Connecting Graph

"class ConnectingGraph:

    # @param {int} n
    def __init__(self, n):
        # initialize your data structure here.
        self.father = [0 for i in xrange(n+1)]
    def find(self, x):
        if self.father[x] == 0:
            return x
        self.father[x] = self.find(self.father[x])
        return self.father[x]
    # @param {int} a, b
    # return nothing
    def connect(self, a, b):
        # Write your code here
        root_a = self.find(a)
        root_b = self.find(b)
        if root_a != root_b:
            self.father[root_a] = root_b

    # @param {int} a, b
    # return {boolean} true if they are connected or false
    def query(self, a, b):
        # Write your code here
        root_a = self.find(a)
        root_b = self.find(b)
        return root_a == root_b"

Connecting Graph II

"class ConnectingGraph2:

    # @param {int} n
    def __init__(self, n):
        # initialize your data structure here.
        self.father = [0 for i in xrange(n+1)]
        self.size = [1 for i in xrange(n+1)]

    def find(self, x):
        if self.father[x] == 0:
            return x
        self.father[x] = self.find(self.father[x])
        return self.father[x]


    # @param {int} a, b
    # return nothing
    def connect(self, a, b):
        # Write your code here
        root_a = self.find(a)
        root_b = self.find(b)
        if root_a != root_b:
            self.father[root_a] = root_b
            self.size[root_b] += self.size[root_a]

    # @param {int} a
    # return {int}  the number of nodes connected component
    # which include a node.
    def query(self, a):
        # Write your code here
        root_a = self.find(a)
        return self.size[root_a]"

Connecting Graph III

"class ConnectingGraph3:

    # @param {int} n
    def __init__(self, n):
        # initialize your data structure here.
        self.father = [0 for i in xrange(n+1)]
        self.count = n

    def find(self, x):
        if self.father[x] == 0:
            return x
        self.father[x] = self.find(self.father[x])
        return self.father[x]


    # @param {int} a, b
    # return nothing
    def connect(self, a, b):
        # Write your code here
        root_a = self.find(a)
        root_b = self.find(b)
        if root_a != root_b:
            self.father[root_a] = root_b
            self.count -= 1


    # @param {int} a
    # return {int} the number of connected component
    # in the graph
    def query(self):
        # Write your code here
        return self.count"