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Answers
(1) (10 pts) What does the initially empty stack aStack “look like” after each line of the following pseudocode? aStack.push(9) /Line 1/ aStack.push(8) /Line 2/ aStack.push(9) /Line 3/ aStack.pop() /Line 4/ if (!aStack.isEmpty()) aStack.push(7) /Line 5/ aStack.pop(y) /Line 6/ aStack.push(10)/Line 7/ aStack.push(y) /Line 8/ Write the state of the stack after the given line has executed under the label for that line in the space below. Solution:
Line 1
Line 2
8 9
Line 3 9 8 9
Line 4
8 9
Line 5
7 8 9
Line 6
Line 7
10 8 9
Line 8 7 10 8 9
1
(2) (10 pts) Given a queue of integers iQueue, and using only the methods of the ADT Queue (enqueue, dequeue, isEmpty, etc.), write code which prints out the all the positive integers in the queue, first, in order. Then the code should print out all the negative (and 0) integers, again in the order in which they ap- peared in the original queue. All items should be dequeued from iQueue by the end of your code. So if iQueue initially contains (from front to back) 4 , 5 , − 9 , 9 , 9 , 0 , − 7 , 1 , the output to the screen should be 4 5 9 9 1 -9 0 - Hint: You need a loop to go through and dequeue all of iQueue first. The positive integers should be printed out immediately, and the nonpositive ones stored for later printout. How should the negative (and 0) integers be stored (in a list, an array, a stack, or a queue)? Your answer may be in C++ code or (pre- cise) pseudocode. Solution: int x; Queue tempQueue; while (!iQueue.isEmpty()){ iQueue.dequeue(x); if (x>0) cout << x << " "; else tempQueue.enqueue(x); } while (!tempQueue.isEmpty()){ tempQueue.dequeue(x); cout << x << " "; } cout << endl;
Answer for Problem 3: Solution: The path found is E,C,I,B,G. Here is the value of the stack at each step: G B B D I I I C C C C C C E E E E E E E (4) (10 pts) Consider the language the following grammar defines:
= | = A | B = 1 | 2 Circle those strings which are in the language. No explanation necessary.
SLAB A 2 2A1BB B22 DSS 1BA
Solution: Only A, 2A1BB, and 1BA are in the language:
- SLAB is not in the language, since the only characters allowed are A,B,1,2 (not S or L)
- A is in the language:
= = A. - 2 is not in the language, since any digit must be fol- lowed by
. - 2A1BB is in the language:
= = 2 = 2A1 = 2A1BB. - B22 is not in the language, since any digit must be followed by
. - DSS is not in the language, since the only characters al- lowed are A,B,1,2 (not D or S)
- 1BA is in the language, since
= = 1 = 1BA.
(5) (10 pts) Recall the data members for the pointer-based imple- mentation of class Stack class Stack{ /* public members here ... / private: struct StackNode{ StackItemType item; StackNode next; }; // end struct StackNode StackNode* topPtr; }; // end class Stack (a) Write a C++ implementation of the member function push, which pushes an item onto the top of the stack (you don’t have to worry about error handling). Here is the first line of the function definition: void Stack::push(StackItemType newItem) Solution: void Stack::push(StackItemType newItem){ StackNode* newPtr = new StackNode; newPtr->item = newItem; newPtr->next = topPtr; topPtr = newPtr; } (b) Write a C++ implementation of the member function isEmpty of class Stack. Here is the first line: bool Stack::isEmpty() const Solution: bool Stack::isEmpty() const{ return topPtr == NULL; }
