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.
/************************************************************************* > File Name: hist.cpp > Author: Yuji CAO > Mail: yujicao@amazon.com > Created Time: 2016年08月13日 星期六 20时06分06秒 ************************************************************************/ #include<iostream> #include<vector> #include<unordered_map> #include<unordered_set> #include<sstream> #include<list> #include<queue> #include<stack> #include<string> #include<utility> #include<algorithm> using namespace std; /* * 2 3 4 2 5 3 1 0 * [] * [] [] * [][] [][] * [][][][][][] * [][][][][][][][]__ * * 2 0/2 * 2 0/2 1/3 * 2 0/2 1/3 2/4 * 4 0/2 1/3 * 6 0/2 * 6 * 8 3/2 * 8 3/2 4/5 * 8 3/2 5/3 * 8 3/2 * 8 * 8 6/1 * 8 7/1 * 8 */ class Hist { public: int calculate(vector<int>& data) { data.push_back(0); int i = 0; stack<int> s; int ans = 0; while (i < data.size()) { if (s.empty()) { ans = max(ans, (i + 1) * data[i]); s.push(i); i += 1; } else { int top = s.top(); if (data[top] < data[i]) { s.push(i); i += 1; } else { s.pop(); ans = max(ans, (i - top) * data[top]); } } } return ans; } }; int main() { Hist h; int a[] = { 2,3,4,2,5,3,1 }; vector<int> data(a, a + sizeof a / sizeof a[0]); int ans = h.calculate(data); cout<<ans<<endl; return 0; }