1. "He's off the map!" - Eternal Sunshine of the Spotless Mind
Map ADT
"He's off the map!"
- Eternal Sunshine of the Spotless Mind

2. Data Structures
Given a program that counts the frequency of all the words in a file.
Assume words are anything set off by whitespace.
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3. Performance using ArrayList
Title
Size (kb)
Total
Words
Distinct Words
Time (sec)
small sample
0.6 89 25
0.001
2BR02B 34
5,638
1,975
0.051
Alice in Wonderland
120
29,460
6,017
0.741
Adventures of Sherlock Holmes
581
107,533
15,213
4.144
2008 CIA Factbook
10,030
1,330,100
74,042
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4. Order? Title Size Total Words Distinct Words Time
Express change in size as factor of previous file.
Title
Size
Total
Words
Distinct Words
Time
small sample
0.6 89 25
0.001
2BR02B
57x
63x
79x
51x
Alice in Wonderland
3.5x
5.2x 3x
14.5x
Adventures of Sherlock Holmes
4.8x
3.7x
2.5x
5.6x
2008 CIA Factbook
17.3x
12.4x
4.9x
41.7x
O(Total Words * Distinct Words) ??
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5. Question
Given it takes 2.88 minutes for the 2008 CIA Factbook with 1,330,100 total words and 74,042 distinct words, how long will take for another text with 1,000x total words and 100x distinct words?
an hour
a day
a week
a month
half a year
2.88 / (1,330,100 * 74, 042) = ? / (1,330,100,000 * 7,404,200)
2.88 = ? / (1,000 * 100)
= 288, 000 minutes
= 28.5 days
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6. Question
Given it takes 2.88 minutes for the 2008 CIA Factbook with 1,330,100 total words and 74,042 distinct words, how long will take for another text with 1,000x total words and 100x distinct words?
an hour
a day
a week
a month
half a year
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7. Why So Slow? Write a contains method for array-based list.
public boolean contains(E target) { }
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8. Why So Slow? Write a contains method for array-based list.
public boolean contains(E target) {
boolean result = false;
int i = 0;
while(!result && i < size())
if(list[i] == target)
result = true;
i++; }
return result;
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9. A Faster Way – Maps A -> 65
A data structure optimized for a very specific kind of search / access.
Also known as:
Dictionary, search table, or associative array.
A -> 65
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10. Maps Models a searchable collection of key-value entries.
Main operations of a map are for searching, inserting, and deleting items
Multiple entries with the same key are not allowed.
In a map we access by asking "give me the value associated with this key."
Applications:
address book
student-record database
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11. Keys and Values Dictionary Analogy:
The key in a dictionary is a word: foo
The value in a dictionary is the definition: First on the standard list of metasyntactic variables used in syntax examples.
A key and its associated value form a pair that is stored in a map.
To retrieve a value, need the key for that value.
An indexed List can be viewed as a Map with integer keys.
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12. More on Keys and Values Keys must be unique.
A given key can only represent one value.
But one value may be represented by multiple keys.
Like synonyms in the dictionary. Example: factor: n. See coefficient of X.
factor is a key associated with the same value (definition) as the key coefficient of X.
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13. The Map ADT
get(k): if the map M has an entry with key k, return its associated value; else, return null.
put(k, v): insert entry (k, v) into the map M; if key k is not already in M, then return null; else, return old value associated with k.
remove(k): if the map M has an entry with key k, remove it from M and return its associated value; else, return null.
size, isEmpty
entrySet(): return an iterable collection of the entries in M.
keySet(): return an iterable collection of the keys in M.
values(): return an iterator of the values in M.
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14. Example Operation Output Map isEmpty() true Ø put(5,A) null (5,A)
put(7,B) null (5,A),(7,B)
put(2,C) null (5,A),(7,B),(2,C)
put(8,D) null (5,A),(7,B),(2,C),(8,D)
put(2,E) C (5,A),(7,B),(2,E),(8,D)
get(7) B (5,A),(7,B),(2,E),(8,D)
get(4) null (5,A),(7,B),(2,E),(8,D)
get(2) E (5,A),(7,B),(2,E),(8,D)
size() 4 (5,A),(7,B),(2,E),(8,D)
remove(5) A (7,B),(2,E),(8,D)
remove(2) E (7,B),(8,D)
get(2) null (7,B),(8,D)
isEmpty() false (7,B),(8,D)

