POJ 2559 Largest Rectangle in a Histogram__poj

Description A histogram is a polygon composed of a sequence to rectangles at a aligned base line. The rectangles have equal widths but may have different. For example, the "figure on" the left shows the histogram, consists of rectangles with the Heights 2, 1, 4, 5, 1, 3, 3, Measured in units where 1 are the width of the rectangles: 

Usually, histograms are used to represent discre Te distributions, e.g., the frequencies of characters in texts. Note This order of the rectangles, i.e., their heights, is important. Calculate the area of the largest rectangle in a histogram this is aligned on 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 are assume that 1<=n<=100000. Then follow n integers h1,..., hn, where 0<=hi<=1000000000. These numbers denote the heights's 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 is output on a single line 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 3 4
1000 1000 1000 1000
0

Sample Output

8
4000

Hint

Huge input, scanf is recommended.

The application of the maximum rectangular area and the monotonic stack is obtained.

#include <set> #include <map> #include <ctime> #include <cmath> #include <stack> #include <queue> #include <bitset> #include <cstdio> #include <string> #include <cstring> #include <iostream> #include <algorithm> #include <functional> #define REP (i,j,k) for (int i = j; I <= K; i++) # Define per (int i = j; I >= K; i--) #define Loop (I,J,K) for (int i = J;i!=-1; i = k[i]) #define Lson x ;< 1, L, mid #define Rson x << 1 | 1, Mid + 1, r #define FI #define SE second #define MP (I,J) Make_pair (i,j) #define PII pair<string,string>
G namespace Std;
typedef long Long LL;
const int low (int x) {return x&-x;} const double EPS = 1e-8;
const int INF = 0x7fffffff;
const int mod = 1E8;
const int N = 3e5 + 10;
	const int Read () {char ch = getchar ();
	while (ch< ' 0 ' | | | ch> ' 9 ') ch = getchar ();
	int x = ch-' 0 '; while (ch = getchar ()) >= ' 0 ' &&ch <= ' 9 ') x = x * + ch-' 0 ';
return x;

int n, A[n], l[n], r[n];
		int main () {while (n = read (), N) {Rep (i, 1, N) scanf ("%d", &a[i]);
		Stack<int> p;
		A[0] = a[n + 1] =-1;
			Rep (i, 1, n + 1) {while (!p.empty () && A[i] < A[p.top ()]) r[p.top ()] = I-1, P.pop ();
		P.push (i);
			Each (i, n, 0) {while (!p.empty () && A[i] < A[p.top ()]) l[p.top ()] = i + 1, p.pop ();
		P.push (i);
		LL ans = 0;
		Rep (i, 1, n) ans = max (ans, 1LL * a[i] * (R[i]-l[i] + 1));
	printf ("%lld\n", ans);
return 0; }