Thursday, November 29, 2012

Find the lowest common ancestor

For a binary tree for a binary search tree

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

Identify all the pythagorian triplets in the given array.

2 , 4 -> 4 + 16 = 20
1, 3 -> 1 + 9 = 10

In efficient way

Wednesday, November 21, 2012

BST, kth

Find the Kth largest integer in a Binary Search Tree.

Tuesday, November 20, 2012

Find non-unique characters in a given string

Optimal complexity in time and space

Monday, November 19, 2012

Generic graph with weights

Here the code based on boost::unordered_map

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

Huge file of parenthesis ( .. ) . Find if they are balanced

The file is huge and you don't want to run out of memory.

Thursday, November 15, 2012

Construct BST from given preorder traversal

Construct BST from given preorder traversal (recursive solution)

Wednesday, November 14, 2012

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

Transormations

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

Here the code.

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

Very nice talk http://videolectures.net/mlss09uk_blei_tm/

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 = inputString.at(i);
int v = atoi(&c);

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


Saturday, October 13, 2012

Facebook has a feature which allows to discover the friends in common among two users.

How would you implement it in a social graph?

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

Tuesday, October 9, 2012

Given a string, find its rank among all its permutations sorted lexicographically.

This is a bit hard

Sunday, October 7, 2012

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? Saturday, October 6, 2012 Generate all the permutations of 1.. N integer numbers Friday, October 5, 2012 Find all the anagrams in a collection of strings 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 Implement a smart pointer class with assignment, constructor and destructor 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 "http://codingplayground.blogspot.co.uk/2011/09/facebook-social-wallet.html ) Thursday, September 27, 2012 Given a BST find the k-th element in an efficient way Wednesday, September 26, 2012 Reverse a single linked list 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. Monday, September 24, 2012 Check if a string has balanced parenthesis Sunday, September 23, 2012 Convert a BST into a double linked list preserving the order Saturday, September 22, 2012 K-Means: describe the intuition behind the algo and write some code for it Friday, September 21, 2012 SVM Explain the intuition behind SVM and optionally try to figure out the math Thursday, September 20, 2012 Describe the intuition behind the esamble of classifiers Wednesday, September 19, 2012 Describe the intuition behind boosting and bagging 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. Monday, September 17, 2012 BST, visit preserving the order Sunday, September 16, 2012 In an array of integers take the k largest elements Saturday, September 15, 2012 Given an array of integers A, compute efficiently the max in any interval [i, j] Compare time and space Friday, September 14, 2012 Implement a readline in C and suppose you have read available 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 akillernewappforwork.com. 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 Monday, September 3, 2012 Given a stream compute the running average and the running median 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 arrays 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. Friday, August 24, 2012 Today, 3 years at Microsoft 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[] Tuesday, August 21, 2012 A collection of algos and data structures published here Monday, August 20, 2012 A collection of feature suggestions published here 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.”" http://www.engadget.com/2012/08/15/windows-8-rtm-whats-new/ Friday, August 17, 2012 Related Searches and Bing My team is shipping this Related Searches ;) ;) http://news.cnet.com/8301-10805_3-57495215-75/bing-windows-8-app-brings-tiled-goodness-to-your-search-results/ 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 Sunday, August 12, 2012 Find the two numbers with odd occurrence​s in an unsorted array 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. Friday, August 10, 2012 Find the smallest positive number missing from an unsorted array Thursday, August 9, 2012 Find a triplet that sum to a given value Given an array of integers Wednesday, August 8, 2012 Given an unsorted array of nonnegative integers, find a continous subarray which adds to a given number Tuesday, August 7, 2012 Given a sequence, find the length of the longest palindromic subsequence in it. Monday, August 6, 2012 Check whether two strings are anagram of each other Sunday, August 5, 2012 ind the maximum sum leaf to root path in a Binary Tree 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. Friday, August 3, 2012 Add two numbers without using arithmetic operators Hint: use bit operators 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? http://academic.research.microsoft.com/Author/77558/antonio-gulli?query=antonio+gull 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 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. Friday, July 27, 2012 Implement an hash table with chains in case of collision 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. Enjoy! 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 Tuesday, July 24, 2012 Implement a tree inorder visit with no recursion Monday, July 23, 2012 What colour would you pain an airplane motivate your answer Sunday, July 22, 2012 LRU How to implement LRU caching scheme? What data structures should be used Saturday, July 21, 2012 Implement set and traditional set operation Please discuss trade-offs in your choice. Friday, July 20, 2012 Given a stream of integers always maintain the median This is a bit difficult, try with heaps 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 Sunday, July 15, 2012 Find the maximum element in an array which is first increasing and then decreasing Go with binary search (well, pretty much) Saturday, July 14, 2012 Maze 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 Beautification 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 IPv4 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 Saturday, July 7, 2012 Check Number is perfect Square or Not Friday, July 6, 2012 Implement a data structure for storing and retrieving non overlapping intervals of integer Thursday, July 5, 2012 Given an array of size n, find all the possible sub set of the array of size k typical recursive problem Wednesday, July 4, 2012 Sum 3 numbers given an array and a target value. Find a,b,c such that a+b+c=target Tuesday, July 3, 2012 fiven n points find m points closer to origin in a r-space 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. Tuesday, June 26, 2012 Find top log(n) or top sqt(n) values in an array of integers in less than linear time. 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

This Ph.D. thesis changed the world as we know. 100 years. A true hero, with solid principles

https://webspace.princeton.edu/users/jedwards/Turing%20Centennial%202012/Mudd%20Archive%20files/12285_AC100_Turing_1938.pdf

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}

Sunday, June 17, 2012

Lucky numbers are numbers whose prime factors are just 2, 3, 5.

Find the first k lucky numbers.

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 .

1

1 1

2 1

1 2 1 1﻿

Wednesday, June 13, 2012

Eggdrops

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}}



Tuesday, June 12, 2012

you have a fleet of trucks and each truck has an autonomy of 1000KMs

How many kms in total you can cover if all the trucks start  from the same place?

You have 25 horses and you can make races of 5 of them in parallell

How many races to get the top 3 horses?

Monday, June 11, 2012

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

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

Stars

Find the closest stars in the sky

Thursday, June 7, 2012

Phonebook

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;
else
n--;
findNthElementByInorder(node->right, n);
}



N-th

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;
else
n--;
findNthElementByInorder(node->right, n);
}


Sunday, June 3, 2012

Node* reverseLL(Node* n) {
Node* curr = n;
Node* prev = null;
while(curr !=null) {
Node* temp = curr.next;
curr.next = 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]);
++i;
} else if (data[i] >= high) {
swap(data[i], data[--q]);
} else {
++i;
}
}


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
right--
else
# moving left border
left++



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;
}
while(carry)
{
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. Do it in Linear time and constant space. Input: A->B->C->D->E Output: A->E->B->D->C

Wednesday, May 23, 2012

Implement a function to compute cubic root what is the time complexity?

pay attention to negative values, but it's a binary search

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]
else:
totalsum = totalsum - prev
totalsum = totalsum + mapping[c] - prev

prev = mapping[c]

print(totalsum)

roman("XCIX")



Thursday, April 19, 2012

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

Birthday

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."

Friday, April 13, 2012

How many zeros at the end of 100!

This is tricky but funny

Tuesday, April 10, 2012

Compute 2^128 -- no computer and possibly no paper

can you just compute it in your mind?

Thursday, April 5, 2012

DBScan

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 (http://codingplayground.blogspot.com/2009/11/dbscan-clustering-algorithm.html). 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
ne.push_back(n1);
//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

aonghus

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?