LeetCode 2654. Minimum Number of Operations to Make All Array El

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

 其实就是判断最大公约数为1的最小数组大小。

如果存在1，那么就一定可以。

剩下就是找最大公约数了，

先写一个函数找最大公约数，也就是递归的辗转相除的方法，

再写一个函数计算每个子数组能不能实现最大公约数是1；

依次返回min值；即可；

下面是代码：

Runtime: 2 ms, faster than 59.08% of Java online submissions for Minimum Number of Operations to Make All Array Elements Equal to 1.

Memory Usage: 42.2 MB, less than 60.27% of Java online submissions for Minimum Number of Operations to Make All Array Elements Equal to 1.