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

Description

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

 

Solutions

Solution: Math

• Time complexity: O(n²)
• Space complexity: O(1)

 

JavaScript

/**
 * @param {number[]} nums
 * @return {number}
 */
const minOperations = function (nums) {
  const n = nums.length;
  const ones = nums.filter(num => num === 1).length;

  if (ones) {
    return n - ones;
  }

  let minOperations = Number.MAX_SAFE_INTEGER;

  const gcd = (a, b) => (b ? gcd(b, a % b) : a);

  const getOperations = (start, current) => {
    for (let index = start; index < n; index++) {
      current = gcd(current, nums[index]);

      if (current === 1) {
        return index - start - 1;
      }
    }

    return Number.MAX_SAFE_INTEGER;
  };

  for (let index = 0; index < n; index++) {
    const operations = getOperations(index, 0);

    minOperations = Math.min(operations, minOperations);
  }

  return minOperations === Number.MAX_SAFE_INTEGER ? -1 : minOperations + n;
};