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You are given a directed cyclic graph represented by an adjacency matrix. The graph has at least one terminal node (i.e. the node with no outgoing edges).

Each edge of the graph is assigned a positive integer representing a probability of taking this edge. E.g. if you have 3 outgoing edges with numbers 3, 2, and 4, this means that the prob. of taking these edges are: 3/9, 2/9 and 4/9, respectively.

You need to find the probability of reaching each terminal node from the starting node 0.

Example:
adjacency matrix 5x5:

m = {{0 1 0 0 1},
        {0 0 3 2 0},
        {4 0 0 1 0},
        {0 0 0 0 0},
        {0 0 0 0 0}}

so we have two terminal nodes here: 3 and 4
we can take the following paths:
0 -> 1 -> 3 = probability: 1/2*2/5 = 1/5
0 -> 1 -> 2 -> 3 = probability: 1/2*3/5*1/5 = 3/50
0 -> 1 -> 2 -> 0 -> 1 -> 3 ... and so on

or to the node 4:
0 -> 4: probability: 1/2
0 -> 1 -> 2 -> 0 -> 4: probability 1/2*3/5*4/5*1/2 = 3/25

and so on, summing up probabilities of all possible paths we get:
total probability to reach node 3: 13/38
total probability to reach node 4: 25/38

design an ip blocking system

Given an n-ary tree and some queries for the tree, in every query you’ll be given a node you are supposed to print preorder traversal of the subtree rooted at that node.

You have an array of numbers. You have to give the range in which each number is the maximum element. For Example, If array is 1, 5, 4, 3, 6 The output would be
1 [1, 1]
5 [1, 4]
4 [3, 4]
3 [4, 4]
6 [1, 5]

Given an array of billion of numbers. Billions of queries are generated with parameters as starting and an ending index. Both these indices lie within that array. Find the maximum number between these two indices in less than O(N)

Multiply two numbers without using * and only be using bitwise operations

Display nodes of a tree in level order using DFS

Implement a deque using stacks

Given the entire dictionary of English words, what data structure will you use to efficiently store and match the custom regex string like "D*sk", where * represents any single alphabet, and return the list of matched words?

Given a skewed tree, an insect is sitting at the root of the tree at t = 0min, every minute insect steps down in the tree, find the probability of the insect being at any node at t = infinity. Once I came up with a solution various other complexities has been added to the problem such as: What if the tree is binary tree (written code for this) What if three is n-ary What if it is now a directed acyclic graph Handle cases that there can be more than one entry point There can be more that one way to reach a node

Given a binary tree of numbers and a search number has given, find out first occurence of that number and smallest distance from root node. if you have given k search numbers find their occurence and nearest from root node in a single walk.

Given a string of numbers put commas so that it become readable like million trillion thousands. eg 1010503 ===> 1,010,503

Given an array of 0s and 1s. find maximum no of consecutive 1s. If you have given chance to flip a bit to 1 such that it maximises the consecutive 1s. find out that flipped bit and after flipping that bit maximum no of consecutive 1s. Above question but you have options to flip k bits.

Design a system which will keep track of product and its inventory count. The service will expose two api incrCnt(int prodId, int cnt) and decrCnt(int prodId, int cnt). Which db would you use ? How will you handle hot products ?

Design a system in which read a file which has data and operation to be performed give a line by line. Ex a=5, next line b= 10, next line a*b. This design extended to support float, doubles, boolean, vector and complex numbers. Like if the file has a=5+i8, then how you handle such scenarios. How you will store and process data.

Design content ingestion system

You are given 2 arrays: one representing the time people arrive at a door and other representing the direction they want to go(in or out) You have to find at what time each person will use the door provided no 2 people can use the door at the same time. Constraints: the door starts with ‘in’ position, in case of a conflict(2 or more people trying to use the door at the same time), the direction previously used holds precedence. If there is no conflict whoever comes first uses the door. Also if no one uses the door, it reverts back to the starting ‘in’ position. Should be linear time complexity.

