• Placement Questions

Placement Papers with Solutions

(#M40059690) MICROSOFT QUESTION Algebra Keep an EYE

If m^2 + m^-2=23
then find
m^3 + m^-3

Asked In Microsoft Pawan Pandey (10 years ago)

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(#M40038199) DATA STRUCTURE QUESTION Palindromic Prime Keep an EYE

A palindrome is a string that reads the same forward and backward. An integer is called prime-palindromic if it is possible to construct a palindrome by concatenating all of its prime factors (without leading zeros). Each prime factor should be used as many times as its power in factorization. 48 is prime-palindromic because its prime factors are 2, 2, 2, 2, 3 (2 should be used 4 times, 3 should be used once) and we can obtain the palindrome 22322. 2261 is prime-palindromic also because its prime factors are 7, 17, and 19, which can be concatenated to form the palindrome 71917 33 is also not prime-palindromic (its prime factors are 3 and 11). Write a program which takes a number from user and then calls a function to extract the prime factors in an array(declare an array of max size 100 and then initialize them to some dummy value).Now write a recursive function to form all possible permutations from these factors and then if any of these permutations is a palindrome then your original number is prime palindromic. ((write recursive function to check palindromes and get permutations)

Asked In DATA STRUCTURE Pawan Pandey (11 years ago)

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(#M40038191) C QUESTION Rabbit and Carrot Keep an EYE

A rabbit walk is defined by a sequence of jumps which starts from a
location and returns back to the starting location. We can repesent such
a Rabbit walk by an array A of n numbers, where A[i] denotes the next
array index to which the rabbit should jumps from the location i.
For example, the sequence: 2 3 4 5 0 1 indicates that the Rabbit follows
the jump sequence: 0->2, 2->4, 4->0 and stops.

Your also given another array B of N numbers, such that
B[i] denotes the number of carrots available at location i.
Your task is to compute the number of carrots that a rabbit can collect
when it makes rabbit walk(s) from various start position(s).
A sample input is provided for more clarification(s).

Input:
The first line will contain a single integer N which is the size of the
array (2<= N <= 10000).
The next line contains a series of N integers which define the array A.
The next line contains a series of N integers which define the array B.
You can be assured that all the calculations fit into a 32 bit signed
integer type(int in C).

The input is given such that, a rabbit walk will always exist with
start position as 0.

Output:
It should contain the number of carrots collected
when 0 is treated as the start location.

Sample Input:
6
2 2 2 2 -4 -4
2 3 6 3 0 1

Sample Output:
8

Asked In C Pawan Pandey (11 years ago)

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(#M40038182) OTHER QUESTION Physical Balance Keep an EYE

Your friend wants to set up a small scale industry which produces weights used in a
physical balance.

His customers are the shopkeepers located in his state. Each shopkeeper wants a set of
weighing objects using which he can produce all integer weights in range [1,n], where n may
vary for each shopkeeper. For a small grocery shop, n could be upto 50 Kg, and for a whole
sale shopkeeper n could be 1000 Kg. For a given n, a trivial solution is that the shopkeeper
keeps n weighing objects each of weight one kilogram. But it is very cumbersome to use and
manage so many weighing objects. So he wants the minimum number of weighing objects
using which he can weigh any object whose weight is in the range [1, n]. Such a set of
weighing objects is called a Min-weighing-objects(n) set. Such set need not be unique. For
example, {1, 3, 5} as well as {1, 2, 6} can serve to be a Min-weighing-objects(9) set.
Your friend wants to expand his business. So he wants to ensure that his customers get
full satisfaction. In particular, for a given n, he would like to present to the shopkeeper all
possible Min-weighing-objects(n) sets. The shopkeeper can place an order for the set of his
choice. Finally your friend delivers weights of that set to the shopkeeper. Your friend is
unable to come up with any solution to this problem. He approaches you with this problem.
Solve this problem. More formally, he wants you to write a program which for a positive
integer n, enumerates all Min-weighing-objects(n) sets.

Asked In Other Pawan Pandey (11 years ago)

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(#M40038181) C++ QUESTION Norvig Spellinbg Corrector Keep an EYE

What I wanted to do here is to develop, in less than a page of code, a toy spelling corrector that achieves 80 or 90% accuracy at a processing speed of at least 10 words per second.

So here, in 21 lines of Python 2.5 code, is the complete spelling corrector:

import re, collections

def words(text): return re.findall('[a-z]+', text.lower())

def train(features):
model = collections.defaultdict(lambda: 1)
for f in features:
model[f] += 1
return model

NWORDS = train(words(file('big.txt').read()))

alphabet = 'abcdefghijklmnopqrstuvwxyz'

def edits1(word):
splits = [(word[:i], word[i:]) for i in range(len(word) + 1)]
deletes = [a + b[1:] for a, b in splits if b]
transposes = [a + b[1] + b[0] + b[2:] for a, b in splits if len(b)>1]
replaces = [a + c + b[1:] for a, b in splits for c in alphabet if b]
inserts = [a + c + b for a, b in splits for c in alphabet]
return set(deletes + transposes + replaces + inserts)

def known_edits2(word):
return set(e2 for e1 in edits1(word) for e2 in edits1(e1) if e2 in NWORDS)

def known(words): return set(w for w in words if w in NWORDS)

def correct(word):
candidates = known([word]) or known(edits1(word)) or known_edits2(word) or [word]
return max(candidates, key=NWORDS.get)
The code defines the function correct, which takes a word as input and returns a likely correction of that word. For example:

>>> correct('speling')
'spelling'
>>> correct('korrecter')
'corrector'

Asked In C++ Pawan Pandey (11 years ago)

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