Data Structures

Consider storing data for 100 employees by their Social Security Numbers (SSN) SSN range: 000000000 – 999999999

A fast search: SSN is index of an array E.g.

myItem is at position 123456789 myItem = myArray[123456789]

Characteristics Good--Efficiency of O(1) Bad-- Requires array of size 109, most of which is

unoccupied Can we have something that

Has efficiency of nearly O(1) and Requires reasonable amount of space

Keys (e.g., SSN) are “hashed” (mish-mashed) to another number, which can be used as index for a smaller array. E.g.,• item1 key: 1234568989 myArray[89] = item1• Item2 key: 1234567575 myArray[75] = item2• Item3 key: 3457892121 myArray[21] = item3• Item4 key: 9234572121 myArray[?] = item4

Last 2 cases: collision, when two keys hash to the same hash value

item1: 1234568989

item2: 1234567575

item3: 3457892121

item4: 9234572121

Item5: 7854387575

Item6: 5432192424

Item7: 3311222020

…

0

1

20

23

75

76

89

…

21

…

myTable

24

Ω

Ω

Ω

Ω

Ω

Ω

Ω

Ω

Ω

item7

item6

item4item3

item5item2

item1

…

Data Key Hashed Index

item1: 1234568989

item2: 1234567575

item3: 3457892121

item4: 9234572121

Item5: 7854387575

Item6: 5432192424

Item7: 3311222020

…

0

1

20

23

75

76

89

…

21

…

myTable

24

Data Key Hashed Index

Item 7

-1

-1

Item3

22 Item4

Item 6

-1

Item 2Item 5

Item 1

Given names as keys: amy tammy frank billy

Convert keys to array indices. Max size of array: 10 name(hashF1) integer (hashF2) index E.g.,

amyAscii(a) + Ascii(m) + Ascii(y) = 97 + 109 + 121 = 327

327 % 10 = 7 tammyAscii(t) + Ascii(a) + Ascii(m) + Ascii(m)

+ Ascii(y) = 116 + 97 + 109 + 109 + 121 = 552 552 % 10 = 2

…

0

1

2

6

8

10

…

myTable

7

Ω

Ω

Ω

Ω

Ω

Ω

Ω

tammy

amy

…

Given: key = 1234567 h(key) = key % 100 1234567 67 3785421 21

Given: key = beth h1(key) = ascii(b) + ascii(e) + ascii(t) +

ascii(h) = 98 + 121 + 116 + 104 = 419

h2(419) = 415 % 100 = 19 h(key) = h2(h1(key)) = 19 Thus, “beth” -> 19

void insert (elemType &item); Inserts item in the table,

bool remove (keyType key); Removes data item corresponding to key. Returns

true when successful; false, otherwise. bool search (keyType key);

Searches the table for item corresponding to key. Returns true when match found; false, otherwise.

elemType search(keyType key); Searches and return the value corresponding to

key book isEmpty(); void clear();

bool search (keyType key);1. hash(key) anIndex T(n) = c12. IF array[anIndex] is not empty THEN T(n) = c2 + c3

search the linked listELSE value is not presentEND IF

3. return true/false T(n) = c4

1. T(n) = c1 + c2 + c3 + c4O(1) almost

1. Describe the data structure to represent a hash table

2. Write a C++ code for the structure, to be included in the private section of the (hash) Table class.

0

1

8

7

2

3

4

5

6

9

Ω

Ω

Ω

Ω

Ω

Ω

ΩΩ

Ω

Ω

Array Struct

To represent a group of data elements of different types as a single unit

Contrast this with an array, whose elements must of the same type.

Is like a class, but every part is public by default. No operations is a struct.

Definition:

struct athlete_t { string name; int weight; // in kg int height; // in cm};

Usage:athlete_t ath;ath.name = “John”;ath.weight = 200;ath.height = 190;cout << ath.name << endl;cout << ath.weight << endl;cout << ath.height << endl;athlete_t team[MAX];team[0] = ath;

private: struct nodeType { elemType data; nodeType *next; };

static const int MAX = 10; nodeType* list[MAX];};

class Table {public: Table(); void insert(elemType item); bool remove(keyType key); bool retrieve(keyType key, elemType &item); void clear(); void print();private: ...};

1. Constructor1. What needs to be done in the

constructor?2. Write a C++ code to implement Table().

2. Insert1. What are the steps necessary to insert an

item into the Hash table?2. Write a C++ code to implement

insert(elemType item) in the Table class.