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We can define a binary tree representation T′ for an ordered general tree T as follows (see Figure 8.21):• For each position p of T, there is an associated position p′ of T′ . • If p is a leaf of T,...

Write a program that can play Tic-Tac-Toe effectively. (See Section 3.1.5.) To do this, you will need to create a game tree T, which is a tree where each position corresponds to a game...

1. Write a program that takes as input a general tree T and a position p of T and converts T to another tree with the same set of position adjacencies, but now with p as its root.2. Write a program...

1. How long would it take to remove the ⌈logn⌉ smallest elements from a heap that contains n entries, using the removeMin operation?2. Suppose you set the key for each position p of a binary tree T...

The min method for the UnsortedPriorityQueue class executes in O(n) time, as analyzed in Table 9.2. Give a simple modification to the class so that min runs in O(1) time. Explain any necessary...