1998. GCD Sort of an Array

Description

image-20210915232017656

image-20210915232028365

Solution

Because we are using gcd to transfer numbers, so the number which shares the same factor should in the same set. So we could use Union-Find to mark numbers.

There is also a tricky point that how to get the prime factor of one number.

https://www.geeksforgeeks.org/print-all-prime-factors-of-a-given-number/

Code

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const  int N = 1E5+1;
class Solution {    
    int p[N];
    static bool cmp(int& a, int &b){return a < b;}
public:
    void merge(int a, int b){
        int x = find(a), y = find(b);
        if(x != y){
            p[x] = y;
        }
    }

    int find(int a){
        if(a != p[a]){
            p[a] = find(p[a]);
        }
        return p[a];
    }

    bool gcdSort(vector<int>& nums) {
        for(int i = 1; i < N; i++) p[i] = i;
        vector<int> nums2 = nums;
        for(int i = 0; i < nums.size(); i++){
            int tmp = nums[i];
            for(int j = 2; j <= tmp/j ; j++){
                bool flag = false;
                while(tmp % j == 0){
                    tmp /= j;
                    flag = true;
                }
                if(flag)
                    merge(nums[i], j);
            }
            if(tmp > 1)
                merge(nums[i], tmp);
        }
        sort(nums.begin(), nums.end(),cmp);
        for(int i = 0; i < nums.size(); i++){
            if(nums[i] == nums2[i])
                continue;
            if(find(nums[i]) != find(nums2[i]))
                return false;
        }
        return true;
    }
};

image-20210915235655302