SDE - 1

Bob has been given a triangular pyramid with its vertices marked as ‘O’, ‘X’, ‘Y’ and ‘Z’ and provided with another integer ‘N’. In a single step, Bob can go to any adjacent vertices. Bob will always start from ‘O’ and has to return to ‘O’ after making exactly ‘N’ steps.

Your task is to find out the number of ways he can take to complete his journey.

Note :

As the answer can be very large, return the answer by taking modulo with 1000000007.

For example :

If ‘N’=1 
So in 1 step we can reach either to ‘X’ , ‘Y’ or ‘Z’ and can not travel back to ‘O’.
Thus there are 0 ways.

If ‘N’ =2
So there are total three ways :
(i)  O->X->O
(ii) O->Y->O
(iii) O->Z->O

If ‘N’ = 3
So there are total 6 ways :
(i) O->X->Y->O
(ii) O->X->Z->O
(iii) O->Y->X->O
(iv) O->Y->Z->O
(v) O->Z->X->O
(vi) O->Z->Y->O

You are given a Singly Linked List of integers and an integer array 'B' of size 'N'. Each element in the array 'B' represents a block size. Modify the linked list by reversing the nodes in each block whose sizes are given by the array 'B'.

Note:

1. If you encounter a situation when 'B[i]' is greater than the number of remaining nodes in the list, then simply reverse the remaining nodes as a block and ignore all the block sizes from 'B[i]'. 

2. All block sizes are contiguous i.e. suppose that block 'B[i]' ends at a node cur, then the block 'B[i+1]' starts from the node just after the node cur.

Example

Linked list: 1->2->3->4->5
Array B: 3 3 5

Output: 3->2->1->5->4

We reverse the first block of size 3 and then move to block 2. Now, since the number of nodes remaining in the list (2) is less than the block size (3), we reverse the remaining nodes (4 and 5) as a block and ignore all the block sizes that follow.

You are given an 'N * N' matrix of integers where each row and each column is sorted in increasing order. You are given a target integer 'X'.

Find the position of 'X' in the matrix. If it exists then return the pair {i, j} where 'i' represents the row and 'j' represents the column of the array, otherwise return {-1,-1}

For example:

If the given matrix is:
[ [1, 2, 5],
  [3, 4, 9],
  [6, 7, 10]] 
We have to find the position of 4. We will return {1,1} since A[1][1] = 4.

Given a Binary Search Tree (BST) and a range [min, max], remove all keys which are outside the given range. The modified tree should also be BST.

You have been given a number of stairs. Initially, you are at the 0th stair, and you need to reach the Nth stair.

Each time, you can climb either one step or two steps.

You are supposed to return the number of distinct ways you can climb from the 0th step to the Nth step.

Note:

Note: Since the number of ways can be very large, return the answer modulo 1000000007.

Example :

N=3

We can climb one step at a time i.e. {(0, 1) ,(1, 2),(2,3)} or we can climb the first two-step and then one step i.e. {(0,2),(1, 3)} or we can climb first one step and then two step i.e. {(0,1), (1,3)}.