minimum-number-of-operations-to-make-all-array-elements-equal-to-1.cpp

// Time:  O(n^2)
// Space: O(1)

// math, number theory, constructive algorithms
class Solution {
public:
    int minOperations(vector<int>& nums) {
        static const int INF = numeric_limits<int>::max();

        const int cnt = count(cbegin(nums), cend(nums), 1);
        if (cnt) {
            return size(nums) - cnt;
        }
        int result = INF;
        for (int i = 0; i < size(nums); ++i) {
            int g = nums[i];
            for (int j = i + 1; j < size(nums); ++j) {
                g = gcd(g, nums[j]);
                if (g == 1) {
                    result = min(result, j - i);
                    break;
                }
            }
        }
        return result != INF ? result + (size(nums) - 1) : -1;
    }
};