261. Graph Valid Tree

swift/261-Graph-Valid-Tree.swift

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+class DisjointSet {
+ private var ranks: [Int]
+ private var roots: [Int]
+
+ init(numVertices: Int) {
+ ranks = [Int](repeating: 0, count: numVertices)
+ roots = [Int](repeating: 0, count: numVertices)
+
+ for i in 0..<numVertices {
+ roots[i] = i
+ ranks[i] = 1
+ }
+ }
+
+ public func union(v1 x: Int, v2 y: Int) {
+ let rootX = find(of: x)
+ let rootY = find(of: y)
+
+ guard rootX != rootY else { return }
+
+ let rankX = ranks[rootX]
+ let rankY = ranks[rootY]
+
+ if rankX > rankY { // go into X
+ roots[rootY] = rootX
+ } else if rankY > rankX { // go into Y
+ roots[rootX] = rootY
+ } else { // go into X by default
+ roots[rootY] = rootX
+ ranks[rootX] += 1
+ }
+ }
+
+ private func find(of x: Int) -> Int {
+ if roots[x] == x { return x }
+ roots[x] = find(of: roots[x])
+ return roots[x]
+ }
+
+ public func areConnected(v1: Int, v2: Int) -> Bool {
+ find(of: v1) == find(of: v2)
+ }
+
+ public func areDisjoint(v1: Int, v2: Int) -> Bool {
+ !areConnected(v1: v1, v2: v2)
+ }
+}
+
+class Solution {
+ func validTree(_ n: Int, _ edges: [[Int]]) -> Bool {
+ // Check if n-1 edges
+ let numEdges = edges.count
+ guard numEdges == (n - 1) else { return false }
+
+ // Check if connected => Can use DisjointSet/UnionFind
+ let ds = DisjointSet(numVertices: n)
+ for edge in edges {
+ let v1 = edge[0]; let v2 = edge[1]
+ guard ds.areDisjoint(v1: v1, v2: v2) else { 
+ return false 
+ }
+ ds.union(v1: v1, v2: v2)
+ }
+
+ return true;
+ }
+}
+
+