HDU 1506 Largest Rectangle in a Histogram(单调栈)
Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 20760 Accepted Submission(s):
6325
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.

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
Recommend
一道挺裸的单调栈
我们预处理出每一个位置向左/向右第一个比他小的位置
然后统计答案,这样很显然是对的
时间复杂度
#include<cstdio> #define LL long long #define max(a,b) (a>b?a:b) #define min(a,b) (a<b?a:b) using namespace std; const int MAXN = 100001; LL a[MAXN]; int s[MAXN], top = 0; int L[MAXN], R[MAXN]; void clear() {top = 0;} int main() { //#ifdef WIN32 //freopen("a.in", "r", stdin); //#endif int N; while(~scanf("%d", &N) && N != 0) { clear(); s[0] = 0; for(int i = 1; i <= N; i++) scanf("%I64d",&a[i]); for(int i = 1; i <= N; i++) { while(top > 0 && a[i] <= a[ s[top] ]) top--; L[i] = min(s[top] + 1, i); s[++top] = i; } clear(); s[0] = N + 1; for(int i = N; i >= 1; i--) { while(top > 0 && a[i] <= a[ s[top] ]) top--; R[i] = max(s[top] - 1, i); s[++top] = i; } LL Ans = 0; for(int i = 1; i <= N; i++) Ans = max(Ans, (R[i] - L[i] + 1) * a[i] ); printf("%I64d\n",Ans); } return 0; }
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