Sets and disjoint sets union123

Sets And Disjoint Sets Union By: Ankita Goyal

Operation we can perform: ,[object Object],[object Object],[object Object]

Possible representations of sets ,[object Object],1 7 8 9 5 2 10 3 4 6

Possible Representations of S1 U S2 1 7 9 8 2 5 10 7 10 2 1 5 9 8 S1 ∪ S2 S1 ∪ S2

Data representation for s1, s2 and s3 1 6 3 5 4 2 10 7 8 9 S1 S2 S3

Array representation of S1, S2 and S3 i [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] p -1 5 -1 3 -1 3 1 1 1 5

Simple algorithms for union and find ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Weighting rule for Union(i,j) ,[object Object]

Trees obtained using the weighted rule ,[object Object],[object Object],1 2 n 3 2 1 5 4 n n 3 2 1 4 n 4 3 2 1 2 n 3 1

Union algorithm with weighting rule ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Sets and disjoint sets union123

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