Thursday, November 29, 2012

Wednesday, November 28, 2012

Serialize and deserialize a generic tree

File * serialize (node * n); node * deserialize (File * f);

Monday, November 26, 2012

Isomorphic trees

Two trees can be called isomorphic if they have similar structure and the only difference amongst them can be is, that their child nodes may or may not be swaped. Write a function to detect whether two trees are isomorphic
int isIsomorphic(Node root1,Node root2) {
   if(root1==null && root2==null)
       return 1;
   if((root1 ==  null && root2 != null) || (root1 !=null && root2 == null ))
     return 0;
    if(root1.val == root2.val){
       if(isIsomorphic(root1.left, root2.left) == 1){
            return (isIsomorphic(root1.right, root2.right));
       } else if(isIsomorphic(root1.left, root2.right) == 1){
            return (isIsomorphic(root1.right, root2.left));
return 0;

Sunday, November 25, 2012

Pascal’s triangle is a triangular array of the binomial coefficients

Method 1 -
Each line n is the binomial coefficient C(n, k) where k is the row. This has complexity n^3. because in this case k has the same order of n

Method 2
Complexity n^2, with space n^2

Method 3
complexity n^2, with space O(1) -- this is more difficult because you need to move in the triangle storing just a constant number of locations. Can you express C(n, k) as function of C(n, k-1)?

Saturday, November 24, 2012

Compute the binomial coefficient in efficient way

C(n, k) = n ! / (n-k) ! k! = n (n-1) ... (n-k+1) / 1. 2. ... (k-1)k

C(n,k) = C(n, n-k) = n! / (n-n +k)! (n-k)!  so we can change r to r-p is r > p-r and keep the operation smaller

for (i = 0; i < k; i++)
    res *= (n - i);
    res /= (i+1);

O(k) time and (1) space

Thursday, November 22, 2012

Wednesday, November 21, 2012

BST, kth

 Find the Kth largest integer in a Binary Search Tree. 

Tuesday, November 20, 2012

Monday, November 19, 2012

Sunday, November 18, 2012

Gas stations

You have a certain number of gas stations in a circle and a car running on the circle. The car has a certain amount of gas available at the beginning. Find the right station to start for not running out of gas

This is a version of max subarray

Saturday, November 17, 2012

Creating a generic graph

Here the code based on C++, template, and boost::unordered_map and boost::unordered_multimap

Friday, November 16, 2012

Thursday, November 15, 2012

Construct BST from given preorder traversal

Construct BST from given preorder traversal (recursive solution)

Wednesday, November 14, 2012

Linked list

Given an unidirectional linked list, return the last but k element. No recursion

Tuesday, November 13, 2012

Deep copy

A random link list is a linked list where every node contains 2 links, one like a normal node which points to the next node. The other link points to a random node in the list, even itself. You are to write a function to perform a deep copy of this random link list.

Monday, November 12, 2012


Given a number n and another number m, which is a permutation of n find the number of moves needed to transform m into n.

Sunday, November 11, 2012

Shortest path

Given a binary square matrix of size n*n. 1 means there is a path, 0 means no path. Find the shortest path and print it from (0,0) to (n-1, n-1)

Friday, November 9, 2012

Matrix of 0/1

Find all the islands and return them. An island is a sub-matrix of contiguous 1s.

Thursday, November 8, 2012

Select a number from a stream with uniform probability

Here the code. the tricky part is the uniform probablity and the stream, which should be ideally processsed with O(1) memory

Tuesday, November 6, 2012

Compute the longest path in a binary tree

Given a binary tree, compute the longest length path

Here the code

Monday, November 5, 2012

Data structures in Boost

I like boost for the rich collection of data structures, which are very handful now and then.

  • Tuples, for tuples in mathematical sense
  • Any, when you have a collection of objects with different types 
  • Variant, when you have a collection of objects with different types, a modern version of union
  • Dynamic bitset, when you need to create a bitset whose dimension is unknown at compile time

Sunday, November 4, 2012

how many unique symbols in a file

Given a file of 1 petabyte containing unicode strings, compute the number of unique symbols contained in the file. Suppose that you have no more than 100Mb of available RAM.

Write some C++ code

Friday, November 2, 2012

Template typedef

In C++ you can have the first definition of a template class. However you cannot have a template typedef. In  C++0x this will be supported but for now the only thing that you can do is to have a typedef within a template struct, which will add a bit of un-necessary redundancy to the code

template <typename T>;
class C {...};
template <typename T>;
typedef T ;

Thursday, November 1, 2012

Back to basic: all the nodes in a level

Given a binary tree create create a list of nodes which are at the same level.

here the code

Monday, October 29, 2012

Back to basics: given a generic list and a pointer

Delete that element. The list is single linked and the element to be deleted is not the tail of the list.

