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  1. Stacks: Balanced Brackets

Stacks: Balanced Brackets

A bracket is considered to be any one of the following characters: (, ), {, }, [, or ].

Two brackets are considered to be a matched pair if the an opening bracket (i.e., (, [, or {) occurs to the left of a closing bracket (i.e., ), ], or }) of the exact same type. There are three types of matched pairs of brackets: [], {}, and ().

A matching pair of brackets is not balanced if the set of brackets it encloses are not matched. For example, {[(])} is not balanced because the contents in between { and } are not balanced. The pair of square brackets encloses a single, unbalanced opening bracket, (, and the pair of parentheses encloses a single, unbalanced closing square bracket, ].

Some examples of balanced brackets are []{}(), [({})]{}() and ({(){}[]})[].

By this logic, we say a sequence of brackets is considered to be balanced if the following conditions are met:

  • It contains no unmatched brackets.
  • The subset of brackets enclosed within the confines of a matched pair of brackets is also a matched pair of brackets.

Given strings of brackets, determine whether each sequence of brackets is balanced. If a string is balanced, print YES on a new line; otherwise, print NO on a new line.

Function Description
Complete the isBalanced function in the editor below.

isBalanced has the following parameter(s):
- string expression: a string of brackets

Returns
- string: either YES or NO

Input Format

The first line contains a single integer, , the number of strings.
Each line of the subsequent lines consists of a single string, , denoting a sequence of brackets.

Constraints

  • , where is the length of the sequence.
  • Each character in the sequence will be a bracket (i.e., {, }, (, ), [, and ]).

Sample Input

STDIN           Function
-----           --------
3               t = 3
{[()]}          first expression
{[(])}          second expression
{{[[(())]]}}    third expression

Sample Output

YES
NO
YES

Explanation

  1. The string {[()]} meets both criteria for being a balanced string.
  2. The string {[(])} is not balanced, because the brackets enclosed by the matched pairs [(] and (]) are not balanced.
  3. The string {{[[(())]]}} meets both criteria for being a balanced string.