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:

class Solution {
public:
int largestRectangleArea(vector<int>& height) {
int len = height.size(), maxarea = 0;
vector<int> left(len);
vector<int> right(len);
for(int i = 0; i < len; ++i)
{
left[i] = i;
while(left[i] > 0 && height[left[i]-1] >= height[i]) left[i] = left[left[i]-1];
}
for(int i = len - 1; i >= 0; --i)
{
right[i] = i;
while(right[i] < len - 1 && height[right[i]+1] >= height[i]) right[i] = right[right[i]+1];
}
for(int i = 0; i < len; ++i)
{
maxarea = max(height[i] * (right[i] - left[i] + 1), maxarea);
}

return maxarea;
}
};