Given a graph (any type - Directed acyclic graph or undirected graphs with loops), find a minimal set of vertices which affect all the edges of the graph.
An edge is affected if the edge is either originating or terminating from that vertex.
given a triangle ABC, how would you use only a compass and a straight edge to find a point P such that triangles ABP, ACP & BCP have equal perimeters?(Assume that ABC is constructed so that a solution does exist)
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Say we have a data structure as follows:
enum {RED,BLUE,GREEN};
struct Ball
{
/*...*/
int color;
};
int ColorOfBall(Ball b)
{
return b.color;
}
Ball arr[SIZE];
The array arr consists of balls of with one of the three colours
(Red,Green,Blue). Now we need to sort the array in such a way that all
the Red coloured balls come first, followed by blue and then green.
The restriction is that call to function ColorOfBall is a very costly
operation. You have to use it as less as possible. (In other words we
would be looking for the solution with least number of calls to the
function ColorOfBall.)
There are 25 horses and 5 lanes. You have no idea about which horse is better than other. Find in minimum possible races, the first three fastest running horses.
Mr. X meet Mr. Y during an early morning walk.
Mr Y asks the age of Mr. X\'s children and Mr. X is a math professor so gives Mr Y a problem to solve.
Mr X says
-> I have 3 children
-> The product of their ages is 36
-> The sum of their age is equal to the number of houses in my street.
-> And my first daughter has blue eyes.
Using these clues Mr Y was able to say the ages of the 3 children.
In Russia you get into a bus, take a ticket, and sometimes say : Wow, a lucky number! Bus tickets are numbered by 6-digit numbers, and a lucky ticket has the sum of 3 first digits being equal to the sum of 3 last digits. When we were in high school (guys from math school No. 7 might remember that ) we had to write a code that prints out all the lucky tickets\' numbers; at least I did, to show my loyalty to the progammers\' clan. Now, if you add up all the lucky tickets\' numbers you will find out that 13 (the most unlucky number) is a divisor of the result. Can you prove it (without writing a code)?
A bank has a collection of n bank cards that they€™ve confiscated, suspecting them of being used in a fraud. Each bank card corresponds to a unique account in the bank. Each account can have many cards corresponding to it, and we€™ll say that two bank cards are equivalent if they correspond to the same account. The only way to say 2 cards are equivalent is by using a high-tech €œequivalence-tester€ that takes in 2 cards, and after performing some computations, determines whether they are equivalent.
Their question is the following: among the collection of n cards, is there a set of more than n/2 of them that are all equivalent to one another? Assume that the only feasible operations you can do with the cards are to pick two of them and plug them in to the equivalence tester. Answer in O(n)
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