Largest Rectangle in a Histogram

Largest Rectangle in a Histogram Time Limit: 1000MS Memory Limit: 65536KTotal Submissions: 21309 Accepted: 6866

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,...,h_n, where  0<=h_i<=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.

Source

Ulm Local 2003

很神奇的一个题目：

题解是用的单调栈的一个用法，感觉也可以说是数组的改版，很神奇的一个用法，

#include <iostream> #include <cstdio> #include <cstring> #include <algorithm> using namespace std; const int maxx=100005; int h[maxx]; int stack[maxx]; int l[maxx],r[maxx]; int n; void solve() { int t=0; for(int i=0;i<n;i++) { while(t>0&&h[stack[t-1]]>=h[i]) t--; l[i]=(t==0)? 0:stack[t-1]+1; stack[t++]=i; } t=0; for(int i=n-1;i>=0;i--) { while(t>0&&h[stack[t-1]]>=h[i]) t--; r[i]=(t==0)? n:stack[t-1]; stack[t++]=i; } long long ans=0; for(int i=0;i<n;i++) { ans=max(ans,(long long)h[i]*(r[i]-l[i])); } cout << ans << endl; } int main() { while(~scanf("%d",&n)) { if(n==0) { break; } for(int i=0;i<n;i++) { scanf("%d",&h[i]); } solve(); } return 0; }