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package com.interview.stackqueue;

import java.util.Deque;

import java.util.LinkedList;

/**

* 12/23/2014

* @author tusroy

*

* Video link https://youtu.be/ZmnqCZp9bBs

*

* Given an array representing height of bar in bar graph, find max histogram

* area in the bar graph. Max histogram will be max rectangular area in the

* graph.

*

* Maintain a stack

*

* If stack is empty or value at index of stack is less than or equal to value at current

* index, push this into stack.

* Otherwise keep removing values from stack till value at index at top of stack is

* less than value at current index.

* While removing value from stack calculate area

* if stack is empty

* it means that till this point value just removed has to be smallest element

* so area = input[top] * i

* if stack is not empty then this value at index top is less than or equal to

* everything from stack top + 1 till i. So area will

* area = input[top] * (i - stack.peek() - 1);

* Finally maxArea is area if area is greater than maxArea.

*

*

* Time complexity is O(n)

* Space complexity is O(n)

*

* References:

* http://www.geeksforgeeks.org/largest-rectangle-under-histogram/

*/

public class MaximumHistogram {

public int maxHistogram(int input[]){

Deque<Integer> stack = new LinkedList<Integer>();

int maxArea = 0;

int area = 0;

int i;

for(i=0; i < input.length;){

if(stack.isEmpty() || input[stack.peekFirst()] <= input[i]){

stack.offerFirst(i++);

}else{

int top = stack.pollFirst();

//if stack is empty means everything till i has to be

//greater or equal to input[top] so get area by

//input[top] * i;

if(stack.isEmpty()){

area = input[top] * i;

}

//if stack is not empty then everythin from i-1 to input.peek() + 1

//has to be greater or equal to input[top]

//so area = input[top]*(i - stack.peek() - 1);

else{

area = input[top] * (i - stack.peekFirst() - 1);

}

if(area > maxArea){

maxArea = area;

}

}

}

while(!stack.isEmpty()){

int top = stack.pollFirst();

//if stack is empty means everything till i has to be

//greater or equal to input[top] so get area by

//input[top] * i;

if(stack.isEmpty()){

area = input[top] * i;

}

//if stack is not empty then everything from i-1 to input.peek() + 1

//has to be greater or equal to input[top]

//so area = input[top]*(i - stack.peek() - 1);

else{

area = input[top] * (i - stack.peekFirst() - 1);

}

if(area > maxArea){

maxArea = area;

}

}

return maxArea;

}

public static void main(String args[]){

MaximumHistogram mh = new MaximumHistogram();

int input[] = {2,2,2,6,1,5,4,2,2,2,2};

int maxArea = mh.maxHistogram(input);

//System.out.println(maxArea);

assert maxArea == 12;

}

}