Add Numbers

Problem Statement:
         Add two given numbers without '+' operator.

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Solution:
      We will be adding two given numbers using 'AND' and 'XOR' logical operators.

Fig: Half Adder , S: Sum and C: Carry

Sum of two number can be achieved with Half adder, if carry is greater than 0 , then it the process is repeated again. This is half adder implementation.

and as per full adder implementation :
   Sum = 2*C + S

Below are the different ways of getting the sum using XOR and AND logical operators.

Method 1 : 

int add(int a, int b) {
  while (b != 0) {
   int carry = a & b;
   a = a ^ b;
   b = carry << 1;
  }
  return a;
 }

Method 2:

 int add(int a, int b) {
  if (b == 0)
   return a;
  else
   return add2(a ^ b, (a & b) << 1);
 }

Method 3:

  int add(int a,int b){
  int carry= a & b;
  int sum= a ^ b;
  
  carry = 2* carry;
  
  sum = sum ^ carry;
  
  return sum;
 }

Method 4:

 int add(int a,int b){
  return ( 2*( a & b) ) ^ (a ^ b);
 }

Please post your comment and suggestions.
Happy Coding !! :)


References: 
Wikipedia

TV remote

Problem Statement: 

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Download Solution

Gaurav has fractured his leg in a bicycle accident.He keeps himself busy by watching television on his Tata Sky DTH. While watching the television, one day he decided to play a small game, where
he has to identify the minimum number of clicks required to surf a given set of channels in a

sequence.
WAP with given instructions:

Instructions

There are 13 buttons on his remote: 10 buttons for the numbers (0-9), an "Up Channel" button,
a "Down Channel" button, and a "Back" button:

● The number buttons allow you to jump directly to a specific channel. (Ex: to go to
channel 63 by typing “6”, “3”.)
● The "Up Channel" button increments the current channel to the next higher viewable
channel, unless the current channel is the highest viewable channel, in which case it
rolls over to the lowest viewable channel.
● The "Down Channel" button decrements to the next lower viewable channel, unless the
current channel is the lowest viewable channel, in which case it rolls over to the highest
viewable channel.
● The "Back" button reverts to whatever channel was on the television before the current
channel. (Ex: If channel 1 is viewed, then channel 100, then when Back is pressed, the
television will go to channel 1.)

Gaurav can get from one channel to the next in one of the two ways:
● Clicking any combination of "Up Channel", "Down Channel", and "Back" buttons.
● Keying in the numbers to the channel. Gaurav will never combine "Back" and number
buttons when moving from one channel to the next.

Gaurav’s parents have set some parental control on some channels on Gaurav's television.
These channels are not viewable, so they are skipped by the "Up Channel" and "Down
Channel" buttons.

Given a list of channels to view, the lowest channel, the highest channel, and a list of blocked
channels, your program should return the minimum number of clicks necessary to get
through all the shows that Gaurav would like to watch.

Constraints 

● The sequence that Gaurav must view contains between 1 and 50 elements, inclusive. All 

channels in this sequence are not in the blocked list and are between lowest channel 

and highest channel, inclusive. 

Pattern Matching: Rabin Karp

Problem Statement:
     Implement Rabin Karp hashing based Pattern-Matching Algorithm.

Example:
         Text (T):   rabing karp uses hashing technique
         Pattern (P) :   hashing

n : length of text
m : length of pattern

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Solution:
      Rabin Karp Algorithm finds a match of the pattern in the text by using hashing. Match is found only if hash of Pattern and hash of text of m characters gives same result.

Our objective is to reduce complexity from O(m x n ) as was in case of Brute force. We will have to desigyn a hash function which take O(1) complexity for finding hash of the pattern.

We will consider Horner's rule to calculate the hash of the pattern and hash of text of 'm' length.

Let us denote pattern as polynomial

here we will call 'x' as radix  , and above polynomial can also be represented as 

So this was about calculating hash by iterative method using the simplified equation.