Here the code

Sunday, October 28, 2012

Back to basics: write a matrix of generic types

Imagine to build a matrix [MxN] of generic type. Implement the classic [x, y] operator for accessing the element [x, y]. How would you implement it in C++?

here the code, where size can be either allocated at compile time or at run-time.

do you have any alternative solution? yes, boost::matrix is a valid one ;)

Saturday, October 27, 2012

Back to basics: a question, a code snippet

During past years, I used this blog to publish code snippets just for personal fun. Some of those snippets became relatively popular (see: A collection of algos and data structures published here).

I am now returning to basics and will restart the series. Everyday will publish a question and a solution with relative code snippet. Again, just for fun and just to keep myself in good shape.

First question: write a C++ generic binary tree and an interative inorder visit (e.g. stack no recursion, and templates)

    here the code

Thursday, October 18, 2012

BigData @ Twitter

Some good information about BigData in Twitter, including Cassandra, Hadoop, Pig and others.

Good talk about topic modelling

Very nice talk

Given a tv screen mxn

Implement a pan-fill algorithm (i.e. given a new color n and an original color o, and a position (x, y) change (x, y) and all the surrounding points until you meet the color 0).

Tuesday, October 16, 2012

Given a matrix nxn

Zero all the columns and rows which contains at least one zero.

Sunday, October 14, 2012

Decode a phone number

Phones have keyboard with letters, decode a phone number

const char* code[]={{"0"}, {"1"}, {"abc"}, {"def"}, {"ghi"}, {"jkl"}, {"mno"}, {"pqrs"}, {"tuv"}, {"wxyz"}};  

void decode(std::string & inputString, std::string result, int i, int n)
 std::string value;

 if (n == 0){
  std::cout << std::endl;
  for(std::string::const_iterator it = result.begin(); it != result.end(); ++it) { std::cout << *it ;}
  std::cout << std::endl;
 } else {

  char c =;
  int v = atoi(&c);
  for (const char *p = code[v]; *p != '\0'; ++p)
   decode (inputString, result + *p, i+1 , n-1);

Friday, October 12, 2012

Estimate the cost of building a typeahead system

Are you familiar with Bing Autosuggest? Now let's say that we store 20M of suggestions what would be the cost in $$ to implement this infrastructure? And what would be the cost if we have 20Billions of suggestions

Sunday, October 7, 2012

Realize a youtube service

Suppose you need to store 10 billions of videos and to address a growth of 10 millions of videos daily, how many space do you need for storing the videos and what would be the cost in $? Also, suppose that you want to have some replica for fault tolerance how this would increase the cost? Also, suppose that each single server can retrieve videos with a QPS=1000 provided that the index is not larger that 10 millions videos so that it can be fit in memory, how many servers do you need for serving 100 millions of queries daily? Is the QPS=1000 reasonable?

Thursday, October 4, 2012

Machine learning on Twitter data

A nice talk about ML on Twitter big data. Keep the model simple and leverage the amount of data and the connections.

Wednesday, October 3, 2012

Biased coin into a unbiased coin

A coin returns head with p=0.6 and tail with p=0.4. How to use this coin to simulate an unbiased one?

Tuesday, October 2, 2012

Sorted matrix

Given a boolean 2D array, where each row is sorted. Find the row with the maximum number of 1s.

Monday, October 1, 2012

Sunday, September 30, 2012

A great machine learning book

Many times people are asking  what is the best book to start studying machine learning. Among other books, I'd like to suggest: Machine Learning, An algorithmic Perspective, which has a good mix of topics covered and where every algorithm is implemented in python

Saturday, September 29, 2012

Exit a labyrinth

given a matrix of 0/1, where the 1s represent the walls of a labyrinth, find the exit

Friday, September 28, 2012

My view on Facebook Gift

Gift could be a changing moment for Facebook. In my view, this is a service with a great user experience and it also has opportunities for increasing FB's revenues. In my view, Facebook can become a cash-cow but they need to add services for allowing money transfer or gift transfers ( see my posting on this topic of about 1 year ago " )

Tuesday, September 25, 2012

Given a tree, return an array A

where A[i] is the head of a linked list containing all the elements at level i.

Friday, September 21, 2012


Explain the intuition behind SVM and optionally try to figure out the math

Tuesday, September 18, 2012

Select friends from your social network

You need to select the maximum number of friends in your network and invite them to a party. The requirement is that each friend knows a minimum of 5 friends and she does not know at least 5 other friends.

Thursday, September 13, 2012

Unsorted array

Given an unsorted array, how to divide them into two equal arrays whose difference of sum is minimum

Wednesday, September 12, 2012

Sort a large set of std::vector

Sort a large set of std::vector, larger than the size of RAM

Tuesday, September 11, 2012

Array rotation

Given an array, rotate the elements of an array within O(n) time and with 0(1) space

Monday, September 10, 2012

A frog jumping

A frog can jump a river of n meters and at each step she can jump either x-1 or x or x+1 meter if she jumped x meter at the previous step. She can jump just if the starting place and the ending place has a stone. The available stones are maintained in an array S[i] given as input. The first just is just 1 meter. Can you compute whether or not the frog will arrive at the destination?

