preimage-size-of-factorial-zeroes-function

java

python

python3

mysql

mssql

oraclesql

csharp

javascript

typescript

bash

swift

kotlin

dart

golang

ruby

scala

rust

racket

erlang

elixir

pythondata

postgresql

cangjie

Algorithms

Let <code>f(x)</code> be the number of zeroes at the end of <code>x!</code>. Recall that <code>x! = 1 * 2 * 3 * ... * x</code> and by convention, <code>0! = 1</code>.

<ul>
	<li>For example, <code>f(3) = 0</code> because <code>3! = 6</code> has no zeroes at the end, while <code>f(11) = 2</code> because <code>11! = 39916800</code> has two zeroes at the end.</li>
</ul>

Given an integer <code>k</code>, return the number of non-negative integers <code>x</code> have the property that <code>f(x) = k</code>.

&nbsp;
Example 1:

<pre>
Input: k = 0
Output: 5
Explanation: 0!, 1!, 2!, 3!, and 4! end with k = 0 zeroes.
</pre>

Example 2:

<pre>
Input: k = 5
Output: 0
Explanation: There is no x such that x! ends in k = 5 zeroes.
</pre>

Example 3:

<pre>
Input: k = 3
Output: 5
</pre>

&nbsp;
Constraints:

<ul>
	<li><code>0 &lt;= k &lt;= 109</code></li>
</ul>

preimageSizeFZF

Preimage Size of Factorial Zeroes Function

Factorial Trailing Zeroes

factorial-trailing-zeroes

阶乘后的零

Math

Binary Search

&nbsp;<code>f(x)</code>&nbsp;是&nbsp;<code>x!</code>&nbsp;末尾是 0 的数量。回想一下&nbsp;<code>x! = 1 * 2 * 3 * ... * x</code>，且 <code>0! = 1</code>&nbsp;。

<ul>
	<li>例如，&nbsp;<code>f(3) = 0</code>&nbsp;，因为 <code>3! = 6</code> 的末尾没有 0 ；而 <code>f(11) = 2</code>&nbsp;，因为 <code>11!= 39916800</code> 末端有 2 个 0 。</li>
</ul>

给定&nbsp;<code>k</code>，找出返回能满足 <code>f(x) = k</code>&nbsp;的非负整数 <code>x</code>&nbsp;的数量。

&nbsp;

示例 1： 

<pre>
输入：k = 0
输出：5
解释：0!, 1!, 2!, 3!, 和 4!&nbsp;均符合 k = 0 的条件。
</pre>

示例 2：

<pre>
输入：k = 5
输出：0
解释：没有匹配到这样的 x!，符合 k = 5 的条件。</pre>

示例 3:

<pre>
输入: k = 3
输出: 5
</pre>

&nbsp;

提示:

<ul>
	<li><code>0 &lt;= k &lt;= 109</code></li>
</ul>