Create 2709. Greatest Common Divisor Traversal (#417)

Author: Chayandas07

2709. Greatest Common Divisor Traversal

@@ -0,0 +1,55 @@
+class Solution {
+public:
+    int get(vector<int> &parent, int a) {
+        return parent[a] = parent[a] == a ? a : get(parent, parent[a]);
+    }
+    void Union(vector<int> &parent, vector<int> &rank, int a, int b) {
+        a = get(parent, a);
+        b = get(parent, b);
+        if(a == b) return;
+        if(rank[a] < rank[b]) swap(a, b);
+        parent[b] = a;
+        rank[a] += rank[b];
+    }
+    vector<int> factorsCalculator(int n) {
+        vector<int> dp(n + 2);
+        iota(dp.begin(), dp.end(), 0);
+        for(int i = 2; i <= n; ++i) {
+            if(dp[i] == i) {
+                for(int j = i * 2; j <= n; j += i) {
+                    if(dp[j] == j) dp[j] = i;
+                }
+            }
+        }
+        return dp;
+    }
+    bool canTraverseAllPairs(vector<int>& nums) {
+        if(nums.size() == 1) return true;
+        int n = nums.size();
+        int maxElement = *max_element(nums.begin(), nums.end());
+        if(*min_element(nums.begin(), nums.end()) == 1) return false;
+        vector<int> factorArray = factorsCalculator(maxElement);
+
+        vector<int> parent(maxElement + 1);
+        iota(parent.begin(), parent.end(), 0);
+        ;
+        vector<int> rank(maxElement + 1, 1);
+        for(int i = 0; i < n; ++i) {
+            int x = nums[i];
+            while(x > 1) {
+                int p = factorArray[x];
+                Union(parent, rank, p, nums[i]);
+                while(x % p == 0) {
+                    x = x / p;
+                }
+            }
+        }
+
+        int p = get(parent, nums[0]);
+        for(int i = 1; i < n; ++i) {
+            if(get(parent, nums[i]) != p) return false;
+        }
+
+        return true;
+    }
+};