c109s00t2 - CSc 109 Test 2 26 April 2000 >ANSWERS< 1(10 pts...

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CSc 109 Test 2 26 April 2000 >>>>>>>>>>>>>>>>>>>>>>>>>>ANSWERS<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<< 1. (10 pts) Assume the algorithm discussed in class for balancing a binary tree is used to maintain the two balanced trees below so that an in order traversal of the tree lists the data in ascending order. Explain why both tree (a) and tree (b) are balanced. Draw tree (a) after 15 has been added to tree (a) with balance maintained. Draw tree (b) after 13 has been added to tree (b) with balance maintained. Draw tree (b) after 28 (instead of 13) has been added to tree (b) with balance maintained. Draw tree (b) after 19 (instead of 13 or 28) has been added to tree (b) with balance maintained. (a) 20 / 12 15 / \ 12 20 (b) 15 15 / \ 13 / \ 12 20 ----> 12 20 / / \ / \ / \ 10 17 25 10 13 17 25 / \ / \ / \ / \ 16 18 23 30 16 18 23 30 15 20 / \ 28 / \ 12 20 -----> 15 25 / / \ / \ / \ 10 17 25 12 17 23 30 / \ / \ / / \ / 16 18 23 30 10 16 18 28 15 17 / \ 19 / \ 12 20 ----> 15 20 / / \ / \ / \ 10 17 25 12 16 18 25 / \ / \ / \ / \ 16 18 23 30 10 19 23 30 2. (10 pts) Write the following expressions in postfix form, assuming the usual precedence of operations in C++ and putting blank spaces between each term. a. 2+3+4 > 5*3 && x-5 >= 0 2 3 + 4 + 5 3 * > x 5 - 0 >= && b. (2+3*4)*(5+6-7/8) 2 3 4 * + 5 6 + 7 8 / - * 3. (25 pts)
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