A startup website has a lot of real-time traffic . I want to see the real-time view (refreshed every 1 min) of top 20 users by hit count within last 10 mins. Full distributed system, I have to resolve all the concurrency issues.

I was asked this during my onsite google interview but was unable to come up with an optimization for it. Here is the question:

There's a list of (x,y) points and a method getCircle with the following signature:

/**
* Given three points returns a circle (Radius, and center) such that all three points lie in its circumference
* or it returns null if no such circle is possible.
*/
Circle getCircle(point1, point2, point3);
getCircle method is already implemented and given to you as a black box. The problems asks you to find the Circle with most points in its perimeter.

The obvious answer is to get all possible triplets of points and find all possible circles and keep track of which one appears most often O(n^3) . Any ideas on how to further optimize this?

There are cards and each card has an identity. e.g. HC1 has ID 1, this ID also represents the cost of the card. Your sister already have some cards and you want to gift her cards which she do not have already. Program is to return the max number of cards you can buy for her.

Constraint : You have amount d, and want to buy as many distinct card as you can.

e.g. Sister Cards = [2, 3, 5], D : 7 Card you buy : 1, 4

Output : 2

You have been given a special and normal status of alphabets.

e.g. “01111001111111111011111111” represents “abcdefghijklmnopqrstuvwxyz”. Here 0 represents normal character and 1 represents special character.

Given an Input String S and a number k, find the maximum continuous sub array with maximum k number of number elements. There is no constraint on special character.

e.g.

S = “giraffe”, K = 1, “011110011111111110111111”

Output : 3

How ?

normal characters : a, g, f

one of the possible solution : gir (as this has only one normal character)

Given a binary String which represents the target state. Minimum number of flips needed to convert a same size Binary String (with all 0’s) to target state. A flip also causes all the right bits to be flipped.

e.g.

Input : 00101 (Represents Target)

Output : 3

Explanation :

00000 -> 00111 -> 00100 -> 00101

N cows are standing at the origin on x-axis, each cow has some appetite, in other word hunger index. A cow can sleep of 1 unit of time or eat for one unit of time or move left or move right. There are some vessels placed on the x-axis, they are having infinite supply of fiod. Find minimum time in which all cows appetite would be filled.

Input:
cow Apetitte = {1,1}
Vessle locations = {-1,1}
Answer would be 2 since both cow can go in different direction they would eat for one seconds. One second for moving and one second for eating.

This problem looks to be similar to rotten eggs/tomatoes.

Design and implement rate limiter for limiting api calls for a service distributed multiple users.

Design data structures which support millions of products coming in streaming manner, we need to find at any moment what are top n products at any day

A dictionary is combination of characters from a-z. let's say a=1,b=2.. and so on z=26. you are given n and k. you have to find sum of length k from given combination.
for example n=51 and k=3 then your answer should be =axz
as there can be many combination for given sum so it is suggested to print those string which comes first in dictonary

beautiful numbers are those numbers which contains digit only 4 and 5 also they are palindrome.length of number can't be odd. for example
44,55,4554 are beautiful numbers where as 38, 444 are not.
your task is to find nth number in this series. let's say if n=4 then output should be 4554. for n=1 output will be 44 always.