Sunday, September 9, 2012

implement a first fit strategy

You have a m set of boxes of different sizes and a set of n envelopes. Find a strategy to fit the box in the envelopes

Thursday, September 6, 2012

an url can contain words

an url can contain words. For instance Device an algorithm for extracting all the words from an url

Wednesday, September 5, 2012

Longest subsequence

Given an array A of integers such that #A = n, find the longest sequence such that i_j < i_{j+1} and A[i_j] <= A[i_{j+1}] for any j \in [1, k-1]

Tuesday, September 4, 2012

Max sum in an array

Given an array of integers A find a, b such that \sum_{i=a}^b A[i] is maximized

Sunday, September 2, 2012

Search engines and monetization

Search engines are making money selling ads. Can you envision any different strategy?

Saturday, September 1, 2012

inverted lists

Given a very large set of document, you can define the following relation d_i ->; w_a, w_b, w_c, ...... meaning that the document d_i contains the word w_a, w_b, w_c, and so on and so forth

Suppose you want to invert the relation and build lists such as

w_a -> d_i, d_j, d_k ...

meaning that the word w_a is contained in documents  d_i, d_j, d_k ...

how would you proceeed?

Friday, August 31, 2012

unique records

you are given 1 billion of records taking 1 petabyte of spaces. Some entries are reperated. How to find the unique records if you have just 8Gb of memory? How much space do you need for processing, what is the complexity?

Thursday, August 30, 2012

View from the top

You are given a million of segments in a 3d space. segments can have different colours. draw the segments you will see on the plane where z-axes is zero.

Wednesday, August 29, 2012


Given an array A and an integer m, find all the i, j such that A[i]+A[j] = m. Find all the i, j, k such that A[i]+A[j]+A[k] = m

Tuesday, August 28, 2012

find elements that appears [n/k] times in the stream

Given a stream of lenght n, and an integer k find all the elements appearing more than (n/k) times. what is the memory you need? how many times you need to process the stream? what about complexity?

Monday, August 27, 2012

cluster users by attributes

A massive social network decided to assign an unsigned int as unique id for each user. Also, each user has a set of attributes represented as string and integers. Define a suitable cluster strategy for users based on the common attributes.

Sunday, August 26, 2012

Intersect two sorted arrays

Given two arrays A and B, where #A = m and #B = n, how would you intersect A and B? Please discuss complexity and real optimization

Saturday, August 25, 2012

Sum maximum

Given an array of n positive integers. Write a program to find the sum of maximum sum subsequence of the given array such that the intgers in the subsequence are sorted in increasing order.

Thursday, August 23, 2012

Sequences in sorted order

Given two integers k and n, write a function that prints all the sequences of length k composed of numbers 1,2..n. You need to print these sequences in sorted orde

Wednesday, August 22, 2012

Find the minimum distance

Given an unsorted array arr[] and two numbers x and y, find the minimum distance between x and y in arr[]. The array might also contain duplicates. You may assume that both x and y are different and present in arr[]

Sunday, August 19, 2012

Bing and Windows 8

Apparently, I am in the video (someone told me ;))

Saturday, August 18, 2012

Autosuggest and Bing

My team is shipping this Autosuggest Backend

 "“As you type results, Bing will offer suggestions and if we do say so, the auto-completion feels pretty quick.”"

Thursday, August 16, 2012

Subset sum

Find subset of elements that are selected from a given set whose sum adds up to a given number K. The set contains non-negative values.

Wednesday, August 15, 2012

Special Stack

Design a Data Structure SpecialStack that supports all the stack operations like push(), pop(), isEmpty(), isFull() and an additional operation getMin() which should return minimum element from the SpecialStack

Tuesday, August 14, 2012

Count in an array

Write a function to count number of smaller elements on right of each element in an array.

Monday, August 13, 2012

Celebrity problem

In a party of N people, only one person is known to everyone. Such a person may be present in the party, if yes, (s)he doesn’t know anyone in the party. We can only ask questions like “does A know B? “. Find the stranger (celebrity) in minimum number of questions

Saturday, August 11, 2012

Longest Bitonic distance

Given an array arr[0 ... n-1] containing n positive integers, a subsequence of arr[] is called Bitonic if it is first increasing, then decreasing.

Saturday, August 4, 2012

Intersection and Union

Given two Linked Lists, create union and intersection lists that contain union and intersection of the elements present in the given lists. Discuss complexity and make your assumptions.

Thursday, August 2, 2012

Bing and Facebook

“Facebook is a partner with Google’s biggest rival, Bing, to handle web searches.”

