HDU1506_Largest Rectangle in a Histogram
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:
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
University of Ulm Local Contest 2003
题目大意:给你一个直方图,告诉你各个条形矩形的高度,求基线对齐构成的矩形中面积
最大的矩形的面积对于每个矩形。面积 = h[i]*(j-k+1),当中j,k是左右边界,h[i]是矩形
的高。而且对于j <= x <= k,h[i] <= h[x]。
本题中,找到左右边界j,k是关键。
利用动态规划的方法,对于位置i,假设左边条形矩形的高度大于它本身,那么左边的左边
界一定也满足位置i的左边界。同理假设右边条形矩形的高度大于它本身,那么右边的右边
界也一定满足位置i的右边界。迭代循环下去。直到找到i的左右边界。
#include<stdio.h>
#include<string.h> int l[100010],r[100010];
__int64 h[100010];
int main()
{
int N;
while(~scanf("%d",&N) && N!=0)
{
memset(h,0,sizeof(h));
for(int i = 1; i <= N; i++)
{
scanf("%I64d",&h[i]);
l[i] = r[i] = i;
} l[0] = 1;
r[N+1] = N;
h[0] = -1;
h[N+1] = -1;
//这上边不加就会超时,不加的话下边就可能一直while,跳不出循环
for(int i = 1; i <= N; i++)
{
while(h[l[i]-1] >= h[i])//找位置i的左边界
l[i] = l[l[i]-1];
}
for(int i = N; i >= 1; i--)
{
while(h[r[i]+1] >= h[i])//找位置i的右边界
r[i] = r[r[i]+1];
}
__int64 MaxArea = -0xffffff0;
for(int i = 1; i <= N; i++)
{
if(h[i]*(r[i]-l[i]+1) > MaxArea)
MaxArea = h[i]*(r[i]-l[i]+1);
}
printf("%I64d\n",MaxArea);
}
return 0;
}
HDU1506_Largest Rectangle in a Histogram的更多相关文章
- poj 2559 Largest Rectangle in a Histogram - 单调栈
Largest Rectangle in a Histogram Time Limit: 1000MS Memory Limit: 65536K Total Submissions: 19782 ...
- DP专题训练之HDU 1506 Largest Rectangle in a Histogram
Description A histogram is a polygon composed of a sequence of rectangles aligned at a common base l ...
- Largest Rectangle in a Histogram(DP)
Largest Rectangle in a Histogram Time Limit : 2000/1000ms (Java/Other) Memory Limit : 65536/32768K ...
- POJ 2559 Largest Rectangle in a Histogram(单调栈)
传送门 Description A histogram is a polygon composed of a sequence of rectangles aligned at a common ba ...
- Largest Rectangle in a Histogram(HDU1506)
Largest Rectangle in a Histogram HDU1506 一道DP题: 思路:http://blog.csdn.net/qiqijianglu/article/details/ ...
- POJ 2559 Largest Rectangle in a Histogram
Time Limit: 1000MS Memory Limit: 65536K Total Submissions: 18942 Accepted: 6083 Description A hi ...
- Largest Rectangle in a Histogram
2107: Largest Rectangle in a Histogram Time Limit: 1 Sec Memory Limit: 64 MBSubmit: 777 Solved: 22 ...
- HDU 1506 Largest Rectangle in a Histogram (dp左右处理边界的矩形问题)
E - Largest Rectangle in a Histogram Time Limit:1000MS Memory Limit:32768KB 64bit IO Format: ...
- hdu---1506(Largest Rectangle in a Histogram/dp最大子矩阵)
Largest Rectangle in a Histogram Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/32768 ...
随机推荐
- 弹出框、遮罩层demo
仿alert.confirm的弹出框. 弹出后,用遮罩层将背景虚化. 代码如下: <html> <meta http-equiv="Content-Type" c ...
- Google map v3 using simple tool file google.map.util.js v 1.1
/** * GOOGLE地图开发使用工具 * @author BOONYACHENGDU@GMAIL.COM * @date 2013-08-23 * @notice 地图容器的z-index不能小于 ...
- linux之SQL语句简明教程---CREATE INDEX
索引 (Index) 可以帮助我们从表格中快速地找到需要的资料.举例来说,假设我们要在一本园艺书中找如何种植青椒的讯息.若这本书没有索引的话,那我们是必须要从头开始读,直到我们找到有关种直青椒的地方为 ...
- mysql启动报错:Fatal error: Can’t open and lock privilege tables: Table ‘mysql.host’ doesn’t exist
mysql在首次启动的时候可能会报错:Can’t open and lock privilege tables: Table ‘mysql.host’ doesn’t exist 这时候可以执行脚本 ...
- java 判断字符串编码
String iso8859 = new String(sb.toString().getBytes("iso8859-1"));String gbk = new String(s ...
- DevExpress.GridControl.gridView的一些注意
1.DevExpress控件组中的GridControl控件不能使横向滚动条有效.现象:控件中的好多列都挤在一起,列宽都变的很小,根本无法正常浏览控件单元格中的内容. 解决: gridView1.Op ...
- iOS开发之性能优化
1.避免过于庞大的XIB 当加载XIB的时候把所有的东西都放在了内存里,包括任何的图片:如果有一个不会即刻用到的view,就会浪费宝贵的内存资源了. 当加载一个引用了图片或者声音资源的nib时,nib ...
- JQuery EasyUI combobox动态添加option
<input class="easyui-combobox" id="rwlb" name="rwlb" style="wi ...
- javascript的调试
1. 关于javascript的调试,最好将浏览器的脚本通知打开. 2. 最好设置为每次访问页面时检查.
- 解析处理常用json数据总结
工作中用ajax接收到接口返回的数据需要进行解析后操作,这里总结一下平时的方法,用的jquery,复制下来的页面把引入的路径改一下即可. <!DOCTYPE html> <html ...