84. Largest Rectangle in Histogram
1. Description
Given an array of integers heights representing the histogram’s bar height where the width of each bar is 1, return the area of the largest rectangle in the histogram.
2. Example
Example 1:
Input: heights = [2,1,5,6,2,3]
Output: 10
Explanation: The above is a histogram where width of each bar is 1.
The largest rectangle is shown in the red area, which has an area = 10 units.
Example 2:
Input: heights = [2,4]
Output: 4
3. Constraints
- 1 <= heights.length <= $10^5$
- 0 <= heights[i] <= $10^4$
4. Solutions
Monotonic Stack
n = heights.size()
Time complexity: O(n)
Space complexity: O(n)
class Solution {
public:
int largestRectangleArea(vector<int> heights) {
int max_area = 0;
heights.push_back(-1);
stack<int> mono_increase;
for (int i = 0; i < heights.size(); ++i) {
while (!mono_increase.empty() && heights[i] < heights[mono_increase.top()]) {
int index = mono_increase.top();
mono_increase.pop();
int left = mono_increase.empty() ? -1 : mono_increase.top();
max_area = max(heights[index] * (i - left - 1), max_area);
}
mono_increase.push(i);
}
return max_area;
}
};