Minimum Number of Operations to Make All Array Elements Equal to 1

Difficulty: Medium
Topics: GCD, Array, Math

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🧩 Problem Statement

You are given a 0-indexed array nums consisting of positive integers.
You can perform 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.

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💡 Example 1

Input: nums = [2, 6, 3, 4]
Output: 4

Explanation:

We can do the following operations:

1. Choose index i = 2 and replace nums[2] with gcd(3, 4) = 1.
   → nums = [2, 6, 1, 4]
2. Choose index i = 1 and replace nums[1] with gcd(6, 1) = 1.
   → nums = [2, 1, 1, 4]
3. Choose index i = 0 and replace nums[0] with gcd(2, 1) = 1.
   → nums = [1, 1, 1, 4]
4. Choose index i = 2 and replace nums[3] with gcd(1, 4) = 1.
   → nums = [1, 1, 1, 1]

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💡 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.

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⚙️ Constraints

2 <= nums.length <= 50
1 <= nums[i] <= 10^6