Now, 

The pattern 'P' will match Text 'T' iff  T[i , i+1 , .....i+m-1] = P [0,1,......, m-1 ] 

ti : represents the hash value from T[i , .....i+m-1]

and ti+1 : represents the hash value from T[i+1 , .....i+m-1 , i+m]

Lets consider a Text containing all numbers as characters , i.e. Character set is {1,2,3,4,5,6,7,8,9,0} and

    lets say radix = 10, therefore calculating the numerical value of  "35678"  which will be 35,678.

Therefore,  p = P[m-1] + 10 { P[m-2] +  10 { P[m-3]  + 10 { ......  + 10 { P[1] + 10 * P[0]  } } } }

for  "35678" 

    

   p  = 8 + 7*10 + 6*102 + 5*103 + 3 *104

       = 8 + 10 { 7 + 10 { 6 + 10 { 5 +  10 {3 + 10 * 0} } } } 

we assume that to calculate this hash takes O(1) complexity , assume if ti is the hash code value of Text Window does not match with pattern P, we will have to calculate T(i +1 ) next , here we can leverage ti to calculate ti+1.

ti = T[i+m-1] + 10 { T[i+m-2] +  10 { T[i+m-3]  +10 { ......  + 10 { T[i+1] + 10 * T[i]  } } } }

Now, 

ti+1  =  10 (ti – 10m-1 T[i]) + T[i+m]

N.B.: 10m-1 value can also be pre-computed. 

Now consider 35678 does not match and next digit to be considered is 4, then 

• Remove Most Significant digit 35678 - 3 * 10000 = 5678
• Multiply above value by 10 and add 4 ,  5678*10 + 4 = 56784

Below is the implementation:

/**
 * Rabin Karp uses hashing technique to search for Strings 
 * @author PRATEEK Rathore
 */
public class RabinKarp {
 
 //Contant prime number
 private static final int CONSTANT_PRIME = 101;
 //Hash Value of the pattern which will remain constant through out the problem
 private long pathash;
 private int radix;
 //Input pattern
 private String pat;
 //Pattern Length
 private int patLen;
 
 //Its the place value of Most Significant bit
 private long RM1;

 //Preprocessing of pattern in the constructor
 public RabinKarp( String pat) {
  radix = 256;
  patLen = pat.length();
  this.pat = pat;

  RM1 = 1;
  for (int i = 1; i < patLen; i++)
   RM1 = (radix * RM1) % CONSTANT_PRIME;

  //return hash value of pattern
  pathash = hash(pat, patLen);
 }

 //Return hash value of given string from 0 to the input length
 private long hash(String pat, int len) {
  long h = 0;
  for (int j = 0; j < len; j++)
   h = (radix * h + pat.charAt(j)) % CONSTANT_PRIME;
  return h;
 }

 /**
  * Sub-routine called when hash-function is equal,
  * character by character comparison is done.
  */
 private boolean doesMatch(String text, int currIndex) {
  for (int j = 0; j < patLen; j++)
   if (pat.charAt(j) != text.charAt(currIndex + 1 + j))
    return false;
  return true;
 }

 /**
  * Search for the pattern in the input string
  * @param text
  * @return: index where pattern is found in text
  */
 public int search(String text) {
  int textLen = text.length();
  if (patLen > textLen)
   return -1;

  long textHash = hash(text, patLen);

  for (int i = 0; i < textLen - patLen; i++) {
   textHash = radix * (textHash - RM1 * text.charAt(i))% CONSTANT_PRIME   +   
       CONSTANT_PRIME + text.charAt(i + patLen) % CONSTANT_PRIME;
   if (textHash == pathash && doesMatch(text, i))
    return i;
  }
  return -1;
 }

 public static void main(String[] args) {

  String pat = "prateek";
  String txt = "Welcome prateek to Bangalore";
  
  RabinKarp rabin = new RabinKarp( pat);
  int index= rabin.search(txt);
  System.out.println("Text found at "+ index + ": " + txt.substring(index, index+ pat.length()+1));
 }
}

Time Complexity: 
Worst Case is : O(m ( n- m+1 ))
Best and Average Case is : O (m + n )

References:
1. http://en.wikipedia.org/wiki/Horner's_method

Please comment and post your suggestions.
Happy Coding !! :)