2654. Minimum Number of Operations to Make All Array Elements Equal to 1 ¶
Problem
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 that0 <= i < n - 1
and replace either ofnums[i]
ornums[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
Follow-up:
The O(n)
time complexity solution works, but could you find an O(1)
constant time complexity solution?