Google Wants Us to Find an Element thats greater then A, in Unsorted Element....Do You Think its Possible or Just They Wants to Test if Possible or Not

First greater number in an array. Given a large array of positive
integers, for an arbitrary integer A, we want to know the first integer in
the array which is greater than or equal A . O(logn) solution required
ex [2, 10,5,6,80]

input : 6 output : 10
input :20 output : 80

Convert integers to roman numbers

Question: write an algorithm to convert an integer into roman number. For example, 1 -> I, 2 -> II, or 4 -> IV.

Solution: in order to solve this problem, we must know the rules of writing roman numerals. For example, I is 1 and V is 5 but IV is not 6 but 4 (5 -1). Moreover, there is no 0 number in roman numeral system. Here is the link to an articleabout roman numerals if you are unfamiliar with the system.

As you may notice, the roman numeral system consists of several fundamental and unique numbers. They are used in conjunction with rules to create other numbers. Therefore, we just have to cache the unique numbers and apply the rules in order to generate any roman number we want. Let's take a look at the implementation below in C++

#include<iostream>
#include<map>
#include<string>
using namespace std;

string int2RomanNum(int intVal)
{
   if (intVal <= 0)
   {
      cout << "Roman numbers don't support 0 or negative! Return NULL" << endl;
      return ""; 
   }

   //build hash table of unique values 
   map valueMap;

   valueMap[1] = "I";
   valueMap[4] = "IV";
   valueMap[5] = "V";
   valueMap[9] = "IX";
   valueMap[10] = "X";
   valueMap[40] = "XL";
   valueMap[50] = "L";
   valueMap[90] = "XC";
   valueMap[100] = "C";
   valueMap[400] = "CD";
   valueMap[500] = "D";
   valueMap[900] = "CM";
   valueMap[1000] = "M";

   //the roman value
   string romanResult = "";

   //traverse the list in reverse order 
   map::reverse_iterator it;
   
   for (it = valueMap.rbegin(); it != valueMap.rend(); it++)
   {
      //if current number is greater than current key in list
      //add the value corresponded with key to result
      //then subtract the equivalent int value from current number
      while (intVal >= it->first)
      {
         romanResult = romanResult + it->second;
         intVal = intVal - it->first;
      }
   }

   return romanResult;
}

 

Explanation: our method accepts an integer as parameter and return a string that contains the roman number equivalent to that integer.

1. First we check the parameter to see if it is equal or less than 0. Because there is no 0 or negative roman numbers, we return an empty string after printing out the warning.
2. Next, we build a hash table of unique roman numbers which are then combined to create other numbers.
3. The heart of this method consists of two loops. The "for" loop runs through the hash table from bottom to top (largest number to smallest number). At each number in the hash table, we run the "while" loop to construct the roman number. This while loop will run until the integer is less than the current number in the hash table. And for every iteration in the while loop we add the current roman number to the returned string. For example, if our integer is 35, at the 10 or X position in the hash table, the while loop will kick in and add XXX into our string. And then the for loop continues at the 5 or V position, letting the while loop add V into our string.

Example: let's say we want to convert the integer 430 into its equivalent roman number. Here is how the method runs:

1. First "for" loop's iteration, intVal = 430 and it->first = 1000. No while loop because intVal is less than it->first.
2. Second iteration, intVal = 430 and it->first = 900. No while loop.
3. Third iteration, intVal = 430 and it->first = 500. No while loop.
4. Fourth iteration, intVal = 430 and it->first = 400. Enter while loop:romanResult = CD and intVal = 30. Because intVal is less than it->first after the first "while" iteration, the while loop exits.
5. Fifth iteration, intVal = 30 and it->first = 100. No while loop.
6. Sixth iteration, intVal = 30 and it->first = 90. No while loop.
7. Seventh iteration, intVal = 30 and it->first = 50. No while loop.
8. Ninth iteration, intVal = 30 and it->first = 40. No while loop.
9. Tenth iteration, intVal = 30 and it->first = 10. Enter while loop: 1) intVal = 20 and romanResult = CDX, 2) intVal = 10 and romanResult = CDXX, and 3) intVal = 0 and romanResult = CDXXX. The while loop exits after that because intVal is less than it->first.
10. Nothing happens in the last four iterations because intVal is 0. Thus, the final result is romanResult = CDXXX

Thank you for reading and until next time :)

Resilient Binary Search-search an element in O(log n) time in the perturbed array?

You are about to search for an element in a sorted array A[1..n] using binary search when the array suddenly gets perturbed. By perturbed, we mean a number in ith position in the array can now be either in i, i-1 or i+1th position; but all the numbers are still in A[1..n]. Can you still search an element in O(log n) time in the perturbed array?

