Wednesday, December 25, 2013

Egg drops

Given k eggs and n floors in a building, find the minimum number of trials required to determine the lowest floor from which when we drop an egg it does not break. Provide a Dynamic Programming solution.

Tuesday, December 24, 2013

Bridge Matching

n cities are sitting on the northern bank of a river and n cities are sitting on the southern bank. You can build a bridge only between cities with the same number. Provide a dynamic programming solution.

Monday, December 23, 2013


Given an array of integers find the longest bitonic sequence. Provide a dynamic programming solution

Sunday, December 22, 2013

Box Stacking

Given a set of 3d boxes compute the largest stack of boxes. A box can be stacked only on the top of another box with lager base. Provide a dynamic programming solution for stacking the boxes

Saturday, December 21, 2013

Boolean Parentization

given a Boolean expression of and, or, xor, true, false, find the number of ways to parenthesize and evaluate to true. Provide a dynamic programming solution

Friday, December 20, 2013

Box Stacking

Given a set of 3d boxes compute the largest stack of boxes. A box can be stacked only on the top of another box with lager base.

Thursday, December 19, 2013

Maximum value contiguous subsequence

given a real numbers’ array find a contiguous subsequence with max sum. Provide a dynamic programming solution

Wednesday, December 18, 2013

Balanced partition

given an array of integers between 0 and M divide the integers into two set such that difference of sums is minimized. Provide a dynamic programming solution

Tuesday, December 17, 2013


given n jobs each of which with a processing time, a profit and a deadline maximize the profit. Provide a dynamic programming solution

Saturday, November 9, 2013

Chapter 3 is done

This chapter is about Graph computation and there are classical algorithms (BFS, DFS, MST). MST is implementing the classical Prim's algo but using Fibonacci heap available in Boost. Here you find the first version of the graph code

Wednesday, October 30, 2013

Writing a programming / algorithmic book

I wanted to take on a new challenge and start writing a book about algorithms and design. The intent is to have Simplicity by Design (SD): every Chapter is a collection of 15-30 questions, followed by the solution, followed by a C++ code snippet which can be easily re-used.

So far, I have drafts for 3 chapters: bit programming, dynamic programming, and graphs. Here an example of graph code with very classical questions: implement a graph, implement bfs, implement dfs, implement topological sort, I already have code for other graph problems.  Dynamic programming has more mathematical content and I will publish an excerpt next weeks.

A number of questions:

  1. Should I publish code for public review? If so, can i still use it for the book?
  2. Should I publish questions for public review?
I think that this will be one of my side projects off work for the next year or so.

Sunday, September 29, 2013

Create your Team

you have a pool of players. Each player ha a set of skills. For creating a team you need to hire the minimum number of players who have together a predetermined set of skills

Wednesday, September 25, 2013

P0 - what people are saying

Here some previous postings

Find i = n^3 + m^3

how can a number be expressed as sum of two cubes?

52 cards

You have 52 cards half of them are red and half of them are black. You have a given amount of money M and every time you can bet k < M money. If you predict the right colour you will win 2k money, if not you will loose k. What is the best strategy?

Sort lexicographically an array of strings in C++ and in C

Monday, September 23, 2013

Conflits in k keywords

A keyword is made up of n bits. Given k keywords generated with uniform probability what is the probability to have collision? Provide an evaluation and write the code.

Sunday, September 22, 2013

Radix Sort -

Write a radix sort implementation in C++

Saturday, September 21, 2013

PageZero and Ted

I enjoyed attending Ted and give a talk about PageZero. While I was listening a number of very inspiring talks, I asked to myself would this PageZero really help users?

So I started to write {Ted} and immediately PageZero suggested {Ted Talks} as first suggestions and {Speakers} Speakers as su-bintent. That's exactly what I was looking for!!! I am impressed.

Then, I thought and what if I was interested in the Movie? PageZero predicted that potential choice too. Kind of cool, no?

