LargestRectangleInHist.java

import java.util.*;

/**
 * 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.
 *
 * Tags: Array, Stack
 */
class LargestRectangleInHist {
    public static void main(String[] args) {
        int[] height = { 2, 1, 5, 6, 2, 3 };
        int[] height2 = { 1, 2, 3, 4, 5, 6 };
        System.out.println(new LargestRectangleInHist().largestRectangleArea(height2));
    }

    /**
     * Only height is smaller do update happens
     * Stack for indices
     * add a zero height into the group
     */
    public int largestRectangleArea(int[] height) {
        if (height == null || height.length == 0) return 0;
        height = Arrays.copyOf(height, height.length + 1); // add a zero
        int max = 0;
        Stack<Integer> s = new Stack<Integer>(); // store indices
        for (int i = 0; i < height.length; i++) {
            while (!s.isEmpty() && height[i] < height[s.peek()]) { // update when current height is smaller
                int h = height[s.pop()];
                int w = (s.isEmpty() ? i : i - s.peek() - 1);
                max = Math.max(max, h * w);
            }
            s.push(i); // push index into stack
        }
        return max;
    }
}