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

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Chapter 2: Elementary Data StructuresAs a result of the lemma, the maximum time to process a findis O(log n) if there are n elements in the tree.Sequence of nunions <strong>and</strong> m finds is bounded by O(m log n). Furtherimprovement is possible if we make use of collapsing rule.Collapsing rule: If j is the node on the path from i to its rootthen set PARENT(j) := ROOT(i).
procedure FIND(i);var j:integer;beginj:= i;while( PARENT(j) > 0) doj := PARENT(j);k := i;while (k j) dot := PARENT(k);PARENT(k) := j;k := t;return(j);end.Chapter 2: Elementary Data Structures
Page 1 and 2: Chapter 2: Elementary Data Structur
Page 37 and 38: procedure F(i);var i,j : integer;be
Page 47: Chapter 2: Elementary Data Structur
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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