SDE - Intern

You are given an integer ‘N’, which denotes there are ‘N’ friends. You are supposed to form some pairs them satisfying the following conditions:

1. Each friend can be paired with some other friend or remain single.

2. Each friend can be a part of at most one pair.

You are supposed to find the total number of ways in which the pairing can be done satisfying both conditions. Since the number of ways can be quite large, you should find the answer modulo 1000000007(10^9+7).

Note:

1. Return the final answer by doing a mod with 10^9 + 7.
2. Pairs {A, B} and {B, A} are considered the same.

Given an array ‘arr’ of integer numbers, ‘arr[i]’ represents the number of pages in the ‘i-th’ book.

There are ‘m’ number of students, and the task is to allocate all the books to the students.

Allocate books in such a way that:

1. Each student gets at least one book.
2. Each book should be allocated to only one student.
3. Book allocation should be in a contiguous manner.

You have to allocate the book to ‘m’ students such that the maximum number of pages assigned to a student is minimum.

If the allocation of books is not possible, return -1.

Example:

Input: ‘n’ = 4 ‘m’ = 2 
‘arr’ = [12, 34, 67, 90]

Output: 113

Explanation: All possible ways to allocate the ‘4’ books to '2' students are:

12 | 34, 67, 90 - the sum of all the pages of books allocated to student 1 is ‘12’, and student two is ‘34+ 67+ 90 = 191’, so the maximum is ‘max(12, 191)= 191’.

12, 34 | 67, 90 - the sum of all the pages of books allocated to student 1 is ‘12+ 34 = 46’, and student two is ‘67+ 90 = 157’, so the maximum is ‘max(46, 157)= 157’.

12, 34, 67 | 90 - the sum of all the pages of books allocated to student 1 is ‘12+ 34 +67 = 113’, and student two is ‘90’, so the maximum is ‘max(113, 90)= 113’.

We are getting the minimum in the last case.

Hence answer is ‘113’.

You are given a string 'exp' which is a valid infix expression.

Convert the given infix expression to postfix expression.

Note:

Infix notation is a method of writing mathematical expressions in which operators are placed between operands. 

For example, "3 + 4" represents the addition of 3 and 4.

Postfix notation is a method of writing mathematical expressions in which operators are placed after the operands. 

For example, "3 4 +" represents the addition of 3 and 4.

Expression contains digits, lower case English letters, ‘(’, ‘)’, ‘+’, ‘-’, ‘*’, ‘/’, ‘^’. 

Example:

Input: exp = ‘3+4*8’

Output: 348*+

Explanation:
Here multiplication is performed first and then the addition operation. Hence postfix expression is  3 4 8 * +.

You are given an arbitrary binary tree, a node of the tree, and an integer 'K'. You need to find all such nodes which have a distance K from the given node and return the list of these nodes.

Distance between two nodes in a binary tree is defined as the number of connections/edges in the path between the two nodes.

Note:

1. A binary tree is a tree in which each node has at most two children. 
2. The given tree will be non-empty.
3. The given tree can have multiple nodes with the same value.
4. If there are no nodes in the tree which are at distance = K from the given node, return an empty list.
5. You can return the list of values of valid nodes in any order. For example if the valid nodes have values 1,2,3, then you can return {1,2,3} or {3,1,2} etc.

Example :

Consider this tree above. The target node is 5 and K = 3. The nodes at distance 1 from node 5 are {2}, nodes at distance 2 from node 5 are {1, 4} and nodes at distance 3 from node 5 are {6, 3}.