• Given a number, describe an algorithm to find the next number which is prime.
• There are 8 stones which are similar except one which is heavier than the others. To find it, you are given a pan balance. What is the minimal number of weighing needed to find out the heaviest stone ?

Answer:
Divide the stones into sets like (3,3,2). Use pan to weigh (3,3).
If the pan is remains balanced, the heavier is in the remaining (2). use pan again to find which is heavy from (2). (Total pan use 2)

If the pan does not remain balanced when weighing (3,3), pick the set of stones that outweigh other. Divide it into (1,1,1). use pan to weigh first two. It it remains balanced, the remaining stone is the heavier, otherwise the one outweighing other is heavier(total pan use 2)

[These questions from 'Taher']

• Order the functions in order of their asymptotic performance

  * 2^n
* n^Googol ( 10^100)
* n!
* n^n

Answer: n^(whatever constant), 2^n, n! (==> n^n / e^n ), n^n

• what is the best and worst performance time for a hash tree and binary search tree?

Answer:
Best is O(c), worst is O(log n)

• Questions regarding a string Class

  * What do you need when you instantiate a string ( i said a byte array and possibly the length) ?
* What is the best and worst time for the operation 'equals'
* How do you spedup the 'equals' operation (i said used  hash  MD5 for example)
This still has some problem ( a hash can be the same for unequal strings)
-> Use Boyer–Moore string search algorithm => O(n)

• Trade offs between a multi threaded and single threaded implementation ?
• N threads .. n resources .. what protocol do you use to ensure no deadlocks occur?
• There are a set of 'n' integers. Describe an algorithm to find for each of all its subsets of n-1 integers the product of its integers.

For example, let consider (6, 3, 1, 2). We need to find these products :

• • 6 * 3 * 1 = 18
  • 6 * 3 * 2 = 36
  • 3 * 1 * 2 = 6
  • 6 * 1 * 2 = 12

last one is simple

int mul = 1;
for i = 1 to N
mul *=a[i];

for i= 1 to N
a[i] = mul/a[i];

(I got this question, your answer is not correct)
First of all if a[i]=0 you get an exception, the guy wanted me to use dynamic programming to solve this.

Here's the dynamic programming solution:
You want to build a table where x[i,j] holds the product of (ni .. nj). If you had such a table, you could just output

for (int i = 1; i <= n; i++)
{

  if (i == 1)
print x[2,n];
else if (i == n)
print x[1,n-1];
else 
print x[1,i-1] * x[i+1,n];

}

To build the table, start along the diagonal (x[i,i] = ni). Then do successive diagonals from previous ones (x[j,k] = x[j-1,k] * x[j,k+1]).

• 1. Describe Sorting algorithms and their complexity - Quick sort, Insertion Sort, Merge Sort
• 2. If you had a million integers how would you sort them and how much memeory would that consume?

Binary tree - requires 1,000,000 integers x 4 bytes = 4 MB + left pointer and right pointer = 12 MB
Insertion sort - can be done in under 4 MB

• 3.Describe an alogrithm to find out if an integer is a square? e.g. 16 is, 15 isn't

a) simple answer - start at 2 and divide the integer by each successive value. If it divides evenly before you reach half way then it is.
b) complex answer after much leading - Do the bitwise AND of n and (n-1). If it is zero then it is a square (I think this is wrong. This actually tests whether n is a power of 2).
No, it almost tests whether n is power of 2. It falsely proclaims 0 to be a power of 2. More info: http://graphics.stanford.edu/~seander/bithacks.html#DetermineIfPowerOf2

C)

i=2;
while(!NO)
{
if((i*i)==Number)
{
NO;
return True;}
if((i*i)>Number)
{
NO;          
return false;} 
i++;
}

• 4. How would you determine if adwords was up and running and serving contextual content ?

5428907816463810488188

Here are some questions I got on my first interview with Google (slightly altered for NDA reasons).

• 1 Suppose you have an NxN matrix of positive and negative integers. Write some code that finds the sub-matrix with the maximum sum of its elements.

• 2 Write some code to reverse a string.

• 3 Implement division (without using the divide operator, obviously).

• 4 Write some code to find all permutations of the letters in a particular string.

• 5 You have to get from point A to point B. You don’t know if you can get there. What would you do?

