历史的进程 Week 1: 从 C 到 C++ —— STL的应用

C. Balanced Brackets

单点时限: 2.0 sec

内存限制: 256 MB

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 (, [, or { occurs to the left of a closing bracket ), ], 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, ].

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.


The first line contains a single integer, $n$, denoting the number of strings.

Each line $i$ of the $n$ subsequent lines consists of a single string, $s$, denoting a sequence of brackets.

  • $1 \leq n \leq 10^3$
  • $1 \leq len_s \leq 10^3$, where $len_s$ is the length of the sequence.
  • Each character in the sequence will be a bracket (i.e., {, }, (, ), [, and ]).


For each string, print whether or not the string of brackets is balanced on a new line. If the brackets are balanced, print YES; otherwise, print NO.




  1. The string {[()]} meets both criteria for being a balanced string, so we print YES on a new line.

  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, so we print YES on a new line.