“Readers: Are you seeing the “search the Web” link in your typeahead search results?”

Facebook had previously allowed users to filter their Facebook searches by web results after clicking over to a main results page, but it hadn’t offered the option from the typeahead, which only included Facebook objects. Making it more efficient to search the web from Facebook’s search bar will give users an incentive to use Facebook search rather than going to a separate search engine like Google. “

Wednesday, August 1, 2012

An hidden gem, not so well known: Academic Search Microsoft. Want it integrated in bing?

Antonio Gulli 
Publications: 22 | Citations: 522 | G-Index: 22 | H-Index: 11 
Collaborated with 10 co-authors from 1997 to 2009; Cited by 905 authors
 Homepage |  Bing

Tuesday, July 31, 2012

Sharing revenues with skilled friends

In my previous postings I discussed about the opportunity of explicitly share your skills on facebook showing  that the authenticity of those skills would be self-regulated by the social network. Also, I claimed that the current web search ads system is not necessarily the only monetization model available.  In web search, when a query is submitted some relevant content is retrieved and ads are sold together with the results. The engine takes the money and the web content producers take no money. Web content producers take benefits from the traffic received by the search engine, but they directly take no money -- which is strange to me.

Now the question is what incentive could we give the users who are sharing their own skills?

First answer would be to send them traffic in analogy to what happen in web search. Anyway, I am not sure that this would be valuable for my friend Giuseppe who claimed that he is an expert in Photography. Why sending traffic to his Facebook page should have any additional value to him?

The second answer is to share revenue between my skilled friend Giuseppe and Facebook whenever Facebook shows Giuseppe among the friends skilled in Photography. The more likes Giuseppe gets the higher would be the chances to be retrieved for a search about Photography. Whenever ads shown for that topic are clicked Giuseppe will get a little amount of the revenues generated. He produced the content, he has the skill so he takes some direct money for it. In my view, this model would give a natural incentive to share skills and to get likes for those skills.

The third answer is still to about sharing revenues, but would be based on inserting ads into skilled pages. What is a skilled page? pretty simple. If Giuseppe declares a skill in Photography he can create a special page on his profile very similar to the traditional timeline but focused just on Photography. All the ads shown in that page are about the Photograpy topic and again there should be some form of revenue sharing as form of incentive to produce high quality, curated skilled pages. After all, Giuseppe is the expert so he has to tell something about his expertise. 

Monday, July 30, 2012

Skilled friends can gain money after they share their skills for free

An anonymous reader told me: "people need an incentive/experience to provide this information for free. They will assume that their friends know - so why should they tell Facebook this information?"

In my previous posting, I showed that skills cannot be faked because they are judged by the rest of the friends. This is nothing but just applying the power of social ties which self-regulates authenticity.

Now, let's go to the next step. I believe that current web ads system is fundamentally flawed. A lot of people produce web content which is then indexed by search engines. When a query about a topic is submitted by a user some relevant content is retrieved and ads are sold together with the results. The engine takes the money and the content producers take no money.

Why that?

Yes, content producers will receive more traffic and this has certainly an economic value. Anyway, who said that this is the only model we can think of?

Do you have any alternative?

Sunday, July 29, 2012

Skills cannot be faked

One more thought about my idea of skilled friends on Facebook. I don't believe the a friend can mystify her skills by declaring a talent which is not there. Her social network will understand this and she will look bad in front of her friends.

So, skills cannot be faked. Plus, when you declare a skill there is always the opportunity to like it and this will be an important signal to rank friends by skills.

Saturday, July 28, 2012

An idea for Facebook: from friends to skilled friends (or how to make money)

Facebook has 900 millions of users, and everyone is connected to a number of friends. Sometime you don't know what are your friends' skills. In my network there are people expert in photography, people expert in art, people experts in skiing, people expert in surfing, and people expert in solar power, and people expert in philosophy, and people with an immense musical background, and many geeks, and people with tremendous interest for electrical cars, and people with a passion for astronomy and celestial stuffs, and ....

So many people, so much talent to discover.

So Facebook, let everyone declare their own skills and talents to their social network. Let my friends be skilled friends. Let me also tag the skills of my friends as I tag my friends' faces in pictures.

Then, let me discover this talent when I search:  if I search for photography give the name of my friend Giuseppe who has a skill in this subject, and If I search surfing give me the name of Luca who is the expert here. If no friend is an expert in that topic, please find a skilled expert among the friends of my friend.

Transform generic search in search for skilled friends.

And when I search a skill, here you have the magic opportunity to sell ads about that topic. 

So If i search for surfing give me the name of Luca, but also ads related to the topic. Give me the name of that online market where I can buy great surf tables or show me where to find swimsuits. Likewise, if I search for camera give me the name of Giuseppe but also ads for the latest Nikon D7000. And...

Transform generic search in a search for skilled friends, and make money out of a great user experience.

