# Directi Interview | Set 3

Online round:
1. There exist a binary tree with each node containing a character (lower case letters for leaf nodes and upper case letters for non-leaf nodes) and exactly two child, Now given a string find the number of root to leaf paths that contain this string as its subsequence. And the binary tree is given in post order notation.

2. A long question and a brute force solution of finding the most optimum subset (2^n)

First Round-

1. Find the k root of a number n. Mention the special cases, if any.

2. Given a connected graph with n-1+k edges and k being less than 10. Convert this graph to a tree removing the most weighted set of edges.

3. Given a set of coins n with each coin i having Pi probability to give heads. Find the probability of getting k heads, when all coins are tossed together.

Second Round-

1. Given a random function which gives some value in the range [-1,1]. Find the value of PIE.

2. Given a set of currencies and the exchange rates from each currency to another. Find if there exist any cycle of exchanges after which the original value of the amount increases.

3. Given a tree find the maximal XOR of any path from root to leaf (simple recursion)

4. Given a tree find the maximal subset XOR of any path from root to leaf. (ie the subset XOR may or may not include all elements from root to leaf)

Third round-

Some HR questions especially regarding the projects done by you and only one algorithmic question-

1. Given a set of restaurants (the number being quite large) and its geographical location(x,y) , you are allowed to do an significant amount of pre-processing on it. Now suppose there are x customers located at position (s,t), design an efficient algorithm to find the k nearest restaurants to these customers.
( This problem is the famous KNN problem- the solution they were expecting were of grid files )

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