Friday, September 20, 2013

Buying with constrains

You have a bag with capacity C and can insert items with value wi which will occupy space si. You cannot exceed the capacity. Write an algorithm in C++

Thursday, September 19, 2013

Project PageZero

SearchBox never changed since 1993, when the first search engine was created. Bing is disrupting the box by bridging the gap with the World of Entities. Names, Web Sites, and Generic Entities are directly accessible and understood as soon as you type. 

Tuesday, September 17, 2013

k balls, n floors

There is a building with n floors and you have k balls.  Balls are identical and when you drop them they can break or not. You need to figure out the highest floor of the building an egg can be dropped without breaking.

Monday, September 16, 2013

Friday, September 13, 2013

Design Patterns : C++ full collection of Gamma's patterns

Design Patterns : C++ full collection of Gamma's patterns

Full collection of Gamma's patterns in Full collection of Gamma's patterns in c++: 
  1. Creational: Abstract Factory, Builder, Factory, Prototype, Object Pool, Singleton,
  2. Structural: Adapter, Bridge, Composite, Decorator, Facade, Flyweight, Proxy patterns,
  3. Behavioral: Chain of Responsibility, Command, Iterator, Mediator, Memento, Observer, State, Strategy, Template, Visitor, and Interpreter

Thursday, September 12, 2013

Capped payrolls

In a company there are different payrolls pi, and we want to find a cap C such that the total amount of money paid is not above a maxim M. How can you determine C?

Wednesday, September 11, 2013

Thursday, September 5, 2013

Monday, September 2, 2013


count the number of trailing zeros

Sunday, September 1, 2013

Given two numbers a and b

Swap them with no temp variable. How many way  do you know for achieving that?

Thursday, August 29, 2013

Load balancing

We have a set of task i={1, ..., n} and each one has a cost b_i, how can we assigned to m servers so that the load is balanced?

Sunday, August 25, 2013

Triangle and Ants

On a triangle, there are 3 ants what is the probability that they collide when they move

Saturday, August 24, 2013

Sunday, August 18, 2013

What is wrong with this code?

string FindAddr( list emps, string name )
  for( list::iterator i = emps.begin();
       i != emps.end();
       i++ )
    if( *i == name )
      return i->addr;
  return "";

Friday, August 16, 2013

generate strings

Write a program that generates from the string "abcdefghijklmnopqrstuvwxyz{" the following: a bcb cdedc defgfed efghihgfe fghijkjihgf ghijklmlkjihg hijklmnonmlkjih ijklmnopqponmlkji jklmnopqrsrqponmlkj klmnopqrstutsrqponmlk lmnopqrstuvwvutsrqponml mnopqrstuvwxyxwvutsrqponm nopqrstuvwxyz{zyxwvutsrqpon

Thursday, August 15, 2013

Sunday, August 4, 2013

Use a dictionary

Given a string like "thisisalongstringwithmisakenoten" and a dictionary of words, split the string so that the number of non matched words are minimized. Try to optimize the code

Saturday, August 3, 2013

Implement a smartpointer class

using templates in C++

Smartpointer s1(T * ptr)
Smartpointer s1(Smartpointer & s2)
and the assigment

Wednesday, July 31, 2013

Shuffle an array of n elements

Suppose to have a uniform random generator in [0, 1)

Monday, July 22, 2013

Bing vs Google suggestions

Spot the difference on {royal baby} - which on has better suggestions the unbranded search engine or the other one?

Friday, July 19, 2013

What they've said about new Knowledge Suggestions @ Bing

"This is one area where Bing has a clearly better user experience than Google, if you’re looking to get actionable results from the actual search box. While Google will put a Pitbull Google+ profile in its autosuggest feature, it does little with suggestions for any of the examples Bing provides"

That’s not to say Google’s Knowledge Graph results don’t provide ways for users to distinguish what they’re looking for, but you have to get through the search query before you can tell Google what you’re actually looking for (like the Harry Potter books vs. movies, for example). Of course, you could always specify in your actual query."