Thursday, July 26, 2012

Bing search meets Facebook: exciting typeahead progress

Very happy about the integration of typeahead/autosuggestion technologies between Bing and Facebook. Now you can Bing directly from Facebook search box. Congratulation to the teams that made this happening by establishing a collaboration with several locations in the world (California, Washington, and London). My team in London provided core backend technologies for Bing Autosuggestion.


Wednesday, July 25, 2012

A phone has two sides. An idea for phone manifactures

Yesterday, I was listening this conversation: "I have always to carry at least two phones. My iphone is great for browsing and the apps, and my blackberry is great for browsing emails". How many of you have a similar  experience: either you have a phone with a large touch display which is great for browsing, or you have a phone with smaller display but with a decent keyboard. So you go out of there and buy your favourite Android, Windows Phone, Iphone AND you possibly buy a traditional Blackberry or the like.

Now I wonder why two devices? Why don't have just one with two sides? On one side you have the large touch display, and on the other side you have the smaller display but a good traditional keyboard.

I should probably patent this idea and sell it to companies out of there, but there is a war so I prefer to publish here and give it for free.. as in freedom

Sunday, July 22, 2012


How to implement LRU caching scheme? What data structures should be used

Saturday, July 21, 2012

Thursday, July 19, 2012

Bitonic arrays

iven an array A[0 ... n-1] containing n positive integers, a subarray A[i ... j] is bitonic if there is a k with i <= k <= j such that A[i] <= A[i + 1] ... <= A[k] >= A[k + 1] >= .. A[j - 1] > = A[j]. Write a function that takes an array as argument and returns the length of the maximum length bitonic subarray.

Wednesday, July 18, 2012

Array and positions

Given an array of n distinct integers sorted in ascending order, write a function that returns true is there is an index i such that arr[i] is equal to i

Tuesday, July 17, 2012

Strange struct.

struct str
    int i: 1;
    int j: 2;
    int k: 3;
    int l: 4;

what is this? is it a good and portable code?

Monday, July 16, 2012

Two arrays

Given two sorted arrays of any length, find out the median of them if they are sorted into single array

Saturday, July 14, 2012


Write a program to find all the possible paths from a starting point to dest point in a maze(2-D array).
ex: 1 0 1 0
 1 1 1 1
 0 1 0 1
 0 0 1 1 
If there is a block it’s represented by 0.
If there is a path it’s represented by 1.

Friday, July 13, 2012


Write a program for beautificaion of a program file in an IDE

Thursday, July 12, 2012

Linked list

Write a program to print the n-nodes from tail of the linked list.

Wednesday, July 11, 2012


Write a program to Validate an IPv4 Address

Tuesday, July 10, 2012

Distributed sort

Given N machines. Each machine contains some numbers in sorted form. The amount of numbers for each machine is not fixed. Output the numbers from all the machine in sorted non-decreasing form.

Monday, July 9, 2012

Unique words

Design a system to calculate the number of unique words in a file.. 1) What if the file is huge ? 2) Assuming that you have more than one computers available, how can you distribute the problem ?

Sunday, July 8, 2012

Array of 0 and 1

You have an array of 0s and 1s and you want to output all the intervals (i, j) where the number of 0s and numbers of 1s are equal. linear

Wednesday, July 4, 2012

Sum 3 numbers

given an array and a target value. Find a,b,c such that a+b+c=target

Monday, July 2, 2012

Solve the coin change problem

def count( n, m ): if n == 0: return 1 if n < 0: return 0 if m <= 0 and n >= 1: #m < 0 for zero indexed programming languages return 0 return count( n, m - 1 ) + count( n - S[m], m )

Sunday, July 1, 2012

Regexp match

Write a function checkRegex() which takes two strings as input, one string represents a regex expression and other is an input string to match with the regex expression. Return true if it matches, else false. Regex may contain characters ‘a-z’, ‘.’ and ‘*’ where ‘.’ matches any character and ‘*’ means 0 or more occurrences of the previous character preceding it.

Saturday, June 30, 2012

Min and Max

Find the min and max in an array. Now do it in less than 2n comparisons

Friday, June 29, 2012

Event store

Question: Design a component that implements the following functionality.. 1) Record an Event (For the sake of simplicity, treat the Event as an integer code) 2) Return the number of Events recorded in the last one minute. 3) Return the number of Events recorded in the last one hour. i.e implement the following interface

Thursday, June 28, 2012

Points closer to a point

You are given a list of points in the plane, write a program that outputs each point along with the three other points that are closest to it. These three points ordered by distance.

Wednesday, June 27, 2012

Last 60secs

Create a data structure which is supposed to log number of user requests per second. At any point of time your boss can ask you the number of hits for the last 60 seconds.

Monday, June 25, 2012

Reverse words

Given a file with billions of records data. The file is too large to in main memory, and you need to reverse each word in that file and then save the reversed words to another file.