Valid Strings-erase the smallest possible number of characters such that the remaining string after the erasures is valid

A string over the characters (, [, ] and ) is said to be valid if one can reduce the string to the null string by repeatedly erasing two consecutive characters of the form () or []. For example, the string [([])[]] is valid but neither ([)] nor ([ is valid.
Give a polynomial time algorithm to solve the following problem: Given a string, erase the smallest possible number of characters such that the remaining string after the erasures is valid. For example, given the string [(], we can erase ( to get [].

Nab the thief-prove that Alice can win in at most 3n moves.

Alice and Bob play the following game: Two cops(c) and a thief(t) are positioned at some vertices of an nxn grid. Alice controls the two cops and Bob controls the thief. The players take turns to play, starting with Alice. In one turn, Alice can move each cop to a neighboring vertex, i.e. left, right, up or down or keep the cop in the same place. In his turn, Bob can move the thief similarly.
If the thief and a cop end up in the same vertex, Alice wins.
For any arbitrary positioning of the two cops and the thief, prove that Alice can win in at most 3n moves.

Estimating Distance-Find maximum distance between any pair of points in a plane

A set of n points are on a plane. Let d denote the maximum distance between any pair of points. Design a linear time algorithm to guess the value of d. Your guess is good if it lies between 0.7d and d. also proove correctness of algorithm.

Beaded Necklace-Find a sequence of such operations with minimum total cost for a given initial distribution of beads.

You are given a circular necklace containing n beads. Each bead maybe black or white. You have to rearrange the beads so that beads of the same color occur consecutively.

The only operation allowed is to cut the necklace at any point, remove some number of beads from both ends and put them back in any order, and join the cut ends. The cost of this operation is the number of beads removed. Any number of such operations can be used. You have to find a sequence of such operations with minimum total cost for a given initial distribution of beads.

For example, if the initial string is wbwbwb, this can be done by a single operation of cost 4, or two operations of cost 2 as shown.

Describe a polynomial-time algorithm for this problem; with short proof of correctness. You get points only if you match (or better) the judge solution's time complexity.

Save Me Please, Doctor!

Mr. Bean drinks from a water bottle that he carried for a long time without re lling, and
the stale water has resulted in him su ering from mild dysentery. He goes to a nearby nursing
home and gets diagnosed with Amoebiasis. The doctor identi es the pathogen to be a partic-ular kind of amoeba that has two variants, namely Asperdabrum (a) and Bostonostrum (b).
Each amoeba reproduces every hour by splitting into two, a !ab, and b !ba, and they stick
together in a chain in that particular sequence. At every step of reproduction, all the present
amoeba undergo binary ssion. For e.g. starting with type a, after 1st step the chain is ab,
after 2nd step the chain is abba, after the 3rd step the chain is abbabaab and so on. Mr.Bean
was infected n hours ago by a single amoeba and the doctor needs to know the type of the kth amoeba in the chain present now to be able zo nd a cure. Help the doctor cure him.

Input Format:
First line contains the number of test cases T. For each test case, there will be a single line of
input that starts with a character denoting the type of amoeba, , that infected him initially (a
or b) followed by two integers, n - the number of hours that have passed since he was infected,
and k - the position at which the doctor needs to know the type of amoeba.
Limits: 1<= T<=1000000, 1<= N<=4100, 1<=K<=2^N
.
Moreover, for the rst test le you can assume N, K lie within integer range (32 bits).

Output Format:
For each test case, output on a separate line the type of the kth amoeba in the current chain.

Sample Input:
2
a 3 3
b 4 6
Sample Output:
b
b

Source BITWise IITKGP,

Place N number from 1 to N, in 2N positions in such a way so that there are Exactly “n” number of cells between two placed locations of number “n”

Write a program to display numbers placed in this way.

Example:-

(1) One of the possible placement for 7 numbers in 14 positions is :

5 7 2 3 6 2 5 3 4 7 1 6 1 4

write an algorithm that outputs each point along with the three other points that are closest to it.

You are given a list of points in the plane, write a program that
outputs each point along with the three other points that are closest
to it. These three points ordered by distance.
The order is less then O(n^2) .

For example, given a set of points where each line is of the form: ID
x-coordinate y-coordinate


1  0.0      0.0
2  10.1     -10.1
3  -12.2    12.2
4  38.3     38.3
5  79.99    179.99



Your program should output:


1 2,3,4
2 1,3,4
3 1,2,4
4 1,2,3
5 4,3,1