Bing Autosuggest Expands to Take on Instant Search, Knowledge Graph In One Fell Swoop
Bing has taken search suggestions, autocomplete, and semantic search to a whole new level. --
Bing initially provided info directly in the search box for a celebrity, politician, athlete or a connection on LinkedIn with a public profile. This has now expanded to include brands, 

I find the experience pretty darn pleasant. Controversial article but our share is increasing. via @MarketingPilgrm
Bing is still out there, folks. Interestingly enough every time I use the engine (which is usually only because I have been urged to do so d

PCMag talks about the new searchbox with Knowledge understanding -
Bing's People Autosuggest today got a boost, expanding category options to include brands, movies, albums, places, software, sports teams, animal species, and more.

Techcrunch talks about Bing Autosuggest -
Microsoft's Bing today announced an update to its autosuggest feature that expands the number of categories that will trigger this feature. In May, Bing first introduced this tool for celebrities, politicians, athletes and publicly available LinkedIn profiles. Today, it is adding bran

According to webpronews we clearly beats Google -
Bing announced today that it is now including more types of entities in its autosuggest feature, including brands, movies, albums, places, software, sports teams, and …

Searchengineland talks about the searchbox disruption -
Bing announced they have expanded their search autosuggestions to add more than seven new categories. Bing added autosuggest completions for brands, movies, albums, places, software, sport teams, animal species and more. This is in addition to Bing adding people, 

Microsoft is pushing a bit further by surfacing these differences directly below the search box. --
Microsoft today announced it is expanding its Bing's People Autosuggest feature to include more than just humans. In fact, the search engine will now automatically suggest brands, movies, ...

Help vague Bing users get off of Microsoft's landing page and on with their lives. via @engadget
Having a hard time finding something on the internet? You're probably doing it wrong -- at least that seems to be Microsoft's supposition. The company

Other articles:

Bing Autosuggest Categories Revamped
UberGizmo (blog)

Microsoft expands Bing’s autosuggest for people to include animals, brands, movies, albums, places, and more 

Wednesday, July 17, 2013

Disrupting the searchbox

I published a blog on Microsoft search and it has been quoted by many

This is one area where Bing has a clearly better user experience than Google, if you’re looking to get actionable results from the actual search box. While Google will put a Pitbull Google+ profile in its autosuggest feature, it does little with suggestions for any of the examples Bing provides.
That’s not to say Google’s Knowledge Graph results don’t provide ways for users to distinguish what they’re looking for, but you have to get through the search query before you can tell Google what you’re actually looking for (like the Harry Potter books vs. movies, for example). Of course, you could always specify in your actual query.”

Sunday, July 14, 2013

SQL-like engines on the top of hadoop map/reduce

I missed to notice that there are new engines, in addition to standard hive and pig.

  • stinger is an optimized compiler aiming at introducing almost real time computations in hive
  • Impala is another real-time sql engine released by Cloudera
  • Drill is yet another real-time sql engine

Apache Kafka

A nice system for distributed logging from multiple platform - apache kafka

Tuesday, July 9, 2013

Monday, July 8, 2013


Othello is a game played on a square board, with black and white pieces. If a white/black piece is surrounded by a  black/white one (either left/right or up/down) then the piece will change color. Players play in turn until they have valid moves left. Implement Othello following Object Oriented criteria (e.g. what is a piece, what is a board, what is a game, who keeps the score, what is a valid move).

represent a double in [0,1) as binary

First need to understand what is the binary representation for a double in [0,1). Let's see an analogy.  If the number is an integer such as 123 I would probably make something like this

2 ^ 7  = 128 > 123 too large
123 - 2 ^ 6 = 59 -> set bit 1
59 - 2 ^ 5 = 27 -> set bit 1
27 - 2 ^ 4 = 11 -> set bit 1
11 - 2 ^ 3 = 3 -> set bit 1
3 - 2 ^ 2 < 0 -> set bit 0
3 - 2 ^ 1 = 1 -> set bit 1

1 1 1 1 0 1 1  

SearchCharm - Unified Search Experience in Windows 8.1

I am using windows 8.1 preview since many weeks without any problem. Search experience brings together the online and the offline worlds and it allows users to look for information virtually everywhere.

