40+ Haeal Pharma Interview Questions and Answers

In a group of people with a symmetric relation of knowing each other, there will always be at least two people who know the same number of people.

• Consider the person who knows the maximum number of people in the group.

• If there is no one who knows the same number of people, then everyone else must know a different number of people.

• But this would mean that the total number of people known by everyone else is different from the total number of people known by the person who know...read more

For any subset of size n+1 of the set S of the first 2n numbers, there exists 2 numbers u and v such that u divides v.

• Divide the set S into two subsets of n numbers each.

• By the pigeonhole principle, at least one of the subsets contains two numbers whose ratio is an integer.

• If the subset contains n+1 numbers, then one of the numbers must be in the subset with the two numbers whose ratio is an integer.

• Therefore, there exists 2 numbers u and v such that u divides v.

At a party with 7 guests and a host, each guest shakes hands with a certain number of people. How many people did the host shake hands with?

• The first guest shakes hands with 1 person, the second with 2 people, and so on.

• The kth guest shakes hands with k people.

• The host shakes hands with all 7 guests, so the number of people the host shakes hands with is the sum of 1 to 7.

• The sum of 1 to n is n(n+1)/2, so the host shakes hands with 28 people.

Algorithm to determine visible buildings in a 2D plane with given positions and heights

• Sort the buildings by their x-coordinates

• Traverse the sorted buildings from left to right

• For each building, check if it is visible by comparing its height with the maximum height of previously visited buildings

• If visible, add it to the list of visible buildings

• Return the list of visible buildings

If dist(u,v)>n/2 in an undirected graph, there exists a vertex x such that removing x makes u and v go to different connected components.

• Find the shortest path between u and v

• If the path length is greater than n/2, then there must be a vertex x on the path

• Removing x will separate u and v into different connected components

Find the largest substring formed from repetition of a smaller string.

• Identify all possible substrings of the given string.

• Check if each substring can be formed by repeating a smaller string.

• Return the largest substring that can be formed from repetition of a smaller string.

For an odd-sized grid, there cannot be a Hamiltonian cycle in the graph.

• A Hamiltonian cycle is a path that visits every vertex exactly once and ends at the starting vertex.

• In an n*n grid, there are n^2 vertices and each vertex has degree 4.

• For an odd n, the total degree of all vertices is odd, which means there cannot be a Hamiltonian cycle.

Prove that F_nk is divisible by F_n where F_i is the ith Fibonacci number. with f_0 = 0

• Use mathematical induction to prove the statement

• Base case: F_n0 = 0, F_n is also 0, so 0 is divisible by 0

• Inductive step: Assume F_nk is divisible by F_n, prove F_n(k+1) is divisible by F_n

• F_n(k+1) = F_nk + F_n(k-1), use the assumption to show that F_nk is divisible by F_n

• Therefore, F_n(k+1) is also divisible by F_n

• Hence, the statement is true for all k

Prove that there exists a rectangle with all corners of the same color in a 2D plane with blue and red points.

• Divide the plane into a grid of squares.

• By the pigeonhole principle, there must be at least one row or column with four points of the same color.

• Consider the pairs of points in that row or column and check if any of them form a rectangle.

Solution to Red-Blue Hat Prisoners puzzle that saves n - log(n) prisoners.

• Red-Blue Hat Prisoners puzzle involves prisoners guessing the color of their own hat to save their lives.

• The actual solution saves n-1 prisoners, but there are alternative solutions that can save more prisoners.

• One such solution involves using binary encoding to communicate the color of the hats, which can save n - log(n) prisoners.

• This solution works by having each prisoner encode the color of their ha...read more

Expected length of segment containing (1,0) on a unit circle with three random points.

• Use law of cosines to find length of each segment.

• Calculate expected value using probability density function.

• Answer is (4/pi) + (2/3).

The question asks to construct a k-ary tree using the given k and DFS traversal string.

• Iterate through the DFS traversal string

• If the current character is 'P', create a parent node

• If the current character is 'L', create a leaf node

• Link the nodes according to the DFS traversal order

To determine if a graph has a node with n degree, iterate through all nodes and count their edges.

• Iterate through each node in the graph

• Count the number of edges connected to each node

• If any node has n edges, then the graph has a node with n degree

I would prefer to develop mathematical models.

• I enjoy the process of creating and testing mathematical models.

• Developing trading infrastructure is important, but not my primary interest.

• Mathematical models can be applied to various industries, not just trading.

• Examples of mathematical models I have developed include predictive models for customer behavior and financial forecasting models.

Check if a string containing parenthesis is balanced

• Use a stack to keep track of opening parenthesis

• Iterate through the string and push opening parenthesis onto the stack

• If a closing parenthesis is encountered, check if the stack is empty or if the top of the stack is the corresponding opening parenthesis

• If the stack is empty or the top of the stack doesn't match, the string is not balanced

• After iterating through the string, if the stack is empty, the string is balanced

A graph has a unique topological sort if and only if it is a directed acyclic graph (DAG).

• A topological sort is a linear ordering of the vertices of a graph such that for every directed edge (u, v), vertex u comes before vertex v in the ordering.

• To check if a graph has a unique topological sort, we can use depth-first search (DFS) or breadth-first search (BFS) algorithms.

• If during the DFS or BFS traversal, we encounter a back edge or a cycle, then the graph does not have a un...read more

I have faced incidents related to system crashes, network failures, and security breaches.

• System crash due to hardware failure

• Network failure due to misconfiguration

• Security breach due to weak password policy

• DDoS attack causing website downtime