SDE - 2

Given an array of non-negative integers ‘A’ and an integer ‘P’, find the total number of subsequences of ‘A’ such that the product of any subsequence should not be more than ‘P’.

A subsequence is a sequence that can be derived from another sequence by deleting some or no elements without changing the order of the remaining elements.

Note

You need to print your answer modulo 10^9 + 7.

For Example

Let us take  A = [1,2,3] and P = 4. 
All the subsequences not having product more than ‘4’ are {1}, {2}, {3}, {1,2}, {1,3}. Therefore count is equal to ‘5’.

You are given a 2D board('N' rows and 'M' columns) of characters and a string 'word'.

Your task is to return true if the given word exists in the grid, else return false. The word can be constructed from letters of sequentially adjacent cells, where adjacent cells are horizontally or vertically neighboring.

Note:

The same letter cell should not be used more than once.

For Example:

For a given word “design” and the given 2D board 
[[q’, ‘v’, ‘m’, ‘h’],
 [‘d’, ‘e’, ‘s’, ‘i’],
 [‘d’, ‘g’, ‘f’, ‘g’],
 [‘e’, ‘c’, ‘p’, ‘n’]]

The word design can be formed by sequentially adjacent cells as shown by the highlighted color in the 2nd row and last column.

Ninja is having a good time in solving new questions of Binary Trees from Code Studio. He is now encountered with a question having statement as "You are given a binary tree consisting of 'N' nodes numbered from 1 to 'N'. Your task is to print all the root to leaf paths of the binary tree".

Ninja is stuck into this problem and could not able to find the logic. Help Ninja in solving the problem.

Note :

A leaf of a Binary Tree is the node which does not have a left child and a right child.

For Example :

Given a binary tree :

All the root to leaf paths are :
1 2 4
1 2 5 
1 3

Note :

1. Two nodes may have the same value associated with it.
2. The root node will be fixed and will be provided in the function.
3. Note that the nodes in a path will appear in a fixed order. For example, 1 2 3 is not the same as 2 1 3.
4. Each path should be returned as a string consisting of nodes in order and separated by a space.
5. The path length may be as small as ‘1’.

You are given N nodes labelled from 0 to N - 1 and a list of undirected edges( each edge is a pair of nodes). Your task is to find out if these edges make a valid tree. If they make a valid tree return true, else return false.

Tree is a special graph. It has the following properties.

• It is connected
• It has no cycle.

Example :

If n = 5 and if there are 4 edges i.e [ [0, 1], [0, 2], [0, 3], [1, 4]] so the graph formed will look like this:-

Here this graph is connected and it has no cycle so it is a tree.

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