Traditional Web Search
Do I want to access cnn? Easy. I start to insert the query and I get both the web site and some relevant suggestions including cnn news and cnn money. Suggestions are generated by my group in London.

Navigating windows 
Do I want to access windows control panel? No problem, I just use the same interface and search paradigm.

Cloud search
What if I want to access my files stored in the cloud? Here I have my cv saved on Microsoft Skydrive and accessing it is as easy as searching via the charm

Local search
What if I want to access my files stored in my local computer? Here I have some videos saved on my local computer and accessing them is as easy as searching via the charm

Sunday, July 7, 2013

Wednesday, July 3, 2013

Search as you type with snapshots and disambiguation

Exciting day today! Bing is shipping an innovative search feature aiming at helping users to complete their tasks, as soon as they start to type their queries.

Consider the keyword "pitbull". This is a very interesting query because the user can be interested in getting either results about the famous singer (a person) or about the dog (an animal). For this example, we believe no instantaneous decision can be taken on the user's behalf and that only the user has a complete understanding of the intent expressed with a query.

However, we believe that the search engine can help the user to express very quickly this intent. How? In Bing we use the power of Satori (our Microsoft Knowledge Graph) to enrich our suggestions with additional information useful for disambiguating different meanings associated with the query. In this way, the users can select their own most appropriate choice.

Another example is the query {pluto}.  Is the user interested in the planet or is she interested in the cartoon? Those are very different kinds of entities which happens to have the same name but Bing understands the difference and gives to the user the opportunity to select the desired choice.

Now let's suppose that the intent is not ambiguous. For instance consider the keyword {michele obama}, we believe that it is very valuable to have a rich suggestion like the following one.

And what if there are two persons with the same name? In this case, we offer the opportunity to select the desired person as in this example for the query prefix {rachel nich}

One more example. Let's consider the query {u2}. Here, we offer the opportunity to explore all the entities / artists that are playing with the pop band

And what if you search for {harry potter}? In this case Bing provides a snapshot of the filmography, a reference to the book and a reference to the character.

Hope you enjoy it - this is the beginning.

Sunday, May 12, 2013

Friday, May 10, 2013

Stocastic Gradient Descent

Added a stocastic gradient descent to the linear regression code

Thursday, May 9, 2013

Learning linear regression with gradient descend

Last week I restarted an old and good behavior (see A collection of algos and data structures published here). Every day, I take an well known algorithm and code it in boost and C++. Nothing else, just pure training and geeky fun. The only constrain is the time limit of 45mins, after a running session in St. James park.

Here you have the code for linear regression with gradient descent in C++, boost, and ublas.  Linear regression is an approach to modeling the relationship between a scalar dependent variable y and one or more explanatory variables denoted X. Ublas is a powerful set of c routines for efficient matrix and vector computations, Boost:: numeric provides an elegant C++ way of using ublas based on templates.

Here you have the code

Wednesday, April 3, 2013

Scaling requests with MemCached

A nice paper from Facebook about the use of memcached for scaling requests. Classical UDP connection-less techniques, are mixed with TCP coalescing via mcrouter. Also, they implement flow control, new mechanism for cache miss, and excess of requests on a particular key. The concept of pool is quite interesting.

Monday, April 1, 2013

Friday, March 29, 2013

Find largest sum in a subarray

Given an array that may contain both positive and negative integers, find the sum of contiguous subarray of numbers which has the largest sum.

Hint: there is a divide & conquer solution in O(nlogn) and one cool solution in O(n)

Wednesday, March 27, 2013

Find the maxium integer in an array of size N, in O(N) and additional space O(1)

It's easy to make this in O(N) and O(N), or in O(N) and O(K) where K is the maximum int value contained in the array. However, this is requiring O(N) and O(1).

Hint: one way of doing this is to modify the original array.

