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Consider the usual algorithm for determining whether a sequence of parentheses is balanced. Suppose that you run the algorithm on a sequence that contains 2 left parentheses and 3 right parentheses (in some order). The maximum number of parentheses that appear on the stack AT ANY ONE TIME during the computation?
- a)1
- b)2
- c)3
- d)4 or more
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
Consider the usual algorithm for determining whether a sequence of par...
Explanation:
The algorithm for determining whether a sequence of parentheses is balanced is as follows:
1. Start with an empty stack.
2. For each parenthesis in the sequence:
a. If it is a left parenthesis, push it onto the stack.
b. If it is a right parenthesis, pop the top element from the stack. If the popped element is not a left parenthesis or the stack is empty, then the sequence is not balanced.
3. After processing all parentheses, if the stack is not empty, then the sequence is not balanced.
Now, let's consider a sequence that contains 2 left parentheses and 3 right parentheses. The possible orders of these parentheses are:
1. ()()() - This sequence is balanced and the maximum number of parentheses on the stack at any one time is 2.
2. (()()) - This sequence is balanced and the maximum number of parentheses on the stack at any one time is 2.
3. (())() - This sequence is balanced and the maximum number of parentheses on the stack at any one time is 2.
4. ()(()) - This sequence is balanced and the maximum number of parentheses on the stack at any one time is 2.
5. ((())) - This sequence is balanced and the maximum number of parentheses on the stack at any one time is 2.
6. )()()( - This sequence is not balanced and the maximum number of parentheses on the stack at any one time is 1.
7. ()())( - This sequence is not balanced and the maximum number of parentheses on the stack at any one time is 2.
8. ()(() - This sequence is not balanced and the maximum number of parentheses on the stack at any one time is 2.
9. ((()) - This sequence is not balanced and the maximum number of parentheses on the stack at any one time is 3.
10. )((() - This sequence is not balanced and the maximum number of parentheses on the stack at any one time is 2.
From the above analysis, we can see that the maximum number of parentheses on the stack at any one time is 2. Therefore, the correct answer is option B.
The algorithm for determining whether a sequence of parentheses is balanced is as follows:
1. Start with an empty stack.
2. For each parenthesis in the sequence:
a. If it is a left parenthesis, push it onto the stack.
b. If it is a right parenthesis, pop the top element from the stack. If the popped element is not a left parenthesis or the stack is empty, then the sequence is not balanced.
3. After processing all parentheses, if the stack is not empty, then the sequence is not balanced.
Now, let's consider a sequence that contains 2 left parentheses and 3 right parentheses. The possible orders of these parentheses are:
1. ()()() - This sequence is balanced and the maximum number of parentheses on the stack at any one time is 2.
2. (()()) - This sequence is balanced and the maximum number of parentheses on the stack at any one time is 2.
3. (())() - This sequence is balanced and the maximum number of parentheses on the stack at any one time is 2.
4. ()(()) - This sequence is balanced and the maximum number of parentheses on the stack at any one time is 2.
5. ((())) - This sequence is balanced and the maximum number of parentheses on the stack at any one time is 2.
6. )()()( - This sequence is not balanced and the maximum number of parentheses on the stack at any one time is 1.
7. ()())( - This sequence is not balanced and the maximum number of parentheses on the stack at any one time is 2.
8. ()(() - This sequence is not balanced and the maximum number of parentheses on the stack at any one time is 2.
9. ((()) - This sequence is not balanced and the maximum number of parentheses on the stack at any one time is 3.
10. )((() - This sequence is not balanced and the maximum number of parentheses on the stack at any one time is 2.
From the above analysis, we can see that the maximum number of parentheses on the stack at any one time is 2. Therefore, the correct answer is option B.
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Community Answer
Consider the usual algorithm for determining whether a sequence of par...
In the entire parenthesis balancing method when the incoming token is a left parenthesis it is pushed into stack. A right parenthesis makes pop operation to delete the elements in stack till we get left parenthesis as top most element. 2 left parenthesis are pushed whereas one right parenthesis removes one of left parenthesis. 2 elements are there before right parenthesis which is the maximum number of elements in stack at run time.
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Consider the usual algorithm for determining whether a sequence of parentheses is balanced. Suppose that you run the algorithm on a sequence that contains 2 left parentheses and 3 right parentheses (in some order). The maximum number of parentheses that appear on the stack AT ANY ONE TIME during the computation?a)1b)2c)3d)4 or moreCorrect answer is option 'B'. Can you explain this answer?
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