package algo

type Subset struct {
	parent string
	rank   int
}

// find is a recursive function that finds the root of the subset that element 'e' belongs to.
// It uses path compression technique to optimize future find operations.
// The subsets parameter is a map that stores the subsets with their parent information.
// The e parameter is the element for which the root is to be found.
// The function returns the root of the subset that 'e' belongs to.
// see https://ondrej-kvasnovsky-2.gitbook.io/algorithms/finding/union-find-algorithms
// or https://jojozhuang.github.io/algorithm/algorithm-union-find/
func find(subsets map[string]*Subset, e string) string {
	// find root and make root as parent of e
	// (path compression)
	if subsets[e].parent != e {
		subsets[e].parent = find(subsets, subsets[e].parent)
	}
	return subsets[e].parent
}

// Union merges two subsets in the union-find data structure.
// It takes a map of subsets, and the names of the two subsets to be merged.
// The function finds the root of each subset and performs the union operation based on the rank of the subsets.
func Union(subsets map[string]*Subset, x, y string) {
	xroot := find(subsets, x)
	yroot := find(subsets, y)

	// Attach smaller rank tree under root of high
	// rank tree (Union by Rank)
	if subsets[xroot].rank < subsets[yroot].rank {
		subsets[xroot].parent = yroot
	} else {
		if subsets[xroot].rank > subsets[yroot].rank {
			subsets[yroot].parent = xroot
		} else {
			// If ranks are same, then make one as root and
			// increment its rank by one
			subsets[yroot].parent = xroot
			subsets[xroot].rank++
		}
	}
}