

Sample Output

4

 

Source

PKU

 

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思路：

首先按照序号由大到小进行然后是按坐标有小到大，运用线段树进行区间维护，输入数据，对数据进行离散化，此处离散化需要点小技巧，借鉴的其他人的。然后在每个点逐个进行访问。

代码：

#include<iostream>#include<cstdio>#include<cstring>#include<algorithm>using namespace std;#define L(rt) (rt<<1)#define R(rt) (rt<<1|1)const int N=100010;int flag;struct tree{    int l,r;    bool vis;}p[N<<2];struct Point{    int id,x;}q[N<<2];int cmp1(Point a,Point b){    return a.x<b.x;}int cmp2(Point a,Point b){    if(a.id==b.id)        return a.x<b.x;    return a.id>b.id;}void build(int L,int R,int pos){    p[pos].l=L;    p[pos].r=R;    p[pos].vis=0;    if(p[pos].l==p[pos].r)        return ;    int mid=(L+R)>>1;    build(L,mid,L(pos));    build(mid+1,R,R(pos));}void PushUp(int pos){    p[pos].vis=p[L(pos)].vis && p[R(pos)].vis;}void query(int L,int R,int pos){    if(p[pos].vis)        return ;    if(p[pos].l==L && p[pos].r==R){        p[pos].vis=1;        flag=1;        return ;    }    int mid=(p[pos].l+p[pos].r)>>1;    if(R<=mid)        query(L,R,L(pos));    else if(L>=mid+1)        query(L,R,R(pos));    else{        query(L,mid,L(pos));        query(mid+1,R,R(pos));    }    PushUp(pos);}int main(){     int c,n;    scanf("%d",&c);    while(c--){        scanf("%d",&n);        for(int i=0;i<2*n;i+=2){            scanf("%d%d",&q[i].x,&q[i+1].x);            q[i].id=q[i+1].id=i;        }        sort(q,q+2*n,cmp1);        int sum=0,pre=0;        for(int i=0;i<2*n;i++){              if(q[i].x==pre)                q[i].x=sum;            else{                pre=q[i].x;                q[i].x=++sum;            }        }        build(1,2*n,1);        sort(q,q+2*n,cmp2);         int ans=0;        for(int i=0;i<2*n;i+=2){            int ll=q[i].x;            int rr=q[i+1].x;            flag=0;            query(ll,rr,1);            if(flag)                ans++;        }        printf("%d\n",ans);    }    return 0;}