special-binary-string

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Algorithms

Special binary strings are binary strings with the following two properties:

<ul>
	<li>The number of <code>0</code>&#39;s is equal to the number of <code>1</code>&#39;s.</li>
	<li>Every prefix of the binary string has at least as many <code>1</code>&#39;s as <code>0</code>&#39;s.</li>
</ul>

You are given a special binary string <code>s</code>.

A move consists of choosing two consecutive, non-empty, special substrings of <code>s</code>, and swapping them. Two strings are consecutive if the last character of the first string is exactly one index before the first character of the second string.

Return the lexicographically largest resulting string possible after applying the mentioned operations on the string.

&nbsp;
Example 1:

<pre>
Input: s = &quot;11011000&quot;
Output: &quot;11100100&quot;
Explanation: The strings &quot;10&quot; [occuring at s[1]] and &quot;1100&quot; [at s[3]] are swapped.
This is the lexicographically largest string possible after some number of swaps.
</pre>

Example 2:

<pre>
Input: s = &quot;10&quot;
Output: &quot;10&quot;
</pre>

&nbsp;
Constraints:

<ul>
	<li><code>1 &lt;= s.length &lt;= 50</code></li>
	<li><code>s[i]</code> is either <code>&#39;0&#39;</code> or <code>&#39;1&#39;</code>.</li>
	<li><code>s</code> is a special binary string.</li>
</ul>

makeLargestSpecial

Special Binary String

Valid Parenthesis String

valid-parenthesis-string

有效的括号字符串

Number of Good Binary Strings

number-of-good-binary-strings

好二进制字符串的数量

String

Divide and Conquer

Sorting

特殊的二进制字符串 是具有以下两个性质的二进制序列：

<ul>
	<li><code>0</code> 的数量与 <code>1</code> 的数量相等。</li>
	<li>二进制序列的每一个前缀码中 <code>1</code> 的数量要大于等于 <code>0</code> 的数量。</li>
</ul>

给定一个特殊的二进制字符串&nbsp;<code>s</code>。

一次移动操作包括选择字符串 <code>s</code> 中的两个连续的、非空的、特殊子串，并交换它们。两个字符串是连续的，如果第一个字符串的最后一个字符与第二个字符串的第一个字符的索引相差正好为 1。

返回在字符串上应用任意次操作后可能得到的字典序最大的字符串。

&nbsp;

示例 1:

<pre>
输入: S = "11011000"
输出: "11100100"
解释:
将子串 "10" （在 s[1] 出现） 和 "1100" （在 s[3] 出现）进行交换。
这是在进行若干次操作后按字典序排列最大的结果。
</pre>

示例 2：

<pre>
输入：s = "10"
输出："10"
</pre>

&nbsp;

提示：

<ul>
	<li><code>1 &lt;= s.length &lt;= 50</code></li>
	<li><code>s[i]</code>&nbsp;为&nbsp;<code>'0'</code> 或&nbsp;<code>'1'</code>。</li>
	<li><code>s</code>&nbsp;是一个特殊的二进制字符串。</li>
</ul>