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Largest Rectangle in a Histogram(附上几组测试数据)

时间:2018-11-29 15:14:39      阅读:200      评论:0      收藏:0      [点我收藏+]

标签:several   not   air   comm   width   The   algorithm   mis   character   

Largest Rectangle in a Histogram

http://acm.hdu.edu.cn/showproblem.php?pid=1506

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 23458    Accepted Submission(s): 7362


Problem 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:
技术分享图片
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
 

 

Source

 

单调栈经典题

技术分享图片
 1 #include<iostream>
 2 #include<cstring>
 3 #include<algorithm>
 4 #include<cmath>
 5 #include<string>
 6 #include<vector>
 7 #include<cstdio>
 8 #include<queue>
 9 #include<stack>
10 using namespace std;
11 
12 struct sair{
13     long long v;
14     int pos;
15 }a[100005];
16 
17 int main(){
18     std::ios::sync_with_stdio(false);
19     int n;
20     while(cin>>n){
21         if(!n) break;
22         for(int i=1;i<=n;i++){
23             cin>>a[i].v;
24             a[i].pos=i;
25         }
26         stack<sair>st;
27         long long ans=0;
28         long long cnt,pos;
29         for(int i=1;i<=n;i++){
30             if(st.empty()){
31                 st.push(a[i]);
32                 ans=max(ans,st.top().v);
33             }
34             else{
35                 while(!st.empty()&&st.top().v>=a[i].v){
36                     cnt=st.top().v;
37                     pos=st.top().pos;
38                     st.pop();
39                     if(st.empty()){
40                         ans=max(ans,cnt*(i-1));
41                     }
42                     else{
43                         ans=max(ans,cnt*(i-1-st.top().pos));
44                     }
45                 }
46                 st.push(a[i]);
47             }
48         }
49         int Last;
50         if(!st.empty()){
51             Last=st.top().pos;
52         }   
53         while(!st.empty()){
54             cnt=st.top().v;
55             pos=st.top().pos;
56             st.pop();
57             if(st.empty()){
58                 ans=max(ans,cnt*n);;
59             }
60             else{
61                 ans=max(ans,cnt*(Last-st.top().pos));
62             }
63         }
64         cout<<ans<<endl;
65     }
66     system("pause");
67 }
68 /*
69 6 2 5 2 5 5 2
70 5 1 2 3 4 4
71 7 2 1 4 5 1 3 3
72 4 1000 1000 1000 1000
73 3 2 1 2
74 4 2 2 5 5
75 */
View Code

 

Largest Rectangle in a Histogram(附上几组测试数据)

标签:several   not   air   comm   width   The   algorithm   mis   character   

原文地址:https://www.cnblogs.com/Fighting-sh/p/10037519.html

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