MICROSOFT PLACEMENT PAPER 7

Algorithms and Programming
1. Given a rectangular (cuboidal for the puritans) cake with a rectangular piece removed (any size or orientation), how would you cut the remainder of the cake into two equal halves with one straight cut of a knife ?
2. You're given an array containing both positive and negative integers and required to find the sub-array with the largest sum (O(N) a la KBL). Write a routine in C for the above.
3. Given an array of size N in which every number is between 1 and N, determine if there are any duplicates in it. You are allowed to destroy the array if you like. [ I ended up giving about 4 or 5 different solutions for this, each supposedly better than the others ].
4. Write a routine to draw a circle (x ** 2 + y ** 2 = r ** 2) without making use of any floating point computations at all. [ This one had me stuck for quite some time and I first gave a solution that did have floating point computations ].
5. Given only putchar (no sprintf, itoa, etc.) write a routine putlong that prints out an unsigned long in decimal. [ I gave the obvious solution of taking % 10 and / 10, which gives us the decimal value in reverse order. This requires an array since we need to print it out in the correct order. The interviewer wasn't too pleased and asked me to give a solution which didn't need the array ]. 6. Give a one-line C expression to test whether a number is a power of 2. [No loops allowed - it's a simple test.]
7. Given an array of characters which form a sentence of words, give an efficient algorithm to reverse the order of the words (not characters) in it.
8. How many points are there on the globe where by walking one mile south, one mile east and one mile north you reach the place where you started.
9. Give a very good method to count the number of ones in a "n" (e.g. 32) bit number. ANS. Given below are simple solutions, find a solution that does it in log (n) steps.