Given n nodes,
1. generate all possible directed subgraphs.
2. generate all possible undirected subgraphs.
Easier version:
Given n nodes,
1. generate all possible directed subgraphs of n nodes,
2. generate all possible undirected subgraphs of n nodes,
Jun 16, 2008
Generating Graphs
Jun 14, 2008
PubTrivia - a pub where algos are served alongwith drinks!
You and your friends have gotten together for a Trivia night at a local pub.There are N questions asked during the night.Each question is worth a number of points; the i-th element of the points array corresponds to the score received by you if you correctly answer the i-th question, but you lose that many points if you answer that incorrectly. The questions are given in the order specified and you must answer each question before the next is asked. In addition, after each correct answer you will receive a token. If you then have tokensNeeded tokens, the pub will immediately take all of your tokens and award you additional bonus points. However, if you get the question wrong, the pub will take away all of your tokens without giving you any bonuses. The element i of the bonuses array corresponds to the bonus you receive if you win the bonus on question i.
Note that it is possible to win multiple bonuses during the game.
You know the answer to all the questions and want to maximize the number of points you receive.
Give an algorithm to obtain the maximum points that you can receive if you correctly choose which questions to answer.
Inputs :
N
tokensNeeded
p - array of points
b - array of bonuses
May 21, 2008
Calendar Cubes
A corporate businessman has two cubes on his office desk. Every day he arranges both cubes so that the front faces show the current day of the month. What numbers are on the faces of the cubes to allow this?
I have come up with a solution which I would call "sly" and really "unfair"!
May 7, 2008
Difference between Singleton and Static implementations
(1) Static implementations cannot be extended(only static fields and methods can be extended) whereas Singleton implementations can be extended and its methods can be overridden.
(2) Static implementations cannot extend other class's instance fields/methods while Singleton implementations can.
(3) Static implementations must be initialized at the class loading time however Singleton implementations can be lazy initialized or asynchronously initialized.
(4) Static implementations cannot be initialized with a STATE (parameter), whereas Singleton implementations can be.
(5) Static implementations can still have instances (unwanted instances) whereas Singleton implementations prevents it.
Apr 16, 2008
Exchange problem
Its new year time and your company has sent T-Shirts of varying sizes from HQ (read US). The problem is that the sizes in US and the sizes in India don't really match. So a guy with L size in India would like to settle for M size in US, one with XXL in India would like to go for XL and so on. Employees in India are bugged up and want to exchange it with appropriate sized T-Shirt. Now that the management didn't take care of it before sending the T-Shirts to India, you have been assigned by the Indian management to arrange an exchange between the employees. How would you go about it? Also describe your algorithm. If all this information is stored in the database, write a query that would do the job.
Random Number Generation
Given a function random(0,1) which randomly generates 0 or 1 with equal probabilities, extend its functionality to generate random numbers for an interval [a,b], i.e. implement random(a,b), for all 0 =< a < b. Prove that the strategy is uniformly random or would you like to put some conditions on a and b?
Another version: Given a random function random() which generates 0,1 but with uneven probabilities, create a random function newrandom() which generates 0,1 with even probabilities. Uneven probabilities mean if probability of getting 0 from random is p, that of 1 is (1-p) but p!=(1-p)!=1/2
Apr 15, 2008
array question again
Suppose you are having an array of n integer. All the elements in the array are unique
except one element. That one special element in array is repeating in array in order of power two(means even repetition)
example - 1 2 3 4 5 6 5 7 8
all element in this array are unique except 5.. and 5 is repeating 2 times (power of 2).
we need an algo to find this special element in array