PKU 2559解题报告

Largest Rectangle in a Histogram

Time Limit: 1000MS Memory Limit: 65536K

Description

A histogram is a polygon composed of a sequence of rectangles aligned at a common base line. The rectangles have equal widths but may have different heights. For example, the figure on the left shows the histogram that consists of rectangles with the heights 2, 1, 4, 5, 1, 3, 3, measured in units where 1 is the width of the rectangles:

Usually, histograms are used to represent discrete distributions, e.g., the frequencies of characters in texts. Note that the order of the rectangles, i.e., their heights, is important. Calculate the area of the largest rectangle in a histogram that is aligned at the common base line, too. The figure on the right shows the largest aligned rectangle for the depicted histogram.

Input

The input contains several test cases. Each test case describes a histogram and starts with an integer n, denoting the number of rectangles it is composed of. You may assume that 1<=n<=100000. Then follow n integers h1,...,hn, where 0<=hi<=1000000000. These numbers denote the heights of the rectangles of the histogram in left-to-right order. The width of each rectangle is 1. A zero follows the input for the last test case.

Output

For each test case output on a single line the area of the largest rectangle in the specified histogram. Remember that this rectangle must be aligned at the common base line.

Sample Input

7 2 1 4 5 1 3 3
4 1000 1000 1000 1000
0

Sample Output

8
4000

Hint

Huge input, scanf is recommended.

题目意思其实蛮简单的,就是给出宽为1高为h[i]的一系列矩形,求最大连续矩形的面积。据说可以用栈来做,不过我只会用DP来做这个。

分析:建立left[i]和right[i]分别来记录h[i]向左边和右边可以拓展到哪里,然后求出每个h[i]高度的最大矩形面积就可以了。

code

#include<stdio.h>
 
int main()
{
  long long max,tmp;
  int i,j,k,n;
  int h[100005],left[100005],right[100005];
  while(scanf("%d",&n)!=EOF,n){
      for(i=1;i<=n;i++)
	scanf("%d",h+i);
      h[0]=-1;h[n+1]=-1;/*作为哨兵元素*/
      left[1]=1;right[n]=n;
      for(i=2,k=n-1;i<=n;i++,k--){
	  j=i-1,left[i]=i;
	  while(h[j]>=h[i]){
	      left[i]=left[j];
	      j=left[i]-1;
	  }
	  j=k+1,right[k]=k;
	  while(h[j]>=h[k]){
	      right[k]=right[j];
	      j=right[k]+1;
	  }
      }
      max=-1;
      for(i=1;i<=n;i++){
	  tmp=(right[i]-left[i]+1)*(long long)h[i];/*强转,否者会溢出*/
	  if(tmp>max) max=tmp;
      }
      printf("%I64dn",max);
  }
  return 0;
}
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