Suppose we need to broadcast a message to all the nodes in a rooted tree. Initially, only the root node knows the message. In a single round, any node that knows the message can forward it to at most one of its children. See the figure below for an example. Design a polynomial time algorithm to compute the minimum number of rounds to broadcast a message to all nodes in a given binary tree. Analyze the running time of your algorithm, and prove that it is correct.

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