Princeton Algorithms: Part 2 [week 5: Substring Search]

Exercise

Question Explanation

The correct answer is: 1 2 2 4 5 2 7 5


Here is the DFA:

   0  1  2  3  4  5  6  7 
   ----------------------
A  1  2  2  4  5  2  7  5 
B  0  0  3  0  0  6  0  0 
C  0  0  0  0  0  0  0  8 

Question Explanation

The correct answer is: T Y T T H I N H


Here is a trace:

     i  j i+j   0  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 
    ----------------------------------------------------------------------------------------------------
                P  A  N  E  W  A  T  Y  O  U  R  F  E  E  T  T  H  I  N  K  N  O  W  A  N  D  T  H  E  N  
     0  6   6   O  W  A  N  D  T  H  
     1  6   7      O  W  A  N  D  T  H  
     8  6  14                           O  W  A  N  D  T  H  
     9  6  15                              O  W  A  N  D  T  H  
    10  4  14                                 O  W  A  N  D  T  H  
    11  6  17                                    O  W  A  N  D  T  H  
    18  6  24                                                         O  W  A  N  D  T  H  
    21  0  21                                                                  O  W  A  N  D  T  H  

Question Explanation

The correct answer is: 4


hash(3237816904) = 3237816904 (mod 53)
                 = 52

hash(1000000000) = 1000000000 (mod 53)
                 = 28

2378169046 = (3237816904 - 3*1000000000) * 10 + 6
hash(2378169046) = (3237816904 - 3*1000000000) * 10 + 6 (mod 53)
hash(2378169046) = (52 - 3*28) * 10 + 6  (mod 53)
                 = -49 (mod 53)
                 = -49 + 53 (mod 53)
                 = 4

Recall that the Java operator % is remainder, and not modulus. When taking
a dividend mod Q, the result is a value between 0 and Q-1; with remainder,
the result can be a negative value if the dividend is negative.

Interview Questions