go: add «2493. Divide Nodes Into the Maximum Number of Groups»

URL:	https://leetcode.com/problems/divide-nodes-into-the-maximum-number-of-groups/
Signed-off-by: Matej Focko <me@mfocko.xyz>

go/divide-nodes-into-the-maximum-number-of-groups.go

@@ -0,0 +1,100 @@
+package main
+
+import aq "github.com/emirpasic/gods/v2/queues/arrayqueue"
+
+func magnificentSets(n int, edges [][]int) int {
+	g := make([][]int, n)
+	for u, _ := range g {
+		g[u] = make([]int, 0)
+	}
+
+	depth := make([]int, n)
+	parent := make([]int, n)
+	for u, _ := range parent {
+		parent[u] = -1
+	}
+
+	find := func(t int) int {
+		for parent[t] != -1 {
+			t = parent[t]
+		}
+		return t
+	}
+
+	union := func(u, v int) {
+		su, sv := find(u), find(v)
+		if su == sv {
+			// same component
+			return
+		}
+
+		if depth[su] < depth[sv] {
+			su, sv = sv, su
+		}
+		parent[sv] = su
+
+		if depth[su] == depth[sv] {
+			depth[su]++
+		}
+	}
+
+	numberOfGroups := func(src int) int {
+		q := aq.New[int]()
+		seen := make([]int, n)
+		for i, _ := range seen {
+			seen[i] = -1
+		}
+
+		q.Enqueue(src)
+		seen[src] = 0
+
+		deepest := 0
+		for !q.Empty() {
+			size := q.Size()
+			for i := 0; i < size; i++ {
+				u, _ := q.Dequeue()
+				for _, v := range g[u] {
+					if seen[v] == -1 {
+						seen[v] = deepest + 1
+						q.Enqueue(v)
+					} else if seen[v] == deepest {
+						return -1
+					}
+				}
+			}
+			deepest++
+		}
+
+		return deepest
+	}
+
+	for _, edge := range edges {
+		u, v := edge[0]-1, edge[1]-1
+		g[u] = append(g[u], v)
+		g[v] = append(g[v], u)
+		union(u, v)
+	}
+
+	groupsPerComponent := make(map[int]int)
+	for u, _ := range g {
+		groups := numberOfGroups(u)
+		if groups == -1 {
+			// invalid
+			return -1
+		}
+
+		root := find(u)
+
+		current, ok := groupsPerComponent[root]
+		if !ok {
+			current = 0
+		}
+		groupsPerComponent[root] = max(current, groups)
+	}
+
+	totalGroups := 0
+	for _, groups := range groupsPerComponent {
+		totalGroups += groups
+	}
+	return totalGroups
+}