2654 - Minimum Number of Operations to Make All Array Elements Equal to 1\.

Medium

You are given a 0-indexed array nums consisiting of positive integers. You can do the following operation on the array any number of times:

• Select an index i such that 0 <= i < n - 1 and replace either of nums[i] or nums[i+1] with their gcd value.

Return the minimum number of operations to make all elements of nums equal to 1. If it is impossible, return -1.

The gcd of two integers is the greatest common divisor of the two integers.

Example 1:

Input: nums = 2,6,3,4

Output: 4

Explanation: We can do the following operations:

• Choose index i = 2 and replace nums2 with gcd(3,4) = 1. Now we have nums = 2,6,1,4.

• Choose index i = 1 and replace nums1 with gcd(6,1) = 1. Now we have nums = 2,1,1,4.

• Choose index i = 0 and replace nums0 with gcd(2,1) = 1. Now we have nums = 1,1,1,4.

• Choose index i = 2 and replace nums3 with gcd(1,4) = 1. Now we have nums = 1,1,1,1.

Example 2:

Input: nums = 2,10,6,14

Output: -1

Explanation: It can be shown that it is impossible to make all the elements equal to 1.

Constraints:

• 2 <= nums.length <= 50

• <code>1 <= numsi<= 10⁶</code>

Follow-up:

The O(n) time complexity solution works, but could you find an O(1) constant time complexity solution?