There are N stations in a certain region, numbered 1 through N. It takes di,j minutes to travel from Station i to Station j (1 ¥leq i, j ¥leq N)$. Note that di,j=dj,i may not hold.
You are now at Station 1. From here, you have to visit all the stations exactly once. We assume that you have already visited Station 1. However, due to your schedule, there are M restrictions that must be satisfied. The format of each restriction is as follows:
• Station si must be visited before Station ti. (1≤i≤M)
Find the minimum time required to visit all the stations. Note that the last station to visit can be any of the stations.
Constraints
• 1≤N≤14
• 0≤di,j≤108 (1≤i,j≤N)
• di,i=0 (1≤i≤N)
• 0≤M≤N(N−1)⁄2
• 1≤si,ti≤N (1≤i≤M)
• si≠ti (1≤i≤M)
• There exists a path visiting all the stations under the given restrictions.
Input
Input is given from Standard Input in the following format: N d1,1 … d1,N : dN,1 … dN,N M s1 t1 : sM tM
Output
Print the minimum time required to visit all the stations.
Sample Input 1
4
0 2 3 4
1 0 3 4
1 2 0 4
1 2 3 0
3
1 2
2 3
3 4
Sample Output 1
9
Due to the restrictions, we can only travel as follows: Station 1 → Station 2 → Station 3 → Station 4. Thus, the answer is 2+3+4=9 and we should print 9.
Sample Input 2
3
0 1 20
1 0 20
10 20 0
0
Sample Output 2
21

You are given an array of length N consisting of integers, a={a1,…,aN}, and an integer L.
Consider the following subproblem:
• You are given an integer S.
• Find the largest value in the interval [S,S+L−1] in the sequence a, that is, find max(aS,…,aS+L−1).
Solve this subproblem for every S=1,…,N−L+1.
Constraints
• 1≤N≤105
• 1≤L≤N
• −109≤ai≤109
Input
Input is given from Standard Input in the following format: N L a1 … aN
Output
Print the answers in N−L+1 lines. The i-th line should contain the answer to the subproblem where S=i.
Sample Input 1
5 3
3 4 2 1 5
Sample Output 1
4
4
5
• The subproblem where S=1 asks the largest value among a={a1,a2,a3}={3,4,2}, so the first line in the output should contain 4.
• The subproblem where S=2 asks the largest value among a={a2,a3,a4}={4,2,1}, so the second line in the output should contain 4.
• The subproblem where S=3 asks the largest value among a={a3,a4,a5}={2,1,5}, so the third line in the output should contain 5.
Sample Input 2
4 1
-1000000000 1000000000 -1000000000 1000000000
Sample Output 2
-1000000000
1000000000
-1000000000
1000000000

There are N rooms in a row. The i-th room (1≤i≤N) from the left is called Room i. You are given M closed intervals [ai,bi] (1≤i≤M). At time 0, all rooms j such that ai≤j≤bi for some i (1≤i≤M) are occupied, and the other rooms are vacant.
You are given Q queries. The i-th query (1≤i≤Q) represents an event happening at time i, as follows:
• In the i-th query (1≤i≤Q), a closed interval [ci,di] (1≤i≤Q) is given.
• This query asks: "Are all rooms j such that ci≤j≤ci" vacant?
• If all those rooms are vacant, the query should be responded by OK, then all rooms j such that ci≤j≤ci get occupied.
• Otherwise, the query should be responded by OK, then nothing happens.
Process these queries.
Constraints
• 1≤N≤109
• 0≤M≤1000
• 1≤ai≤bi≤N (1≤i≤M)
• There are no rooms k such that ai≤k≤bi and aj≤k≤bj at the same time (1≤i<j≤M).
• 1≤Q≤1000
• 1≤ci≤di≤N
Input
Input is given from Standard Input in the following format: N M a1 b1 : aM bM Q c1 d1 : cQ dQ
Output
Print the responses in Q lines. The i-th line should contain the response to the i-th query.
Sample Input 1
5 2
1 1
4 4
3
3 3
2 3
5 5
Sample Output 1
OK
NG
OK
At time 0, Room 1 and 4 are occupied.
• At time 1, a query asks: "is Room 3 occupied?" Since Room 3 is vacant, we should print OK, then Room 3 gets occupied.
• At time 2, a query asks: "are Room 2 and 3 occupied?" Since Room 3 is occupied, we should print NG.
• At time 3, a query asks: "is Room 5 occupied?" Since Room 5 is vacant, we should print OK, then Room 5 gets occupied.
Sample Input 2
1000000000 1
2 999999999
4
1 1000000000
500000000 500000000
1 1
1000000000 1000000000
Sample Output 2
NG
NG
OK
OK