Tuesday, March 26, 2013

My talk at ECIR2013

Gave an invited talk @ ECIR2013 and covered:

  • Bing, as a platform, new trends for Microsoft search
  • Bing suggestion technologies, an overview
  • Bing & Cosmos, massive data mining models compared to Hadoop, Map & Reduce, Hive, Pig

Saturday, March 23, 2013

Find the row with max num of 1s

Given a matrix nxm where all the rows are 0/1 and sorted. Find the row with max num of 1s.

Thursday, March 21, 2013

Monday, March 11, 2013

Sorted array and rotated

Given a sorted array of distinct elements, and the array is rotated at an unknown position. Find minimum element in the array.

Sunday, March 10, 2013

Given an array of positive integers, select two sub-sequences having minimum difference

Hint: one element can be either in one sub-sequence or in the other, so this is a typical recursive problem

Thursday, March 7, 2013

Design a data structure where min, max are O(1) , delete and insert are O(logN)

Hint: min is O(1) for an min-heap, delete and insert are O(log N). Same for max. Question is how to make it for both min and max

Wednesday, March 6, 2013

Circular pumps

Given a circular trace with pumps and a car running on a trace. Each pump has a well known distance from the origin, and the amount of kilometers you can run if you stop and refuel your car. Find a suitable starting point so that the car will not run out of fuel and the number of stops are minimal.

Tuesday, March 5, 2013

Special sort

Given an array of numbers, arrange them in a way that generate the largest value. For instance, if the given numbers are {34, 345, 348, 50}, the arrangement 5034834534 gives the largest value. 

Monday, March 4, 2013

Visit a BST in level order

Visit a BST in level order.
Visit a BST in reverse level order

Friday, March 1, 2013

Tuesday, February 12, 2013

Class of problems with Facebook Graph search

Several classes of problems with Facebook graph search have been reported. Here there is a list:
Plus, they frequently give no search results for suggested queries

Thursday, February 7, 2013

Given a set of time intervals in any order, merge all overlapping intervals into one and output the result which should have only mutually exclusive intervals

Tuesday, February 5, 2013

Facebook naive graph search and the need of proper query understanding algos

Search engines use multiple data sources to help users in their query formulation. Among those sources three are very important:
  • The web graph, which includes all the web pages published on the net. Mining the content of those pages and their connections can be very useful for detecting topics/entities and for understanding the correlation among those topics/entities;
  • The query graph, which includes all the queries submitted to a search engine in the past. Mining this graph can be useful for detecting what are the needs expressed by past users and how those needs change over the time;
  • The blog and news graph, which are useful for detecting fresh content;
Facebook is very interesting for search because they have access to other sources of data including:
  •  The friend graph, which keeps track of all the friendship relations for each user;
  •  The content graph, which includes all the postings and the content produced by your friends.
However, it seems like Facebook lacks quality access to the first three types of information. Here there are some examples:

Today, the most important financial news is Dell's acquisition and every single newspaper or financial web site report the news. Bing (and Google) both have this information in their suggestion, while Facebook is completely missing it. It seems like they are not analyzing the news graph (3rd source in the above list)

In the below example, the last two suggestions are provided by Bing. Facebook just tries to complete the prefix {microsoft and} with stuff such as {London} and {Pisa}, which are popular in my social graph but have NO correlation with Microsoft and with today's news.

Query understanding
So, If you spend sometime analyzing Facebook suggestion it's clear that they create synthetic suggestions trying to complete every query prefix with stuffs popular in my social graph. This approach is naive because they DON'T seem to understand the meaning of what the user is looking for. Here there are some more examples:

Again, "Happy Diwali", "Spotify", "Microsoft" and "London" are popular in my social graph but they have NO correlation with Tom Cruise. Still, Facebook is naively generating those suggestions.

A proper search engine understands the right correlation by analyzing the Web graph, the query graph and the news graph something that Facebook is missing at the moment.

There are many web sites out there which clearly say that tom cruise is correlated with {scientology}, {katie holmes} (his wife),  {suri} (his daughter), and {cameron diaz} (since they performed in many films together), and {nicole kidman} (his past wife). However, Facebook does not capture the intent of user query and does not understand the correlation among those entities. Let's see another example:

Last suggestion is from Bing, while Facebook keeps suggesting the same {Happy Diwali} stuff which is popular in my social graph. Again, they are missing a quality access to the 2nd and 3rd sources of information in my above list.

