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1. Implement a hash table where collisions are resolved by linear probing. You will implement the methods

find, insert, and rehash for the class below. Your class will rehash when the load factor is greater or

equal to 0.5. The hash function, hf, will be created when you instantiate a member of this class. But

hf will returna positive integer whose range is much larger than the table size. The book says, “you will

need to perform a final mod operation internally after the” hash function.

template< class HashedObj >

class HashTable

{

public:

explicit HashTable( int size = 101 ):currentSize(0){ array.resize(size); }

std::hash

bool find( const HashedObj & x ) const;

void makeEmpty( );

bool insert( const HashedObj & x );

bool remove( const HashedObj & x);

enum EntryType { ACTIVE, EMPTY, DELETED };

private:

struct HashEntry

{

HashedObj element;

EntryType info;

HashEntry( const HashedObj & e = HashedObj(), EntryType i = EMPTY )

: element( e), info(i) {}

};

vector

int currentSize;

void rehash( );

};

∗

10% extra credit will be given if you turn this assignment in on Tuesday April 26, 2016 at 11:00 p.m.

1

2. Create an adjacency list for the graph of the NYC subway station. You will consider a subway station sa

adjacent to subway station sb if there is a subway train that goes from sa directly to sb without going

through any other stops, or you can transfer from sa to sb. You find what subway stations are adjacent

to other subway stations by using the information in the files transfers.txt and MTA train stop data.

The file transfers.txt is a bit confusing! Here are some of the entries:

from_stop_id,to_stop_id,transfer_type,min_transfer_time

101,101,2,180

103,103,2,180

104,104,2,180

106,106,2,180

107,107,2,180

108,108,2,180

109,109,2,180

110,110,2,180

111,111,2,180

112,112,2,180

112,A09,2,180

113,113,2,180

…

In the file transfers.txt, observe you can transfer from subway station 112 to subway station A09. Thus

A09 is adjacent to (a neighbor of ) 112. You will create an adjacency list as an unordered map>. In the next homework assignment, you will use this

adjacency list in the shortest path algorithm.

Written Part

1. Using big-oh notation, what is the worst case running time for your algorithm to create the adjacency

list?

2. First add 12, then 50, and finally 44, to this red-black tree (i.e. first insert 12 and perform any operations necessary (using only the algorithm presented in class) so the tree is again a red-black tree, then

insert 50 and perform any necessary operations (using only the algorithm presented in class) so the tree is

again a red-black tree, and then insert 44and perform any operations necessary (using only the algorithm

presented in class) so the tree is again a red-black tree.)

Show the following:

• Show the tree after inserting a value. If a violation occurred, state what the violation was (i.e. case

1, 2 or 3).

• If the tree is not a red-black tree, use the algorithm we used in class to turn it into a red-black tree.

Show each step.

22 b

17 b

14 r 18 r

30 b

2

3. Do not turn in. Please do this on your own. I will expect you to know how to do this for the exam.

You can check your solution at https://www.cs.usfca.edu/~galles/visualization/RedBlack.html.

Show the result of inserting (15, 4, 2, 8, 16, 9, 5, 10) into an initially empty red-black tree as

described in class. Include the color of each node. Show the tree before and after each violation, and state

which violation has occurred (i.e. case 1, case 2, or case 3).

4. Write the code needed to perform the method rightRotateRecolor for the RedBlackNode class. The

method has the following prototype:

template

void RedBlackTree

5. When inserting an item into a Red-Black tree, what is the maximum number of pointer changes needed

to adjust the tree? Explain your answer.

6. If your hash table size, n, was equal to 20 (or 40, or 2000), why might the following hash function not be

a good idea: h(k) = 4k mod n?

7. For the following questions: Let the hash function be H(x) = x mod M, where the table size (M) is initially

5.

(a) if the collision strategy was linear probing, what would the hash table look like

• after inserting 4371, 6173

• then removing 6173

• then inserting 3327 and 26

• after resizing1

to a table size of M = 11

• then inserting 4199, 4340, 9679, 1323

(b) if the collision strategy was separate chaining, what would the hash table look like

• after inserting 4371, 1323, 6173, 4199, 4344, 9679

• then removing 6173

• then inserting 3324

• then resizing2

to a table size of M = 11

• inserting 21

1where all the items must be inserted into the table by rehashing

2using the algorithm on the slides

3

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