SDE - 1

A Bitonic Sequence is a sequence of numbers that is first strictly increasing and then strictly decreasing.

A strictly ascending order sequence is also considered bitonic, with the decreasing part as empty, and same for a strictly descending order sequence.

For example, the sequences [1, 3, 5, 3, 2], [1, 2, 3, 4] are bitonic, whereas the sequences [5, 4, 1, 4, 5] and [1, 2, 2, 3] are not.

You are given an array 'arr' consisting of 'n' positive integers.

Find the length of the longest bitonic subsequence of 'arr'.

Example :

Input: 'arr' = [1, 2, 1, 2, 1]

Output: 3

Explanation: The longest bitonic subsequence for this array will be [1, 2, 1]. Please note that [1, 2, 2, 1] is not a valid bitonic subsequence, because the consecutive 2's are neither strictly increasing, nor strictly decreasing.

You have been given a long type array/list 'arr’ of size 'n’.

It represents an elevation map wherein 'arr[i]’ denotes the elevation of the 'ith' bar.

Print the total amount of rainwater that can be trapped in these elevations.

Note :

The width of each bar is the same and is equal to 1.

Example:

Input: ‘n’ = 6, ‘arr’ = [3, 0, 0, 2, 0, 4].

Output: 10

Explanation: Refer to the image for better comprehension:

Note :

You don't need to print anything. It has already been taken care of. Just implement the given function.

Given an n x n matrix mat[n][n] of integers, find the maximum value of mat[c][d] – mat[a][b] over all choices of indexes such that both c > a and d > b.

Example:-

1 2 3 4 
5 6 7 8
1 9 2 3

In this example, the maximum value is 8 (mat[2][1]-mat[0][0]).

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