FindRoot with path compression

        private static int FindRoot(int node, int[] parent)
        {
            // Find the root parent for the node
            int root = node;
            while (parent[root] != root)
            {
                root = parent[root];
            }

            // Optimize(compress) path from ndoe to root
            while (node != root)
            {
                var oldParentNode = parent[node];
                parent[node] = root;
                node = oldParentNode;
            }
            return root;
        }