{ "data": { "question": { "questionId": "3607", "questionFrontendId": "3326", "categoryTitle": "Algorithms", "boundTopicId": 2955549, "title": "Minimum Division Operations to Make Array Non Decreasing", "titleSlug": "minimum-division-operations-to-make-array-non-decreasing", "content": "
You are given an integer array nums
.
Any positive divisor of a natural number x
that is strictly less than x
is called a proper divisor of x
. For example, 2 is a proper divisor of 4, while 6 is not a proper divisor of 6.
You are allowed to perform an operation any number of times on nums
, where in each operation you select any one element from nums
and divide it by its greatest proper divisor.
Return the minimum number of operations required to make the array non-decreasing.
\n\nIf it is not possible to make the array non-decreasing using any number of operations, return -1
.
\n
Example 1:
\n\nInput: nums = [25,7]
\n\nOutput: 1
\n\nExplanation:
\n\nUsing a single operation, 25 gets divided by 5 and nums
becomes [5, 7]
.
Example 2:
\n\nInput: nums = [7,7,6]
\n\nOutput: -1
\nExample 3:
\n\nInput: nums = [1,1,1,1]
\n\nOutput: 0
\n\n
Constraints:
\n\n1 <= nums.length <= 105
1 <= nums[i] <= 106
给你一个整数数组 nums
。
一个正整数 x
的任何一个 严格小于 x
的 正 因子都被称为 x
的 真因数 。比方说 2 是 4 的 真因数,但 6 不是 6 的 真因数。
你可以对 nums
的任何数字做任意次 操作 ,一次 操作 中,你可以选择 nums
中的任意一个元素,将它除以它的 最大真因数 。
你的目标是将数组变为 非递减 的,请你返回达成这一目标需要的 最少操作 次数。
\n\n如果 无法 将数组变成非递减的,请你返回 -1
。
\n\n
示例 1:
\n\n输入:nums = [25,7]
\n\n输出:1
\n\n解释:
\n\n通过一次操作,25 除以 5 ,nums
变为 [5, 7]
。
示例 2:
\n\n输入:nums = [7,7,6]
\n\n输出:-1
\n示例 3:
\n\n输入:nums = [1,1,1,1]
\n\n输出:0
\n\n\n
提示:
\n\n1 <= nums.length <= 105
1 <= nums[i] <= 106
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