LeetCode-Largest Rectangle in Histogram

Given n non-negative integers representing the histogram's bar height where the width of each bar is 1, find the area of largest rectangle in the histogram.



Above is a histogram where width of each bar is 1, given height = 

[2,1,5,6,2,3]

.



The largest rectangle is shown in the shaded area, which has area = 

10

 unit.

For example,

Given height = 

[2,1,5,6,2,3]

,

return 

10

.
Solution:
Code:

<span style="font-size:14px;">class Solution {
public:
int largestRectangleArea(vector<int> &height) {
int length = height.size();
stack<int> stk;
int result = 0;
for (int index = 0; index < length;) {
if (stk.empty() || height[stk.top()] <= height[index])
stk.push(index++);
else {
int position = stk.top();
stk.pop();
result = max(result, height[position]*(stk.empty()?index:(index-1-stk.top())));
}
}
while (!stk.empty()) {
int position = stk.top();
stk.pop();
result = max(result, height[position]*(stk.empty()?length:(length-1-stk.top())));
}
return result;
}
};</span>