Sunday, June 24, 2012

Creative d80 -- Bluetooth wireless music box

I recently bought a Creative d80 -- Bluetooth wireless music box and my impression is WOW!! It is very cheap just less than $40 and the quality of music is impressive. I can stream over Bluetooth from my iphone, ipad, android, winphone, and windows 7. I don't have a Mac but it seems as easy as the remaining ones. If you have win7 make sure that your Bluetooth device has a stack supporting a2dp or enhanced data rate.

Geek is about founding creative and inexpensive cool technologies.

Saturday, June 23, 2012

Monday, June 18, 2012

maximal subsets

Given a set S, find all the maximal subsets whose sum <= k. For example, if S = {1, 2, 3, 4, 5} and k = 7 Output is: {1, 2, 3} {1, 2, 4} {1, 5} {2, 5} {3, 4}

Saturday, June 16, 2012

Value of A and B

Given two sorted positive integer rrays A(n) and B(n). We define a set S = {(a,b) such that a in A and b in B}. Obviously there are n^2 elements in S. The value of such a pair is defined as Val(a,b) = a + b. Now we want to get the n pairs from S with largest values. The tricky part is that we need an O(n) algorithm.

Friday, June 15, 2012

true and false

Given a function bool Zoo(int x) and its called for y times , how you will generate the true with probability x/y times .

Thursday, June 14, 2012

what's next?

1 1
2 1
1 2 1 1

Wednesday, June 13, 2012


Solve the classical Google's interview problem.

Dynamic programming

k: Number of floors
n: Number of Eggs
eggDrop(n, k): Minimum number of trails needed to find the critical
               floor in worst case.

1) If the egg breaks after dropping from xth floor, then we only need to check for floors lower than x with remaining eggs; so the problem reduces to x-1 floors and n-1 eggs
2) If the egg doesn’t break after dropping from the xth floor, then we only need to check for floors higher than x; so the problem reduces to k-x floors and n eggs.

eggDrop(n, k) = 1 + min{max(eggDrop(n - 1, x - 1), eggDrop(n, k - x)): 
                 x in {1, 2, ..., k}}

Monday, June 11, 2012

A feature request for Facebook

Sometime I just want to pin a thread and follow it without expressing an explicit like. Would it be possible to just follow a thread?

Sunday, June 10, 2012

Monetizing free login

Several different providers are offering universal login schema, including Microsoft, Linkedin and Facebook. Apparently, none is monetizing this phase while there are plenty of opportunities to be leveraged.

Let's analyse a simple scenario where Alice, a Spotify user, decides to login using her Facebook account. Facebook knows Alice's geo-location, Alice's profile, Alice's past postings and likes. So Facebook has a lot of information to be mined for serving ads while Spotify does not have the same information. In other words, Facebook can sell ads to Spotify's users. So this could be the "Adsense" program for Facebook.

So my question is why Facebook is not opening this ads platform?

Saturday, June 9, 2012


Find the closest stars in the sky

Thursday, June 7, 2012


Data structure TO use to design a phonebook. What is time complexity for retrieving, adding, and deleting entries

Monday, June 4, 2012

Write a function that takes 2 arguments: a binary tree and an integer n, it should return the n-th element in the inorder traversal of the binary tree

int findNthElementByInorder(Node *node, int &n)
    if (node == null)
        return -1;
    findNthElementByInorder(node->left, n);
    if (n == 0)
        return node-> value;
   findNthElementByInorder(node->right, n);


Write a function that takes 2 arguments: a binary tree and an integer n, it should return the n-th element in the inorder traversal of the binary tree.
int findNthElementByInorder(Node *node, int &n)
    if (node == null)
        return -1;
    findNthElementByInorder(node->left, n);
    if (n == 0)
        return node-> value;
   findNthElementByInorder(node->right, n);

Sunday, June 3, 2012

Reverse a linked list

Node* reverseLL(Node* n) {
   Node* curr = n;
   Node* prev = null;
   while(curr !=null) {
        Node* temp =; = prev;
        prev = curr;
        curr = temp;
   return prev;

Saturday, June 2, 2012

Duch national problem

void threeWayPartition(int data[], int size, int low, int high) {
  int p = -1;
  int q = size;
  for (int i = 0; i < q;) {
    if (data[i] < low) {
      swap(data[i], data[++p]);
    } else if (data[i] >= high) {
      swap(data[i], data[--q]);
    } else {

Friday, June 1, 2012

Given array find 3 elements that sum up to 0

For each i = 1..length do
  left = 0, right = length
  While left < i and right > i do
     if values[left] + values[i] + values[right] == 0
      # Got solution here
    if values[left] + values[i] + values[right] > 0
      # means that right border should be moved
     # moving left border

Thursday, May 31, 2012

Sort an array of objects

There are just three sizes large, small, medium. what is the optimal complexity? Can you make this in-place?