15. Implementing a Map
One easy implementation uses an Unsorted List ADT that uses a double-linked list.
Other common implementations of maps use a binary search tree or a hash table as the internal storage container.
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16. A Simple List-Based Map
We can implement a Map ADT using an Unsorted List.
Store the items of the map in a list S in arbitrary order.
tail
head
nodes/positions
entries 9 c 6 5 8
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17. The get(k) Algorithm Algorithm get(k) itr <- S.iterator
while itr.hasNext do
entry <- itr.next // next entry in list
if entry.getKey = k then
return entry.getValue
return null //no entry with key value of k
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18. The put(k,v) Algorithm Algorithm put(k,v): itr <- S.iterator
while itr.hasNext do
entry <- B.next // next entry in list
if entry.getKey = k then
value <- entry.getValue
entry.setValue(v)
entry.setKey(k)
return value // return the old value
S.addLast((k,v))
count <- count + 1 // increment num of entries
return null // no entry with key value k
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19. The remove(k) Algorithm
Algorithm remove(k):
itr <- S.iterator
while itr.has do
entry <- itr.next
if entry.getKey = k then
value <- entry.getValue
S.remove(entry)
count = count – 1
return value // return value
return null // no entry with key value k
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20. Performance of a List-Based Map
Takes O(n) time in the worst-case for all operations.
Same for average case. Why?
The Unsorted List implementation is effective only for Maps of small size.
More often use Binary Trees or Hash Tables.
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21. Results with HashMap Title Size (kb) Total Words Distinct Words
Time List
Time Map
small sample
0.6 89 25
0.001
0.0008
2BR02B 34
5,638
1,975
0.051
0.0140
Alice in Wonderland
120
29,460
6,017
0.741
0.0720
Adventures of Sherlock Holmes
581
107,533
15,213
4.144
0.2500
2008 CIA Factbook
10,030
1,330,100
74,042
4.0000
CS Maps

22. Order? Title Size Total Words Distinct Words Time List Time Map
small sample
0.6 89 25
0.001
0.0008
2BR02B
57x
63x
79x
51x
18x
Alice in Wonderland
3.5x
5.2x
3.0x
14.5x 5x
Adventures of Sherlock Holmes
4.8x
3.7x
2.5x
5.6x
2008 CIA Factbook
17x
12.3x
42x
16x
O(Total Words)?
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23. Question
Given it takes 4 seconds for the 2008 CIA Factbook with 1,330,100 total words and 74,042 distinct words, how long will take for another text with 1,000x total words and 100x distinct words?
an hour
a day
½ a week
a week
a month
4 / (1,330,100 * 74, 042) = ? / (1,330,100,000 * 7,404,200)
4 = ? / (1,000 * 100)
= 400, 000 seconds
= 4.6 days
CS Maps

24. Question
Given it takes 4 seconds for the 2008 CIA Factbook with 1,330,100 total words and 74,042 distinct words, how long will take for another text with 1,000x total words and 100x distinct words?
an hour
a day
½ a week
a week
a month
4 / (1,330,100 * 74, 042) = ? / (1,330,100,000 * 7,404,200)
4 = ? / (1,000 * 100)
= 400, 000 seconds
= 4.6 days
CS Maps

25. CS Maps

26. The Map<K, V> Interface in Java
void clear()
Removes all mappings from this map (optional operation).
boolean containsKey(Object key)
Returns true if this map contains a mapping for the specified key.
boolean containsValue(Object value)
Returns true if this map maps one or more keys to the specified value.
Set<K> keySet()
Returns a Set view of the keys contained in this map.
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27. The Map Interface Continued
V get(Object key)
Returns the value to which this map maps the specified key.
boolean isEmpty()
Returns true if this map contains no key-value mappings.
V put(K key, V value)
Associates the specified value with the specified key in this map
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28. The Map Interface Continued
V remove(Object key)
Removes the mapping for this key from this map if it is present
int size()
Returns the number of key-value mappings in this map.
Collection<V> values()
Returns a collection view of the values contained in this map.
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