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

Problem Link

Description

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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 nums[2] with gcd(3,4) = 1. Now we have nums = [2,6,1,4].
- Choose index i = 1 and replace nums[1] with gcd(6,1) = 1. Now we have nums = [2,1,1,4].
- Choose index i = 0 and replace nums[0] with gcd(2,1) = 1. Now we have nums = [1,1,1,4].
- Choose index i = 2 and replace nums[3] 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
• 1 <= nums[i] <= 106

Solution

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Python3

class Solution:
    def minOperations(self, nums: List[int]) -> int:
        N = len(nums)
        ones = nums.count(1)
        ans = inf
 
        if ones > 0: return N - ones
 
        for i in range(N):
            g = nums[i]
            for j in range(i + 1, N):
                g = gcd(g, nums[j])
 
                if g == 1:
                    ans = min(ans, j - i)
                    break
            
            if g != 1: break
        
        return -1 if ans == inf else N + ans - 1