class Solution {
    public boolean isBipartite(int[][] graph) {
        UnionFind uf = new UnionFind(graph.length);
        for(int i = 0; i < graph.length; i++) {
            for(int j = 0; j < graph[i].length; j++) {
                if(uf.find(i) == uf.find(graph[i][j]))
                    return false;
                uf.union(graph[i][0], graph[i][j]);
            }
        }
        
        return true;
    }
    
    public class UnionFind {
        private int size;
        private int numComponents; // number of connected components
        private int[] parent;
        private int[] rank;

        public UnionFind(int n) {
            if (n <= 0) throw new IllegalArgumentException("Size <= 0 is not allowed");
            size = numComponents = n;
            parent = new int[n];
            rank = new int[n];
            for (int i = 0; i < n; i++) {
                parent[i] = i;
            }
        }

        public int find(int p) {
            while (p != parent[p]) {
                parent[p] = parent[parent[p]];    // path compression by halving
                p = parent[p];
            }
            return p;
        }

        public void union(int p, int q) {
            int rootP = find(p);
            int rootQ = find(q);

            // These elements are already in the same group!
            if (rootP == rootQ)
                return;

            // Merge smaller component/set into the larger one.
            if (rank[rootQ] > rank[rootP]) {
                parent[rootP] = rootQ;
            } else {
                parent[rootQ] = rootP;
                if (rank[rootP] == rank[rootQ]) {
                    rank[rootP]++;
                }
            }

            // Since the roots found are different we know that the number of components/sets has decreased by one
            numComponents--;
        }

        // Return whether or not the elements 'p' and 'q' are in the same components/set.
        public boolean connected(int p, int q) {
            return find(p) == find(q);
        }

        // Returns the number of remaining components/sets
        public int components() {
            return numComponents;
        }

        // Return the number of elements in this UnionFind/Disjoint set
        public int size() {
            return size;
        }
    }
}