Heap sort and complexity, Disjoint Union & Find, Complexity ...

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Chapter 2: Elementary Data StructuresAdvantages: It can be easily determined whether or notparticular element i is present. Union and Intersection can bedone using “logical and” and “logical or”.Disadvantages: This representation is inefficient when thevalue of n is large (say larger than the number of bits in theword) and the size of the set is smaller compare to U. The timewill be proportional to n rather than the number of elements inthe set.
Chapter 2: Elementary Data StructuresAlternate representation: Represent each set by its element.If there is any ordering relationship between them then theoperation such as union and intersection can be carried out intime proportional to the length of the sets.We represent sets as trees.We assume that they are pair wise disjoint and perform theseoperations.
Page 1 and 2: Chapter 2: Elementary Data Structur
Page 31: Chapter 2: Elementary Data Structur
Page 37 and 38: procedure F(i);var i,j : integer;be
Page 49 and 50: procedure FIND(i);var j:integer;beg
Page 51 and 52: Maze Application• Build a random
Page 53 and 54: Maze Application• Repeatedly pick
Page 55 and 56: A CycleStartEndRef: Ben Lerner Slid
Page 57 and 58: A Hidden TreeStartEndRef: Ben Lerne
Page 59 and 60: Basic Algorithm• S = set of sets
Page 61 and 62: ExampleS{1,2,7,8,9,13,19}{3}{4}{5}{
Page 63 and 64: Example at the EndStart1 2 3 4 5 67

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