84. Largest Rectangle in Histogram

/*
 * @lc app=leetcode id=84 lang=cpp
 *
 * [84] Largest Rectangle in Histogram
 *
 * https://leetcode.com/problems/largest-rectangle-in-histogram/description/
 *
 * algorithms
 * Hard (45.83%)
 * Likes:    18224
 * Dislikes: 326
 * Total Accepted:    1.2M
 * Total Submissions: 2.5M
 * Testcase Example:  '[2,1,5,6,2,3]'
 *
 * 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.
 *
 *
 * 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
 *
 *
 *
 * Constraints:
 *
 *
 * 1 <= heights.length <= 10^5
 * 0 <= heights[i] <= 10^4
 *
 *
 */

// @lc code=start
class Solution {
public:
    int largestRectangleArea(vector<int>& heights)
    {
        heights.push_back(0);
        stack<int> stk;
        int i = 0;
        int n = heights.size();
        int maxArea = 0;
        for (int i = 0; i < n; ++i)
        {
            while (!stk.empty() && heights[stk.top()] > heights[i])
            {
                int h = heights[stk.top()]; stk.pop();
                int w = stk.empty() ? i : i - stk.top() - 1;
                maxArea = max(maxArea, h * w);
            }
            stk.push(i);
        }
        return maxArea;
    }
};
// @lc code=end

• T: $O(N)$
• S: $O(N)$