AC1202 Sets 4' Set operations Difference Subset

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AC1202Sets4. Set operationsDifference -
Subset
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C code for sets

• typedef struct mylist
• int element
• struct mylist next
• MYLIST
• typedef MYLIST LISTPTR

Linked list node definition as before

• typedef struct set
• LISTPTR elements
• SET

int cardinality
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C code for sets
CreateSet AddToSet Intersection Union Differen
ce IsSubset IsSetEmpty
(SET set, int newElement)
(SET setA, SET setB, SET newSet)
(SET setA, SET setB, SET newSet)
(SET setA, SET setB, SET newSet)
(SET setA, SET setB)
(SET set)
or IsListEmpty(LISTPTR head)
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Calculating a set difference
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Difference of 2 sets using ordered linked list
A-B
1
4
7
11
12
14
19
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Set A
Define two markers for sets A and B. Start
them off at the first elements in each set.
Set B
1
4
8
12
Difference
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Difference of 2 sets using ordered linked list
A-B
1
4
7
11
12
14
19
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Set A
If info at A B same move markers on
Set B
1
4
8
12
Difference
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Difference of 2 sets using ordered linked list
A-B
1
4
7
11
12
14
19
27
Set A
and advance BOTH markers...
Set B
1
4
8
12
Difference
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Difference of 2 sets using ordered linked list
A-B
1
4
7
11
12
14
19
27
Set A
If info at A lt info a B add info at markerA to
setD and ...
Set B
1
4
8
12
Difference
7
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Difference of 2 sets using ordered linked list
A-B
1
4
7
11
12
14
19
27
Set A
... advance MarkerA
Set B
1
4
8
12
Difference
7
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Difference of 2 sets using ordered linked list
A-B
1
4
7
11
12
14
19
27
Set A
If info at A gt info at B ...
Set B
1
4
8
12
Difference
7
11
Difference of 2 sets using ordered linked list
A-B
1
4
7
11
12
14
19
27
Set A
... advance MarkerB
Set B
1
4
8
12
Difference
7
12
Difference of 2 sets using ordered linked list
A-B
1
4
7
11
12
14
19
27
Set A
If info at A lt info at B add info at markerA to
setD, and advance A
Set B
1
4
8
12
Difference
7
11
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Difference of 2 sets using ordered linked list
A-B
1
4
7
11
12
14
19
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Set A
Continue until one Marker is NULL...
Set B
1
4
8
12
NULL
Difference
7
11
14
Difference of 2 sets using ordered linked list
A-B
1
4
7
11
12
14
19
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Set A
NULL
If more elements in setA, add to setD
until markerANULL
Set B
1
4
8
12
NULL
Difference
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7
11
14
14
19
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Psuedocode for difference

• markerA points to setA
• markerB points to setB
• create empty setD
• markerD points to setD
• repeat
• until markerA or markerB at end of sets

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in difference

• If info at markerA info at markerB
• move both markers on
• else
• if info at markerA lt info at markerB
• add info at markerA to setD
• move markerA on
• else
• move markerB on

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After repeat

• If markerA not at end of setA
• add info to setD
• End

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• void Difference(SET Set1, SET Set2, SET Set3)
• LISTPTR Marker1, Marker2
• Marker1 Set1.elements
• Marker2 Set2.elements
• while (Marker1 Marker2)
• if (Marker1-gtdata Marker2-gtdata)
• Marker1 Marker1-gtnext
• Marker2 Marker2-gtnext
• else if(Marker1-gtdata lt Marker2-gtdata)
• AddInOrder(Set3, Marker1-gtdata)
• Marker1 Marker1-gtnext
• else
• Marker2 Marker2-gtnext

