SDE - Intern

You are given a positive integer N, your task is to find all the Jumping Numbers smaller than or equal to N.

A number is defined as a Jumping Number if all adjacent digits in it have an absolute difference of 1.

Example :

2, 23, and 4343456 are Jumping numbers but 296 and 89498 are not.

Note:

The difference between ‘9’ and ‘0’ is not considered as 1. All single-digit numbers are considered as Jumping Numbers. 

You are given a matrix ‘A’ with 'N' rows and 'M' columns and a matrix ‘B’ with 'P' rows and 'Q' columns. You have to find the Kronecker Product of both the matrices, which is defined as follows :

C = A tensor B

Let matrix A be |a11 a12 . . . a1m|
                |a21 a22 . . . a2m|
                . . . . . . . . . .
                . . . . . . . . . .
                |an1 an2 . . . anm|

Let matrix B be |b11 b12 . . . b1q|
                |b21 b22 . . . b2q|
                . . . . . . . . . .
                . . . . . . . . . .
                |bp1 bp2 . . . bpq|


Then,
C = A tensor B = |a11B a12B . . . a1mB|
                 |a21B a22B . . . a2mB|
                 . . . . . . . . . . .
                 . . . . . . . . . . .
                 |an1B an2B . . . anmB|

Example:

Let matrix A be |a11   a12|
                |a21   a22|

Let matrix B be |b11   b12|
                |b21   b22|
                |b31   b32|

Then,
C = A tensor B = |a11B   a12B|
                 |a21B   a22B|

               = |a11b11   a11b12   a12b11  a12b12|
                 |a11b21   a11b22   a12b21  a12b22| 
                 |a11b31   a11b32   a12b31  a12b32|
                 |a21b11   a21b12   a22b11  a22b12|
                 |a21b21   a21b22   a22b21  a22b22|
                 |a21b31   a21b32   a22b31  a22b32|

You have been given two arrays having an equal number of elements. You have to find whether one array is the valid stack permutation of the other. An array is said to be a valid stack permutation of the other if and only if after applying some push and pop operations onto the sequence of elements in that array, will result in the other array.

Example:

Consider array : 2 4 6.
Valid stack permutations are as follows:
2 4 6
    push ‘2’
    pop ‘2’
    push ‘4’
    pop ‘4’
    push ‘6’
    pop ‘6’
2 6 4
    push ‘2’
    pop ‘2’
    push ‘4’
    pop ‘6’
    push ‘6’
    pop ‘4’
4 2 6
    push ‘2’ 
    pop ‘4’ 
    push ‘4’ 
    pop ‘2’ 
    push ‘6’ 
    pop ‘6’ 
4 6 2
    push ‘2’ 
    pop ‘4’ 
    push ‘4’ 
    pop ‘6’ 
    push ‘6’ 
    pop ‘6’ 
6 4 2
    push ‘2’ 
    pop ‘4’ 
    push ‘6’ 
    pop ‘6’ 
    push ‘4’ 
    pop ‘6’ 

Now, If the other array is [2,4,6], [2,6,4], [4,2,6], [4,6,2], or [6,4,2] then the answer is “YES” otherwise “NO”.

Note:

Please note that the arrays will only contain unique elements.

The names to a series of houses are given as:
A, B, C, ..., Z,
AA, AB, ..., AZ,
BA, .. BZ,
….., ……,
ZA ….. ZZ,
AAA … AAZ, … AZZ,
BAA, .. BAZ,... BZZ,
…….,.....
ZAA, .... ZZZ.
The total number of houses is 16,384. Find the name of the last house.