• 6 What method would you use to look up a word in a dictionary?

• 7 Imagine you have a closet full of shirts. It’s very hard to find a shirt. So what can you

do to organize your shirts for easy retrieval?

• 8 You have eight balls all of the same size. 7 of them weigh the same, and one of them weighs slightly more. How can you fine the ball that is heavier by using a balance and only two weighings?

Phone interview

1. Describe the data structure that is used to manage memory. (stack)

2. whats the difference between local and global variables?

3. If you have 1 million integers, how would you sort them efficiently? (modify a specific sorting algorithm to solve this)

4. In Java, what is the difference between static, final, and const. (if you dont know java they will ask something similar for C or C++).

5. Talk about your class projects or work projects (pick something easy)… then describe how you could make them more efficient (in terms of algorithms).

In person interview

1. In Java, what is the difference between final, finally, and finalize?

2. What is multithreaded programming? What is a deadlock?

3. Write a function (with helper functions if needed) called toExcel that takes an excel column value (A,B,C,D…AA,AB,AC,… AAA..) and returns a corresponding integer value (A=1,B=2,… AA=26..).

4. You have a stream of infinite queries (ie: real time Google search queries that people are entering). Describe how you would go about finding a good estimate of 1000 samples from this never ending set of data and then write code for it.

5. Tree search algorithms. Write BFS and DFS code, explain run time and space requirements. Modify the code to handle trees with weighted edges and loops with BFS and DFS, make the code print out path to goal state.

6. You are given a list of numbers. When you reach the end of the list you will come back to the beginning of the list (a circular list). Write the most efficient algorithm to find the minimum # in this list. Find any given # in the list. The numbers in the list are always increasing but you don’t know where the circular list begins, ie: 38, 40, 55, 89, 6, 13, 20, 23, 36.

Here is a bunch more:

1. How many golf balls can fit in a school bus? This is a Fermi question.
2. You are shrunk to the height of a nickel and your mass is proportionally reduced so as to maintain your original density. You are then thrown into an empty glass blender. The blades will start moving in 60 seconds. What do you do?
3. How much should you charge to wash all the windows in Seattle?
4. How would you find out if a machine’s stack grows up or down in memory?
5. Explain a database in three sentences to your eight-year-old nephew.
6. How many times a day does a clock’s hands overlap?
7. You have to get from point A to point B. You don’t know if you can get there. What would you do?
8. Imagine you have a closet full of shirts. It’s very hard to find a shirt. So what can you do to organize your shirts for easy retrieval?
9. Every man in a village of 100 married couples has cheated on his wife. Every wife in the village instantly knows when a man other than her husband has cheated, but does not know when her own husband has. The village has a law that does not allow for adultery. Any wife who can prove that her husband is unfaithful must kill him that very day. The women of the village would never disobey this law. One day, the queen of the village visits and announces that at least one husband has been unfaithful. What happens?
10. In a country in which people only want boys, every family continues to have children until they have a boy. if they have a girl, they have another child. if they have a boy, they stop. what is the proportion of boys to girls in the country?
11. If the probability of observing a car in 30 minutes on a highway is 0.95, what is the probability of observing a car in 10 minutes (assuming constant default probability)?
12. If you look at a clock and the time is 3:15, what is the angle between the hour and the minute hands? (The answer to this is not zero!)
13. Four people need to cross a rickety rope bridge to get back to their camp at night. Unfortunately, they only have one flashlight and it only has enough light left for seventeen minutes. The bridge is too dangerous to cross without a flashlight, and it’s only strong enough to support two people at any given time. Each of the campers walks at a different speed. One can cross the bridge in 1 minute, another in 2 minutes, the third in 5 minutes, and the slow poke takes 10 minutes to cross. How do the campers make it across in 17 minutes?
14. 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?
15. How many piano tuners are there in the entire world?
16. You have eight balls all of the same size. 7 of them weigh the same, and one of them weighs slightly more. How can you find the ball that is heavier by using a balance and only two weighings?
17. You have five pirates, ranked from 5 to 1 in descending order. The top pirate has the right to propose how 100 gold coins should be divided among them. But the others get to vote on his plan, and if fewer than half agree with him, he gets killed. How should he allocate the gold in order to maximize his share but live to enjoy it? (Hint: One pirate ends up with 98 percent of the gold.)