count-palindromic-subsequences

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Algorithms

Given a string of digits <code>s</code>, return the number of palindromic subsequences of <code>s</code> having length <code>5</code>. Since the answer may be very large, return it modulo <code>109 + 7</code>.

Note:

<ul>
	<li>A string is palindromic if it reads the same forward and backward.</li>
	<li>A subsequence is a string that can be derived from another string by deleting some or no characters without changing the order of the remaining characters.</li>
</ul>

&nbsp;
Example 1:

<pre>
Input: s = &quot;103301&quot;
Output: 2
Explanation: 
There are 6 possible subsequences of length 5: &quot;10330&quot;,&quot;10331&quot;,&quot;10301&quot;,&quot;10301&quot;,&quot;13301&quot;,&quot;03301&quot;. 
Two of them (both equal to &quot;10301&quot;) are palindromic.
</pre>

Example 2:

<pre>
Input: s = &quot;0000000&quot;
Output: 21
Explanation: All 21 subsequences are &quot;00000&quot;, which is palindromic.
</pre>

Example 3:

<pre>
Input: s = &quot;9999900000&quot;
Output: 2
Explanation: The only two palindromic subsequences are &quot;99999&quot; and &quot;00000&quot;.
</pre>

&nbsp;
Constraints:

<ul>
	<li><code>1 &lt;= s.length &lt;= 104</code></li>
	<li><code>s</code> consists of digits.</li>
</ul>

countPalindromes

Count Palindromic Subsequences

Arithmetic Slices II - Subsequence

arithmetic-slices-ii-subsequence

等差数列划分 II - 子序列

Count Different Palindromic Subsequences

count-different-palindromic-subsequences

统计不同回文子序列

Unique Length-3 Palindromic Subsequences

unique-length-3-palindromic-subsequences

长度为 3 的不同回文子序列

String

Dynamic Programming

给你数字字符串&nbsp;<code>s</code>&nbsp;，请你返回&nbsp;<code>s</code>&nbsp;中长度为&nbsp;<code>5</code>&nbsp;的 回文子序列&nbsp;数目。由于答案可能很大，请你将答案对&nbsp;<code>109 + 7</code>&nbsp;取余&nbsp;后返回。

提示：

<ul>
	<li>如果一个字符串从前往后和从后往前读相同，那么它是 回文字符串&nbsp;。</li>
	<li>子序列是一个字符串中删除若干个字符后，不改变字符顺序，剩余字符构成的字符串。</li>
</ul>

&nbsp;

示例 1：

<pre>输入：s = "103301"
输出：2
解释：
总共有 6 长度为 5 的子序列："10330" ，"10331" ，"10301" ，"10301" ，"13301" ，"03301" 。
它们中有两个（都是 "10301"）是回文的。
</pre>

示例 2：

<pre>输入：s = "0000000"
输出：21
解释：所有 21 个长度为 5 的子序列都是 "00000" ，都是回文的。
</pre>

示例 3：

<pre>输入：s = "9999900000"
输出：2
解释：仅有的两个回文子序列是 "99999" 和 "00000" 。
</pre>

&nbsp;

提示：

<ul>
	<li><code>1 &lt;= s.length &lt;= 104</code></li>
	<li><code>s</code>&nbsp;只包含数字字符。</li>
</ul>