Find if there is only one bit set in a number

In the bit representation of a number, find if there is exactly one bit that is set.

e.g. your approach should say true for the following numbers :
1,2,4,8,16
and false for the following numbers :
3,5,7,10

[PS] Catch the Fox

Consider five holes in a line. One of them is occupied by a fox. Each night, the fox moves to a neighboring hole, either to the left or to the right. Each morning, you get to inspect a hole of your choice. What strategy would ensure that the fox is eventually caught?

Algorithms from "100 Interview Questions for Software Developers" : Part 1

Q1. How do you find out if a number is a power of 2?
Q2. And how do you know if it is an odd number?

Source : Algorithms from 100 Interview Questions for Software Developers

All purpose problem solving algorithm

LOL - Only if he had put in all that logic into solving the real problem ;-)

[ALGO] Water jugs problem

Suppose that you are given 'n' red and 'n' blue water jugs, all of different shapes and sizes. All red jugs hold different amounts of water, as do the blue ones. For every red jug, there is a blue jug that holds the same amount of water & vice versa.

How can you find the grouping of the jugs into pairs of red & blue jugs that hold the same amount of water, in the minimum number of comparisons.

Operations allowed

1. always compare between a red and a blue jar (no two reds, no two blues)
2. fill water in red / blue jug
3. pour from red jug to blue (& vice versa). This will help compare the capacity of the jugs.
   

Source : Introduction to Algorithms (by Cormen..., Problem 8-4)

Find if number occurs exactly n/2 times in an array

You have an array of number/characters. If there is a number which occurs exactly n/2 times.
and all other elements in the set/array are distinct, can you find the the repeating number?

Expected time complexity : O(n)
Expected space complexity : O(1)

What if the other members are not distinct?
Can we solve the problem in O(log n) time complexity? (distinct and / or not distinct)

Source : http://inder-gnu.blogspot.com/2009/08/number-occuring-n2-times.html

Dividing array into groups

Divide a list of numbers into groups of consecutive numbers but their original order should be preserved.

Example:
<8,2,4,7,1,0,3,6>

should be divided into two groups like this:
<2,4,1,0,3> <8,7,6>

Source : http://discuss.techinterview.org/default.asp?interview.11.770712.8