Largest rectangle in a histogram

Hard
0/120
Average time to solve is 25m
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Problem statement

You have been given an array/list 'HEIGHTS' of length ‘N. 'HEIGHTS' represents the histogram and each element of 'HEIGHTS' represents the height of the histogram bar. Consider that the width of each histogram is 1.

You are supposed to return the area of the largest rectangle possible in the given histogram.

For example :
``````In the below histogram where array/list elements are {2, 1, 5, 6, 2, 3}.
``````

``````The area of largest rectangle possible in the given histogram is 10.
``````
Detailed explanation ( Input/output format, Notes, Images )
Constraints :
``````1 <= T <= 10
1 <= N <= 10^6
0 <= HEIGHTS[i] <= 10^9

Where ‘T’ is the number of test cases.
'N' is the length of the given array/list.
And, HEIGHTS[i] denotes the height of the 'ith' histogram bar.

Time Limit: 1 sec.
``````
Sample Input 1 :
``````2
10
1 0 1 2 2 2 2 1 0 2
10
1 2 1 0 1 1 0 0 2 2
``````
Sample Output 1 :
``````8
4
``````
Explanation For Sample Input 1 :
``````In the first test case, the area of the largest rectangle of the given histogram is 8 in the rectangle starting from index 4 to index 7 in the given array/list.

In the second test case, the area of the largest rectangle of the given histogram is 4 in the rectangle starting from index 9 to index 10 in the given array/list.
``````
Sample Input 2 :
``````2
10
8 6 3 5 0 0 4 10 2 5
10
6 1 8 10 5 7 0 4 5 8
``````
Sample Output 2 :
``````12
20
``````
Explanation For Sample Input 2 :
``````In the first test case, the area of the largest rectangle of the given histogram is 12.

In the second test case, the area of the largest rectangle of the given histogram is 20.
``````
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