Wednesday, May 30, 2012

Given 2 very large numbers, each of which is so large it can only be represented as an array of integers, write a function to multiply them

const unsigned MULTIPLY_BASE = 10;

void multiplyLittleEndian(const vector < unsigned > &a, const vector < unsigned > &b, vector < unsigned >  &r)
    r.assign(a.size()+b.size(), 0);
    unsigned ri=0;
    for(unsigned ai=0; ai < a.size(); ++ai)
        unsigned cri = ri++, carry = 0, am = a[ai], cr;
        for(unsigned bi=0; bi < b.size(); ++bi, ++cri)
            cr = carry + am*b[bi] + r[cri];
            r[cri] = cr % MULTIPLY_BASE;
            carry = cr / MULTIPLY_BASE;
            cr = carry + r[cri];
            r[cri++] = cr % MULTIPLY_BASE;
            carry = cr / MULTIPLY_BASE;
    while((!r.empty()) && r.back() == 0) r.pop_back(); // trim result

Sunday, May 27, 2012

add two numbers represented by strings

First need to reverse both strings, then add char by character and reverse final String again.

Friday, May 25, 2012

Interweave a linked list

Interweave a linked list. Do it in Linear time and constant space. Input: A->B->C->D->E Output: A->E->B->D->C

Wednesday, May 23, 2012

Tuesday, May 22, 2012

Roman strings

Get numeric number out of a roman string, linear time Given: mapping I = 1, V = 5, X = 10, L = 50, C = 100, D = 500, M = 1000 Input/Output: II = 2, III = 3, IV = 4 VI, VII, VIII IX = 9 XL = 40, XLIX = 49

mapping = {
            'I' : 1,
            'V' : 5,
            'X' : 10,
            'L' : 50,
            'C' : 100,
            'D' : 500,
            'M' : 1000,

def roman(string):
  prev = 0
  totalsum = 0

  for c in string:
    if mapping[c] <= prev:
      totalsum = totalsum + mapping[c]
      totalsum = totalsum - prev
      totalsum = totalsum + mapping[c] - prev

    prev = mapping[c]



Thursday, April 19, 2012

About the openness

Google is complaining about the direction where Internet is going. Apparently, they say that there is less openness these days and it seems that the bad guy is Facebook, which is collecting user generated content which is not shared in an open way.  I am puzzled.

If this is a genuine rant why are they building Google+ which is just a copycat of Facebook? Also, why they collect search data since 1998 about everyone's behaviour but they don't share this data with the rest of the world?

Long time ago, I dreamt about a different world with open standards for exchanging facebook-like news feeds but hosted by different providers (remember RSS and ATOM? something similar but social) so that data is public. Then, the aggregation is centralized and you access aggregated information in a similar way to what is happening nowadays with search engines. In that ideal world, login would be no longer centralized but it would be based on openID. The social graph would be shared across different servers and remote nodes would be just special form of href, so that someone can index public data.

(this is my personal idea and it's not representing any opinion expressed by my company)

Tuesday, April 17, 2012


you are at a party with a friend and 10 people are present including you and the friend. your friend makes you a wager that for every person you find that has the same birthday as you, you get $1; for every person he finds that does not have the same birthday as you, he gets $2. would you accept the wager?

Saturday, April 14, 2012

An interesting project for parallel machine learning:

Interesting collection of data parallel machine learning algorithms

"MADlib is an open-source library for scalable in-database analytics. It provides data-parallel implementations of mathematical, statistical and machine-learning methods for structured and unstructured data.
The MADlib mission: to foster widespread development of scalable analytic skills, by harnessing efforts from commercial practice, academic research, and open-source development."

Tuesday, April 10, 2012

Thursday, April 5, 2012


Hi Antonio,

First of all apologies if this query is out of scope- I appreciate you may have moved on to other things, or may be just too busy at the moment.

I was looking for a simple implementation of DBSCAN to use as a starting point for some work and I found your implemention here ( I found it worked quite well for small enough data sets, but for large ones it was allocating excessive amounts of memory, and I eventually looked at the code to see where the problem could be. It seems to me there may be an issue with the cluster expansion part of your algorithm- this issue may not affect the results (I think it may still produce the correct clusters), but it uses much more memory than it needs and this problem is more severe for larger input datasets.

