SDE - 1

Ninjas are often known for their stealth execution and accuracy to get the job done right. While honing their art of moving through dense forests stealthily, they need the maximum number of continuous trees one after the other for practicing.

Trees are represented by 1s and empty places by 0s (basically a binary representation of a given integer). You are also given an extra tree which you can plant at any empty place (i.e. you can flip one of the zeroes in the binary representation to 1). The tree should be planted such that the maximum number of consecutive trees is maximized.

Your task is to report the maximum number of consecutive trees after plantation.

Note:

You may also choose not to plant that extra tree at all.

For Example:

Input: 54
Output: 5

The binary representation of 54 is 110110.
After flipping the third bit from the left, we get consecutive 5 bits. i.e. 111110.

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 * +.

Ninja likes to travel a lot, but at the same time, he wants to save as much money as possible.

There are ‘N’ Stations connected by ‘M’ Trains. Each train that he boards starts from station ‘A’ and reaches destination station ‘B’ with a ticket price ‘P’.

Your task is to return the cheapest price from the given ‘source’ to ‘destination’ with up to ‘K’ stops. If there is no such route, return ‘-1’.

For example:

Input:
5 6
0 1 10
0 2 10
0 3 40
1 4 10
2 4 20
4 3 5
0 3 40 

There are three ways to reach station ‘3’ from station ‘0’. The first path is 0->1->4->3, which will cost us 10+ 10+ 5= 25 and the second path 0->2->4->3 will cost us, 10+ 20+ 5 = 35, and the third path 0->3 will cost us 40. 

We can’t take the first path since K = 1 and in this path, we are taking 2 stops, at station ‘1’ and station ‘4’. 

Similarly, there are 2 stops in the second path. Hence we’ll finally choose the 3rd path i.e. 0->3, which is colored in blue.

You are given D dice, each having F faces numbered 1 to F, both inclusive. The task is to find the possible number of ways to roll the dice together such that the sum of face-up numbers equal the given target S.

Note :

As the answer can be large, return your answer modulo 10^9  + 7.

Follow Up :

Can you solve this using not more than O(S) extra space?

Ninja has been given a matrix/list 'EDGES' denoting 'E' edges of a directed graph having ‘N’ nodes. Ninja starts walking from some node (say ‘START’) in the graph along a directed edge of the graph. If Ninja reaches an end node (say ‘END’) (a node that has no outgoing directed edges), Ninja stops walking.

Now a starting node ‘START’ is a safe node only if Ninja must eventually walk to an end node ‘END’. More specifically, there must be a natural number ‘K’, so that Ninja must have stopped at an end node in less than ‘K’ steps for any choice of where to walk.

For Example: For the graph, as shown in the picture below, [2, 4] are the only safe nodes.

Ninja wants to know all the safe nodes in the graph in sorted order. Can you help Ninja to find out all the safe nodes?

You have been given a network of ‘N’ nodes from 1 to ‘N’ and ‘M’ edges. For each edge, you are given three values (ui, vi, wi) where “ui” and “vi” denote the nodes and “wi” denotes an integer value which represents the time taken by a signal to travel from “ui” to “vi”. Now, you are supposed to find the time which a signal takes to travel from a given node ‘K’ to all nodes. If it is impossible for all nodes to receive the signal then print -1.

Note:

The signal which starts from the source node travels to all nodes simultaneously.