SDE - 1

Given an array/list of integer numbers 'CHOCOLATES' of size 'N', where each value of the array/list represents the number of chocolates in the packet. There are ‘M’ number of students and the task is to distribute the chocolate to their students. Distribute chocolate in such a way that:

1. Each student gets at least one packet of chocolate.

2. The difference between the maximum number of chocolate in a packet and the minimum number of chocolate in a packet given to the students is minimum.

Example :

Given 'N' : 5 (number of packets) and 'M' : 3 (number of students)

And chocolates in each packet is : {8, 11, 7, 15, 2}

All possible way to distribute 5 packets of chocolates among 3 students are -

( 8,15, 7 ) difference of maximum-minimum is ‘15 - 7’ = ‘8’
( 8, 15, 2 ) difference of maximum-minimum is ‘15 - 2’ = ‘13’ 
( 8, 15, 11 ) difference of maximum-minimum is ‘15 - 8’ = ‘7’
( 8, 7, 2 ) difference of maximum-minimum is ‘8 - 2’ = ‘6’
( 8, 7, 11 ) difference of maximum-minimum is ‘11 - 7’ = ‘4’
( 8, 2, 11 ) difference of maximum-minimum is ‘11 - 2’ = ‘9’
( 15, 7, 2 ) difference of maximum-minimum is ‘15 - 2’ = 13’
( 15, 7, 11 ) difference of maximum-minimum is ‘15 - 7’ = ‘8’
( 15, 2, 11 ) difference of maximum-minimum is ‘15 - 2’ = ‘13’
( 7, 2, 11 ) difference of maximum-minimum is ‘11 - 2’ = ‘9’

Hence there are 10 possible ways to distribute ‘5’ packets of chocolate among the ‘3’ students and difference of combination (8, 7, 11) is ‘maximum - minimum’ = ‘11 - 7’ = ‘4’ is minimum in all of the above.

You have been given a 9 X 9 2D matrix 'MATRIX' with some cells filled with digits(1 - 9), and some empty cells (denoted by 0).

You need to find whether there exists a way to fill all the empty cells with some digit(1 - 9) such that the final matrix is a valid Sudoku solution.

A Sudoku solution must satisfy all the following conditions-

1. Each of the digits 1 - 9 must occur exactly once in each row.
2. Each of the digits 1 - 9 must occur exactly once in each column.
3. Each of the digits 1 - 9 must occur exactly once in each of the 9, 3 x 3 sub-matrices of the matrix.

Note

1. There will always be a cell in the matrix which is empty.
2. The given initial matrix will always be consistent according to the rules mentioned in the problem statement.

You are given a binary tree having 'n' nodes.

The boundary nodes of a binary tree include the nodes from the left and right boundaries and the leaf nodes, each node considered once.

Figure out the boundary nodes of this binary tree in an Anti-Clockwise direction starting from the root node.

Example :

Input: Consider the binary tree A as shown in the figure:

Output: [10, 5, 3, 7, 18, 25, 20]

Explanation: As shown in the figure

The nodes on the left boundary are [10, 5, 3]

The nodes on the right boundary are [10, 20, 25]

The leaf nodes are [3, 7, 18, 25].

Please note that nodes 3 and 25 appear in two places but are considered once.

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