Editing Disjoint sets
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A configuration of disjoint sets is a model of an [[equivalence relation]], with each set an equivalence class; two elements are equivalent if they are in the same set. Often, when discussing an equivalence relation, we will choose one element in each equivalence class to be the ''representative'' of that class (and we say that such an element is in ''canonical form''). Then the ''find'' operation can be understood as determining the representative of the set in which the query element is located. When we unite two sets, we either use the representative of one of the two sets as the representative of the new, united set, or we pick a new element altogether to be the representative. | A configuration of disjoint sets is a model of an [[equivalence relation]], with each set an equivalence class; two elements are equivalent if they are in the same set. Often, when discussing an equivalence relation, we will choose one element in each equivalence class to be the ''representative'' of that class (and we say that such an element is in ''canonical form''). Then the ''find'' operation can be understood as determining the representative of the set in which the query element is located. When we unite two sets, we either use the representative of one of the two sets as the representative of the new, united set, or we pick a new element altogether to be the representative. | ||
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==A first idea== | ==A first idea== |