HDOJ2795 线段树查询区间最大值

本文介绍了一个关于公告板布局的问题及其实现算法。该算法利用线段树查询区间最大值的方法来确定不同宽度的公告如何在有限空间内进行有效排列。具体应用场景为大学公告板上的公告张贴,每条公告作为单位高度的纸带被放置到最合适的位置。

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Billboard

Time Limit: 20000/8000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 24704    Accepted Submission(s): 10143


Problem Description
At the entrance to the university, there is a huge rectangular billboard of size h*w (h is its height and w is its width). The board is the place where all possible announcements are posted: nearest programming competitions, changes in the dining room menu, and other important information.

On September 1, the billboard was empty. One by one, the announcements started being put on the billboard.

Each announcement is a stripe of paper of unit height. More specifically, the i-th announcement is a rectangle of size 1 * wi.

When someone puts a new announcement on the billboard, she would always choose the topmost possible position for the announcement. Among all possible topmost positions she would always choose the leftmost one.

If there is no valid location for a new announcement, it is not put on the billboard (that's why some programming contests have no participants from this university).

Given the sizes of the billboard and the announcements, your task is to find the numbers of rows in which the announcements are placed.
 

Input
There are multiple cases (no more than 40 cases).

The first line of the input file contains three integer numbers, h, w, and n (1 <= h,w <= 10^9; 1 <= n <= 200,000) - the dimensions of the billboard and the number of announcements.

Each of the next n lines contains an integer number wi (1 <= wi <= 10^9) - the width of i-th announcement.
 

Output
For each announcement (in the order they are given in the input file) output one number - the number of the row in which this announcement is placed. Rows are numbered from 1 to h, starting with the top row. If an announcement can't be put on the billboard, output "-1" for this announcement.
 

Sample Input
  
3 5 5 2 4 3 3 3
 

Sample Output
  
1 2 1 3 -1
 

Author
hhanger@zju
 

Source
 

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比较easy的线段树查询区间最值运用,注意的是h不应该超过n。
#include <iostream>
#include <cstdio>
#include <cmath>
using namespace std;

const int maxn = 8e5 + 20;
int a[maxn];
int i,j,k;
int h,w,n;

void build(int left, int right, int root){
    a[root] = w;
    if (left == right) return;
    int mid =(left+right)>>1;
    build(left,mid,root<<1);
    build(mid+1,right,(root<<1)+1);
}

int query(int left, int right, int root, int num){
        if (left==right) {
             a[root] -= num;
             return left;
        }
        int mid = (left+right)>>1;
        int res = (a[root<<1]>=num)?query(left,mid,root<<1,num):query(mid+1,right,(root<<1)+1,num);
        a[root] = max(a[root<<1],a[(root<<1)+1]);
        return res;
}

int main(){
    while (scanf("%d %d %d",&h,&w,&n)!=EOF){
         if (h>n) h = n;
         build(1,h,1);
         while (n--) {
              scanf("%d",&k);
              if (a[1]<k) printf("-1\n");
              else printf("%d\n",query(1,h,1,k));
         }
    }
    return 0;
}


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