1250. Check If It Is a Good Array

Given an array nums of positive integers. Your task is to select some subset of nums, multiply each element by an integer and add all these numbers. The array is said to be good if you can obtain a sum of 1 from the array by any possible subset and multiplicand.

Return True if the array is good otherwise return False.

Example 1:

Input: nums = [12,5,7,23]
Output: true
Explanation: Pick numbers 5 and 7.
5*3 + 7*(-2) = 1

Example 2:

Input: nums = [29,6,10]
Output: true
Explanation: Pick numbers 29, 6 and 10.
29*1 + 6*(-3) + 10*(-1) = 1

Example 3:

Input: nums = [3,6]
Output: false

Constraints:

• 1 <= nums.length <= 10^5

• 1 <= nums[i] <= 10^9

對任意整數x, y，可以利用任意整數a, b使得ax + by = gcd(x, y)

bool isGoodArray(vector<int>& nums) {
    int x = nums[0], y;
    for (int num : nums) {
        while (num > 0) {
            y = x % num;
            x = num;
            num = y;
        }
    }
    return x == 1;
}

bool isGoodArray(vector<int>& nums) {
    int res = nums[0];
    for (int num : nums) {
        res = gcd(res, num);
    }
    return res == 1;
}