Bing (and Google) analyse the Web graph, the query graph, the news graph and many other sources and therefore they detect the right correlations among entities (strangely enough Google misses the correlation between {Obama} and {Michelle}).

Please note that if you try the above examples you may get different suggestions from Facebook because those are personalized with stuff popular in your social graph. However, it's easy to reproduce similar naive suggestions when you understand the pattern.

Thursday, January 24, 2013

Facebook Graph Search and problems with synthetic suggestions

I spent sometime playing with the suggestions mined by Facebook for their recent Graph Search. It seems to me that many of them are synthetic e.g. they are generated by mining the friends's graph and not the queries past queries submitted by users.

This approach seems to create many nonsensical suggestions. In this example, I was searching {hotels in new york city close} and the top suggestions are "hotels in new york city close to London", which is clearly a no sense. It seems to me that they are using some kind of frequent itemset algorithm and they notice that I have many friends in London, hence the  synthetically generated nonsensical suggestion. As you see, Bing suggestions are not suffering this problem and correct locations are shown.

Another example: I am an Italian guy and for me Milan is in Italy (btw, this Milan is way more popular on the Web that the one in Tennessee). Plus, none of those Milan cities are near to London. Web suggestions are nailing the correct location "il duomo" is central area in Milan, Italy.

Here there is another example of nonsensical suggestion. I assume that there are no Google employees who work for Microsoft at the same time. However, both the companies are quite popular in my social network hence the synthetic suggestion.

Now, let's consider another class of defects. There are queries which are not directly answered and the proposed suggestions are quite unrelated. In this example, I was searching for {actors who won the oscar} and Facebook graph search suggestions are clearly unrelated since I am not interested in "actors who like Oscar wilde"

Here there is another example of unrelated suggestion. I am searching {visit the taja} and this is not related to   "People named 'taja' who work at Visit Holland". In this case the semantic of the query is quite not understood.

If you try to replicate my examples, please note that you could get a different set of suggestions because those are generated by using your personal friend graph. However, it would be easy to generate similar situations once you understand the pattern.

See also my past postings:

Friday, January 18, 2013

Spelling, Spelling, Spelling. Facebook Graph Search and Bing Web Search

Continuing with my personal analysis on the Facebook Graph Search and Bing Web Search's integration,  here is another example of why you can get the best of two worlds. In this case, I will discuss misspelled words, a common problem for English (see for instance this funny article: "Why misspelled names are so common and what journalists are doing to prevent them").

Let's suppose that users start to type the word {swarzin}: their intent is to get information about the actor, but they are unsure of the correct spelling. As you see in the below image, Bing’s Speller processes tens of millions of data points mined from searches, web pages, clicks and user actions to help you find the right “Schwarzenegger".

Another example is {terramis} a delicious Italina cake of which the correct spelling is {tiramisu} - technically, {terramis} is a mispelled query prefix  for the full query{tiramisu}. Other mispelled prefixes are {bufet warr} and one of the myriad variants of {britnay s}. In all of these cases, Bing nails the correct suggestions and  are integrated into Facebook typeahead search.

Bing has a significant investment in building a state-of-art speller and those technologies are also leveraged by our team in London in securing the right suggestions. In this context, the additional problem is dealing with the mispelled fragments represented by the query prefix, correct the errors and, at the same time, predict which the more relevant suggestions are, and we need to do this every time new characters are typed in real time!

Can you imagine how fast the predictions and corrections need to be?

Thursday, January 17, 2013

Facebook Graph Search, with Bing Web Search

Many people asked what are the benefits of merging Facebook internal search (aka Facebook Graph Search), with Bing Web Search results. This is my poster query {Conrad Bain} just died, and Facebook knows many people with that name from their internal data, while Bing nails the name of the actor performing 'Different Strokes' series. 

Try your own queries and give us feedback