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Apply Algorithm 12.3 to insert an element with key M into the binary search tree shown in Figure 12.7. Step 1 starts the iterator p at the root K. Since M is greater than K (i.e., it follows it lexicographically) and node K has a right child, the algorithm proceeds to step 6, resetting the iterator p to node P, and then goes back to step 3. Next, since M is less than P (i.e., it precedes it lexicographically) and node P has a left child, the algorithm proceeds to step 4, resetting the iterator p to node N, and then goes back to step 3. Next, since M is also less than N but node N has no left child, the Figure 12.8 A binary search tree algorithm proceeds to step 5, inserts the new element as the left child of node N, and then returns. This is illustrated in Figure 12.8.

To protect their trade secret rights, the owner must also mark any material related to the secret as proprietary The source code itself, training manuals, and other documentation should include a statement that the software is proprietary A trade secret can last indefinitely, and it costs nothing except being serious about protecting the secret The courts will enforce the owner s rights to the trade secret, as long as the owner remains diligent in efforts to protect the secret However, if the owner becomes sloppy about security surrounding the secret, the owner can lose the trade secret rights Suppose, for instance, that (perhaps mistakenly) the owner posts the source code on a web page for a while Such disclosure of the secret to the public could invalidate any future claim of the owner to legal protection of the secret.

Find the Thevenin equivalent for the network to the left of terminals a; b in Fig. 1-15 (b) if k 0:1. Use the Thevenin equivalent to verify the results of Problem 1.4. Ans: a VTh 200 V; ZTh RTh 100 ; b VTh 250 V; ZTh RTh 125

with all sorting algorithms, it applies to an array (or vector) But the underlying heap structure (a binary tree) that the array represents is used to define this algorithm Like the merge sort and the quick sort, the heap sort uses an auxiliary function that is called from the sort() function And also like the merge sort and the quick sort, the heap sort has complexity function O(n lg n) But unlike the merge sort and the quick sort, the heap sort is not recursive The heap sort essentially loads n elements into a heap and then unloads them By Theorem 131 on page 247, each element takes O(lgn) time to load and O(lgn) time to unload, so the entire process on n element runs in O(n lgn) time Algorithm 148 The Heap Sort (Precondition: s = {s0 sn 1} is a sequence of n ordinal values.

Find the Thevenin equivalent for the circuit to the left of terminals a; b in Fig. 1-16, and use it to verify the results of Problem 1.6. Ans: VTh 1 1 vs ; ZTh RTh 1 3 2 2 An alternative solution for Problem 1.3 involves nding a Thevenin equivalent circuit which, when connected across the nonlinear R2 0:25i, allows a quadratic equation in current i to be written via KVL. Find the elements of the Thevenin circuit and the resulting current. Ans: VTh 25 V; ZTh RTh 5 ; i 4:142 A Use (1.10) to (1.15) to nd expressions for the z parameters in terms of the h parameters. Ans: z11 h11 h12 h21 =h22 ; z12 h12 =h22 ; z21 h21 =h22 ; z22 1=h22

Patents A patent protects an inventor s intellectual property for a limited period of time After 20 years, the patented idea becomes public property, and anyone can use it During the lifetime of the patent, the patent gives the owner the right to prevent others from making or using the invention, unless the owner grants permission The purpose of seeking a patent, which often costs many thousands of dollars in legal and filing fees, is to gain protection from competition, so the inventor can bring the invention to market and profit from it A patent is a short-term monopoly right granted to reward the genius of the inventor To be patentable, an invention must be novel, nonobvious, and useful Many suitcases today have wheels on them, so they can be rolled about as well as carried.