Largest Rectangle in a histogramTime
limit:2000/1000 MS (java/others) Memory limit:65536/32768 K (java/others)
Total submission (s): 12554 Accepted Submission (s): 3509
Problem Descriptiona Histogram is a polygon composed of a sequence for rectangles aligned at a common base line. The rectangles has equal widths but could 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 is used to represent discrete distributions, e.g., the frequencies of characters in texts. Note the order of the rectangles, i.e, their heights, is important. Calculate the area of the largest rectangle in a histogram that's aligned at the common base line, too. The shows the largest aligned rectangle for the depicted histogram.
Inputthe 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. Assume that 1 <= n <= 100000. Then follow n integers h1, ..., HN, where 0 <= hi <= 1000000000. These numbers denote the heights of the rectangles in histogram order. The width of each rectangle is 1. A Zero follows the input for the last test case.
Outputfor each test case output on a single line the area of the largest rectangle in the specified histogram. Remember that this rectangle must is aligned at the common base line.
Sample Input
7 2 1 4 5 1 3 34 1000 1000 1000 10000
Sample Output
84000
Test instructions: Enter n columns and discharge. Ask the largest rectangular area.
To maintain two monotone queues, LfT and RIT. LFT [i] represents the I point, the left row is higher than I point column, the leftmost column number recorded in LfT [i]. RIT in the same vein, record the number of pillars of the right-most continuous I-high column.
First case: ID 1 2 3 4 5 6 7h 2 1 4 5 1 3 3lft 1 1 3 4 1 6 6
RIT 1 7 4 4 7 7 7
With LfT and RIT, you can enumerate each column to calculate the maximum width of the column that extends two times. Multiply the height of the column to include the largest area of the column.
#include <stdio.h> #include <stdlib.h> #include <string.h> #include <limits.h> #include < malloc.h> #include <ctype.h> #include <math.h> #include <string> #include <iostream># Include <algorithm>using namespace std, #include <stack> #include <queue> #include <vector># Include <deque> #include <set> #include <map> long long h[100010],lft[100010],rit[100010];int main () { Long Long N,m,t;while (cin>>n,n) {for (Long long i=1;i<=n;i++) {cin>>h[i]; lft[i]=rit[i]=i;} H[0]=h[n+1]=-1;for (Long long i=1;i<=n;i++) {while (h[i]<=h[lft[i]-1]) lft[i]=lft[lft[i]-1];} For (long long i=n;i>=1;i--) {while (h[i]<=h[rit[i]+1]) rit[i]=rit[rit[i]+1];} Long Long maxx=0;for (long long i=1;i<=n;i++) Maxx=max (maxx,h[i]* (rit[i]-lft[i]+1));p rintf ("%i64d\n", Maxx); for ( int i=1;i<=n;i++) {printf ("%d", Lft[i]);} Puts (""); for (int i=1;i<=n;i++) {printf ("%d", Rit[i]);} Puts ("");} return 0;} /*7 2 1 4 5 1 3 34 1000 1000 1000 10000*/
HDU 1506 largest Rectangle in a histogram monotone queue