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Calculating a subset
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Is set A a subset of set B?
4
7
12
19
Set A
Set B
1
4
7
11
12
14
19
27
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Is set A a subset of set B?
If info at B lt info at Amove along B
4
7
12
19
Set A
Set B
1
4
7
11
12
14
19
27
Counter
0
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Is set A a subset of set B?
If info at B lt info at Amove along B
4
7
12
19
Set A
Set B
1
4
7
11
12
14
19
27
Counter
0
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Is set A a subset of set B?
If info at B info at Aadd one to counter move
along both
4
7
12
19
Set A
Set B
1
4
7
11
12
14
19
27
Counter
0
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Is set A a subset of set B?
If info at B info at Aadd one to counter move
along both
4
7
12
19
Set A
Set B
1
4
7
11
12
14
19
27
Counter
1
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Is set A a subset of set B?
If info at B info at Aadd one to counter move
along both
4
7
12
19
Set A
Set B
1
4
7
11
12
14
19
27
Counter
2
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Is set A a subset of set B?
If info at B lt info at Amove along B
4
7
12
19
Set A
Set B
1
4
7
11
12
14
19
27
Counter
2
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Is set A a subset of set B?
If info at B lt info at Amove along B etc. until
reach end of one of them
4
7
12
19
Set A
Set B
1
4
7
11
12
14
19
27
Counter
2
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Is set A a subset of set B?
4
7
12
19
Set A
Set B
1
4
7
11
12
14
19
27
Counter
4
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Is set A a subset of set B?
Test counter cardinality of A Yes A subset of
B No A not subset of B
4
7
12
19
Set A
Set B
1
4
7
11
12
14
19
27
Counter
4
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Subset contd
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Is set A a subset of set B?
Define two markers for sets A and B. Start them
off at the first elements in each set. Set
counter to 0
4
8
12
19
Set A
Set B
1
4
11
12
14
19
27
Counter
0
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Is set A a subset of set B?
If info at B lt info at Amove along B
4
8
12
19
Set A
Set B
1
4
11
12
14
19
27
Counter
0
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Is set A a subset of set B?
If info at B lt info at Amove along B
4
8
12
19
Set A
Set B
1
4
11
12
14
19
27
Counter
0
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Is set A a subset of set B?
If info at B info at Aadd one to counter move
along both
4
8
12
19
Set A
Set B
1
4
11
12
14
19
27
Counter
0
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Is set A a subset of set B?
If info at B info at Aadd one to counter move
along both
4
8
12
19
Set A
Set B
1
4
11
12
14
19
27
Counter
1
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Is set A a subset of set B?
If info at A lt info at B means there is
something in A that isn't in B so we can stop
4
8
12
19
Set A
Set B
1
4
11
12
14
19
27
Counter
1
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Psuedocode for IsSubset

• If cardinality of A gt B then
• A cant be a subset of B
• else
• markerA points to setA markerB points to setB
• matches0 mismatchFALSE
• Repeat
• until markerA or markerB at end of sets or
  mismatch TRUE
• Subset if matches cardinality of A
• end

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in IsSubset

• If info at markerA info at markerB
• increment matches
• move both markers on
• else
• if info at markerA lt info at markerB
• mismatchTRUE
• else
• move markerB on

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• int IsSubSet(SET Set1, SET Set2)
• LISTPTR Marker1, Marker2
• int nMatches, nMisMatch
• if (Set1.cardinality gt Set2.cardinality)
• return false
• Marker1 Set1.elements
• Marker2 Set2.elements
• nMatches0 nMisMatch0
• while (Marker1 Marker2 !nMisMatch)
• if (Marker1-gtdata Marker2-gtdata)
• Marker1 Marker1-gtnext
• Marker2 Marker2-gtnext
• nMatches
• else if(Marker1-gtdata lt Marker2-gtdata)
• nMisMatch1

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Summary

• Pseudocode and implementation for
• Difference, Subset
• Key points
• Work through sets in order
• If data at markerA lt data markerB then move
  markerA on
• Remember to store results in ordered set
• What to do after getting to the end of one set
• Difference if any elements left in setA after
  subtracting setB, copy these into difference
  set
• Subset
• Check count of elements each set had in common,
  does it equal the cardinality of setA
• Special case if element in SetA lt element in
  SetB - stop
• Next lecture recursion!