The problem is with these lines of code

  Neighbors ne1 = findNeighbors(nPid, _eps);

              // enough support
              if (ne1.size() >= _minPts)
              debug_cerr << "\t Expanding to pid=" << nPid << std::endl;   
              // join
              BOOST_FOREACH(Neighbors::value_type n1, ne1)
                  // join neighbord
                  //debug_cerr << "\tPushback pid=" << n1 << std::endl;
              //debug_cerr << std::endl;
              //debug_cerr << " ne: " << ne << endl;
              debug_cerr << " ne size " << ne.size() << " " << ne1.size() << endl;

specifically the line "ne.push_back(n1)". At this point in the algorithm you have found a cluster and are looking for density connected neighbours. You are adding all the new neighbours to the list to be considered, when you only need to add the ones that have not been considered yet. So rather than extending the original list with the full contents of the new list, you need to extend it with the difference of the two lists. This small change stabilises the memory usage and makes it run much faster.

kind regards


Wednesday, April 4, 2012

Check if Alice has my phone number, and don't tell Eve

Alice is a friend of mine, Bob is my assistant but I don't want him to know my super-private phone number. Also, I want to check whether Alice has my super-private phone number but I don't want to communicate the number to Bob. What can I do to preserve my number?

Tuesday, April 3, 2012

An airplane is going from city A to city B

what would be the impact of the wind for a round-trip travel A to B?

Monday, April 2, 2012

Helium balloon in a car

What direction will the balloon go when you accelerate?

Sunday, April 1, 2012

One biased coin

You have a biased coin and the result can be H or T but biased towards T. How can you make sure whatever is the toss the result will be fair?

Saturday, March 31, 2012

magic square

You have a 3x3 square, fill with integers such that the sum for each row, for each column and in diagonal is 15. All the numbers must be different.

Hint: brute force is difficult (how many?), what would be number you put in the middle?

Friday, March 30, 2012

Table of reals

Given a table of real numbers of size mxn, is there an algorithm for making all the column sums and all the row sums positive? The only operation allowed is to change the sign of all the numbers in a column or in a row (one or more times).

Thursday, March 29, 2012


In a group of persons, a celebrity is know by everyone and all the other people are known by none. Detect all the celebreties

Wednesday, March 28, 2012

Monday, March 26, 2012

A classical one: reduced size and put into a bladder

This is one of those classical interview questions that are supposed to probe your creativity. i don't like those problems, if you want to test creativity just present some really hard problem you are trying to solve and perhaps you can be surprised by a new approach.

Anyway, suppose that you are reduced by 90% but still retaining your mass (what a sci-fi situation?) and you are put in a bladder (really?). What can you to do to safe your life?

Sunday, March 25, 2012

Ads -- betting on a query

You are a search engine which is selling ads for the query Q and your current valuation is 100$. Your competitor  has similar search performance but it's selling at 40$. What will you do?

Saturday, March 24, 2012

Given N horses, how many races do you need?

Given N horses, how many races do you need to identify top 3 horses. Assume that a race cannot have more than 5 horse together.

Given N horses, how many races do you need?

Given N horses, how many races do you need to identify top 3 horses. Assume that a race cannot have more than 5 horse together.

Friday, March 23, 2012

You have 25 bits

Every time you turn a bit on, you should put it as far away as possible from the the other bit already turned on. What is the best bit to turn on at the beginning?

Thursday, March 22, 2012

D'oh: Facebook Buys 750 IBM Patents For Defense

Facebook is purchasing 750 patents from IBM in order to bolster defenses against patent infringement suits, especially the one filed by Yahoo.

Tuesday, March 20, 2012

Saturday, March 17, 2012

IP to Countries

Write a function that will return a two character string representing a country code given an IP address as its input. Can this be made in memory?

Friday, March 16, 2012

a classical problem: coin change

Given a value in money N, and we want to change N into coins extracted from a set S={S1, ... Sm} of different coin values. How many diffferent ways to do we have to make the change. Assume that there are infinite coins of type Si.


Define C(S, N, M) the way of changing the N given the M coins in S and compute the recursive solution

Sunday, March 4, 2012

Why people are not using LinkedIn for Search? my opinion: their ranking is broken

Read an article about LinkedIn where the founder was complaining about people who are not using LinkedIn for searching new talents.  He says: "I have a frustration that people don't understand it. I had a CEO at one of my portfolio companies say to me, 'How do I use LinkedIn to find a CFO?' I said, 'Well have you tried typing "CFO" into the search box?' It's flabbergasting"

Perhaps, this is because the ranking system and the recommendation system in Linkedin are both fundamentally broken. Everyone can write whatever she likes in her CV and she can collude with other members for increasing the number of external references. There is no control and no sound ranking system in place. In short, anyone can inflate the value of her own LinkedIn profile.

Now why this is happening? Linkedin ranks users just using on their distance from my position in the social graph. Also, they consider textual match as a ranking feature. In my view, this is indeed a very primitive form of ranking and they should start investigating the idea of assigning credits to users. In this model, you spend a credit whenever you endorse a user and you gain credit when your endorsement was judged as positive by other users. This is a model used in real world where you spend some part of your social credit when you endorse someone. Plus, you earn some money when your endorsement will become a new hire.

So, Just a little feature suggestion for my friends in LinkedIn.

Saturday, March 3, 2012