Suppose we are given a string of parentheses. First show that telling whether they are properly matched and nested, such as (()()) or ((()))() but not ()) or ())((), is in L. Now suppose there are two types of parentheses, round ones and square brackets. We wish to know if they are properly nested: for instance, ([])[] and [()[]] are allowed, but ([)] is not. Show that this problem is in L. Hint: Each opening parentheses ( or [ has a “closing partner” ) or ]. Ensure that the type of each opening is the same as the type of its closing partner. Since the only goal is to minimize space, consider a time-inefficient solution that repeats work you’ve already done.
Suppose we are given a string of parentheses. First show that telling whether they are properly matched and nested, such as (()()) or ((()))() but not ()) or ())((), is in L. Now suppose there are two types of parentheses, round ones and square brackets. We wish to know if they are properly nested: for instance, ([])[] and [()[]] are allowed, but ([)] is not. Show that this problem is in L. Hint: Each opening parentheses ( or [ has a “closing partner” ) or ]. Ensure that the type of each opening is the same as the type of its closing partner. Since the only goal is to minimize space, consider a time-inefficient solution that repeats work you’ve already done.
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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Suppose we are given a string of parentheses. First show that telling whether they are properly
matched and nested, such as (()()) or ((()))() but not ()) or ())((), is in L.
Now suppose there are two types of parentheses, round ones and square brackets. We wish to
know if they are properly nested: for instance, ([])[] and [()[]] are allowed, but ([)] is not.
Show that this problem is in L.
Hint: Each opening parentheses ( or [ has a “closing partner” ) or ]. Ensure that the type
of each opening is the same as the type of its closing partner. Since the only goal is to minimize
space, consider a time-inefficient solution that repeats work you’ve already done.
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