poj2528-Mayor's posters

Mayor's posters

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.

The picture below illustrates the case of the sample input.

Sample Input

1

5

1 4

2 6

8 10

3 4

7 10

Sample Output

4

Source

Alberta Collegiate Programming Contest 2003.10.18

思路：离散化+线段树

AC代码：

#include<iostream>
#include<algorithm>
#include<math.h>
using namespace std;
int n;
struct CPost
{
   int L,R;
};
CPost posters[10100];//用来存放海报的两个端点的结构体数组；
int x[20200];//海报的端点瓷砖编号
int hash[10000010];//hash[i]表示瓷砖i所处的离散化后的区间编号
struct CNode
{
   int L,R;
   bool bCovered;//区间[L,R]是否已经被完全覆盖
   CNode *pLeft,*pRight;
};
CNode Tree[1000000];//存放海报区间的线段树
int nNodeCount=0;//结构体指针下标
int Mid(CNode *pRoot)
{
   return (pRoot->L+pRoot->R)/2;
}
void BuildTree(CNode *pRoot,int L,int R)
{
   pRoot->L=L;
   pRoot->R=R;
   pRoot->bCovered=false;
   if(L==R)
     return;
   nNodeCount++;
   pRoot->pLeft=Tree+nNodeCount;
   nNodeCount++;
   pRoot->pRight=Tree+nNodeCount;
   BuildTree(pRoot->pLeft,L,(L+R)/2);
   BuildTree(pRoot->pRight,(L+R)/2+1,R);
}
bool Post(CNode *pRoot,int L,int R)
{/*插入一张正好覆盖区间[L,R]的海报，返回ture说明区间[L,R]，是部分
或全部可见的 */
   if(pRoot->bCovered) return false;//如果该部分已经被完全覆盖，返回false
   /*如果该部分没有被完全覆盖，则完全覆盖此部分 ，并返回ture说明 插入的海报是部分
或全部可见的*/
   if(pRoot->L==L&&pRoot->R==R){
        pRoot->bCovered=true;
        return true;
   }
   //没有找到海报区间要继续寻找
   bool bResult;
   if(R<=Mid(pRoot))
        bResult=Post(pRoot->pLeft,L,R);
   else if(L>=Mid(pRoot)+1)
        bResult=Post(pRoot->pRight,L,R);
   else{
        bool b1=Post(pRoot->pLeft,L,Mid(pRoot));
        bool b2=Post(pRoot->pRight,Mid(pRoot)+1,R);
        bResult=b1||b2; //只要有true的，最终都是true
   }
   //要更新根节点的覆盖情况
   if(pRoot->pLeft->bCovered&&pRoot->pRight->bCovered)
         pRoot->bCovered=true;
   return bResult;

}
int main()
{
    int i,j,k,t;
    scanf("%d",&t);
    int nCaseNo=0;
    while(t--)
    {
       nCaseNo++;
       scanf("%d",&n);
       int nCount=0;
       for(i=0;i<n;i++)
       {
          scanf("%d%d",&posters[i].L,&posters[i].R);
          x[nCount++]=posters[i].L;
          x[nCount++]=posters[i].R;
       }
       sort(x,x+nCount);
       nCount=unique(x,x+nCount)-x;//去掉重复元素
       //下面离散化
       int nIntervalNo=0;
       for(i=0;i<nCount;i++)
       {
          hash[x[i]]=nIntervalNo;
          if(i<nCount-1)
          {
             if(x[i+1]-x[i]==1)
                nIntervalNo++;
             else
                nIntervalNo+=2;
          }
       } 

       BuildTree(Tree,0,nIntervalNo);
       int nSum=0;
       for(i=n-1;i>=0;i--)
       {
          if(Post(Tree,hash[posters[i].L],hash[posters[i].R]))
          nSum++;
       }
       printf("%d\n",nSum);
    }
    return 0;
}