Find operation and smart union algorithm
- 2. A union-find algorithm is an algorithm that perform two useful operation they are.., Find: determine which subset a particular element is in .this can be used for determining if two elements are in the same subset
- 3. Union: join two subset into a single subset. Union-find algorithm: Can be used to check whether an undirected graphs contain cycle or not.
- 4. Introduction Disjoint-set/union-find forest Disjoint set operation Disjoint set optimised Union by rank Two set of union Pseudo code
- 5. A disjoint –set data structure is also called a union-find data structure or merge-find set is a data structure that stores a collection of disjoint set It stores a *partition of a set into disjoint subset It provides operation for adding new set, merging set and finding a representative members of a set. The last operation allows to find out efficiently if any two elements are in the same or different set.
- 6. Type : multiway tree invented : 1964 Invented by : Michael j. Fischer
- 7. Make set(x) Find(x) Union(x , y)
- 8. Disjoint set is optimised by two main types they are: Union by rank Path by compression
- 9. User find to determine the roots of the trees x and y belongs to If the roots are distinct the tree are combined by attaching the root of one to the root of the other If this is done naively such as by always making x a child of y, the height of the tree can grow as o(n).we can optimized it by using union by rank
- 10. Union by rank always attaches the shorter tree to the root of the taller tree To implement union by rank , each element is associated with a rank. Initially a set has one element and a rank of zero.
- 11. Union have a two set they are: Both trees have the same rank-the resulting set’s rank is one longer. Both trees have the different rank-the resulting set’s rank is larger of the two. Rank are used instead of height or depth because path compression will change the tress's height over time.
- 12. Function union(x , y) xroot:=find(x) yroot:=find(y) //x and y are not in same set , so If xroot.rank< yroot.rank xroot.parent:=yroot Else if xroot.rank> yroot.rank yroot. Parent:= xroot Else xroot.parent:=yroot yroot.rank:=yroot.rank+1.
- 13. Thank you..☺️