{ "data": { "question": { "questionId": "809", "questionFrontendId": "793", "categoryTitle": "Algorithms", "boundTopicId": 1561, "title": "Preimage Size of Factorial Zeroes Function", "titleSlug": "preimage-size-of-factorial-zeroes-function", "content": "
Let f(x)
be the number of zeroes at the end of x!
. Recall that x! = 1 * 2 * 3 * ... * x
and by convention, 0! = 1
.
f(3) = 0
because 3! = 6
has no zeroes at the end, while f(11) = 2
because 11! = 39916800
has two zeroes at the end.Given an integer k
, return the number of non-negative integers x
have the property that f(x) = k
.
\n
Example 1:
\n\n\nInput: k = 0\nOutput: 5\nExplanation: 0!, 1!, 2!, 3!, and 4! end with k = 0 zeroes.\n\n\n
Example 2:
\n\n\nInput: k = 5\nOutput: 0\nExplanation: There is no x such that x! ends in k = 5 zeroes.\n\n\n
Example 3:
\n\n\nInput: k = 3\nOutput: 5\n\n\n
\n
Constraints:
\n\n0 <= k <= 109
f(x)
是 x!
末尾是 0 的数量。回想一下 x! = 1 * 2 * 3 * ... * x
,且 0! = 1
。
f(3) = 0
,因为 3! = 6
的末尾没有 0 ;而 f(11) = 2
,因为 11!= 39916800
末端有 2 个 0 。给定 k
,找出返回能满足 f(x) = k
的非负整数 x
的数量。
\n\n
示例 1:
\n\n\n输入:k = 0\n输出:5\n解释:0!, 1!, 2!, 3!, 和 4! 均符合 k = 0 的条件。\n\n\n
示例 2:
\n\n\n输入:k = 5\n输出:0\n解释:没有匹配到这样的 x!,符合 k = 5 的条件。\n\n
示例 3:
\n\n\n输入: k = 3\n输出: 5\n\n\n
\n\n
提示:
\n\n0 <= k <= 109
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