2022.02.28 - SX11-05. The largest rectangle in the histogram

1. subject

2. Ideas

(1) Monotonic stack

• left[i] Indicates subscript i The first height on the left is less than i The subscript ,right[i] Indicates subscript i The first height on the right is less than i The subscript .
• Use the subscript whose monotone stack height is less than the current subscript , Then the top element of the stack is the first subscript on the left or right that is smaller than the current subscript .

3. Code

import java.util.Deque;
import java.util.LinkedList;

public class Test {
    
    public static void main(String[] args) {
    
    }
}

class Solution {
    
    public int largestRectangleArea(int[] heights) {
    
        int n = heights.length;
        Deque<Integer> stack = new LinkedList<>();
        int[] left = new int[n];
        for (int i = 0; i < n; i++) {
    
            while (!stack.isEmpty() && heights[stack.peek()] >= heights[i]) {
    
                stack.pop();
            }
            if (stack.isEmpty()) {
    
                left[i] = -1;
            } else {
    
                left[i] = stack.peek();
            }
            stack.push(i);
        }
        stack = new LinkedList<>();
        int[] right = new int[n];
        for (int i = n - 1; i >= 0; i--) {
    
            while (!stack.isEmpty() && heights[stack.peek()] >= heights[i]) {
    
                stack.pop();
            }
            if (stack.isEmpty()) {
    
                right[i] = n;
            } else {
    
                right[i] = stack.peek();
            }
            stack.push(i);
        }
        int res = Integer.MIN_VALUE;
        for (int i = 0; i < n; i++) {
    
            res = Math.max(res, heights[i] * (right[i] - left[i] - 1));
        }
        return res;
    }
}