SDE - Intern

You are given a Binary Tree.

Return the length of the diameter of the tree.

Note :

The diameter of a binary tree is the length of the longest path between any two end nodes in a tree.

The number of edges between two nodes represents the length of the path between them.

Example :

Input: Consider the given binary tree:

Output: 6

Explanation:
Nodes in the diameter are highlighted. The length of the diameter, i.e., the path length, is 6.

You are given a cartesian plane, having ‘N’ points in the form of the array ‘PointX’ and ‘PointY’ where ‘PointX[i]’ and ‘PointY[i]’ represent the ‘X’ coordinates and ‘Y’ coordinates of the i’th point, respectively. You have to find the number of pairs satisfying the following conditions:

1. The points in the pair are distinct.
2. Euclidean distance and the Manhattan distance between the points of the pair should be equal.

Note :

1. Pair (‘P’, ‘Q’) is the same as pair (‘Q’, ‘P’).
2. Euclidean distance is given by: (( ‘X2’ - ‘X1’) ^ 2 + (‘Y2’ - ‘Y1’) ^ 2) ^ 0.5.
3. Manhattan distance is given by: |’X2’ - ‘X1’| + |’Y2’ - ‘Y1’|, where points are (‘X1’, ‘Y1’) and (‘X2’, ‘Y2’).

For example :

Let points be: (1, 2), (2, 3), (1, 3)
The Euclidean distance between points (1, 2) and (1, 3) is: 1
The Manhattan distance between points (1, 2) and (1, 3) is: 1
The Euclidean distance between points (2, 3) and (1, 3) is: 1
The Manhattan distance between points (2, 3) and (1, 3) is: 1
So the pairs can be: [(1, 2), (1, 3)] and [(2, 3), (1, 3)].
So the number of pairs is 2.

You’re given a doubly-linked list with N nodes, where each node deviates at max K position from its position in the sorted list. Your task is to sort this given doubly linked list.

For example :

Let us consider K is 3, an element at position 4 in the sorted doubly linked list, can be at positions 1, 2, 3, 4, 5, 6, 7 in the given linked list because the absolute difference of all these indices with 4 is at most 3.

Note :

All elements are distinct.

A doubly linked list is a type of linked list that is bidirectional, that is, it can be traversed in both directions, forward and backward. 

You are given two sorted linked lists. You have to merge them to produce a combined sorted linked list. You need to return the head of the final linked list.

Note:

The given linked lists may or may not be null.

For example:

If the first list is: 1 -> 4 -> 5 -> NULL and the second list is: 2 -> 3 -> 5 -> NULL

The final list would be: 1 -> 2 -> 3 -> 4 -> 5 -> 5 -> NULL

You have been given a Binary Tree where the value of each node is either 0 or 1. Your task is to return the same Binary Tree but all of its subtrees that don't contain a 1 have been removed.

Note :

A subtree of a node X is X, plus every node that is a descendant of X.

For Example :

Look at the below example to see a Binary Tree pruning.
Input: [1, 1, 1, 0, 1, 0, 1, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1]

Output: [1, 1, 1, -1, 1, -1, 1, -1, -1, -1, -1]

For example, the input for the tree depicted in the below image would be :

1
2 3
4 -1 5 6
-1 7 -1 -1 -1 -1
-1 -1

Explanation :

Level 1 :
The root node of the tree is 1

Level 2 :
Left child of 1 = 2
Right child of 1 = 3

Level 3 :
Left child of 2 = 4
Right child of 2 = null (-1)
Left child of 3 = 5
Right child of 3 = 6

Level 4 :
Left child of 4 = null (-1)
Right child of 4 = 7
Left child of 5 = null (-1)
Right child of 5 = null (-1)
Left child of 6 = null (-1)
Right child of 6 = null (-1)

Level 5 :
Left child of 7 = null (-1)
Right child of 7 = null (-1)

The first not-null node (of the previous level) is treated as the parent of the first two nodes of the current level. The second not-null node (of the previous level) is treated as the parent node for the next two nodes of the current level and so on.
The input ends when all nodes at the last level are null (-1).

Note :

The above format was just to provide clarity on how the input is formed for a given tree.

The sequence will be put together in a single line separated by a single space. Hence, for the above-depicted tree, the input will be given as:
1 2 3 4 -1 5 6 -1 7 -1 -1 -1 -1 -1 -1

You are given an array of size ‘N’. The elements of the array are in the range from 1 to ‘N’.

Ideally, the array should contain elements from 1 to ‘N’. But due to some miscalculations, there is a number R in the range [1, N] which appears in the array twice and another number M in the range [1, N] which is missing from the array.

Your task is to find the missing number (M) and the repeating number (R).

For example:

Consider an array of size six. The elements of the array are { 6, 4, 3, 5, 5, 1 }. 
The array should contain elements from one to six. Here, 2 is not present and 5 is occurring twice. Thus, 2 is the missing number (M) and 5 is the repeating number (R). 

Follow Up

Can you do this in linear time and constant additional space?