From cfd09b680867ee962be94e36bcb693cd072c194c Mon Sep 17 00:00:00 2001
From: Shahriar Shatil <52494840+ShatilKhan@users.noreply.github.com>
Date: Sun, 25 Feb 2024 16:38:04 +0600
Subject: [PATCH] Time: 367 ms (60.00%) | Memory: 68.3 MB (60.00%) - LeetSync

---
 .../greatest-common-divisor-traversal.js      | 58 +++++++++++++++++++
 1 file changed, 58 insertions(+)
 create mode 100644 2827-greatest-common-divisor-traversal/greatest-common-divisor-traversal.js

diff --git a/2827-greatest-common-divisor-traversal/greatest-common-divisor-traversal.js b/2827-greatest-common-divisor-traversal/greatest-common-divisor-traversal.js
new file mode 100644
index 0000000..7fc073f
--- /dev/null
+++ b/2827-greatest-common-divisor-traversal/greatest-common-divisor-traversal.js
@@ -0,0 +1,58 @@
+/**
+ * @param {number[]} nums
+ * @return {boolean}
+ */
+var canTraverseAllPairs = function(nums) {
+    const numElements = nums.length;
+    if (numElements === 1) return true;
+    
+    const disjointSet = Array.from({ length: numElements }, (_, index) => index);
+    const setSize = Array(numElements).fill(1);
+    const factorFirstOccurrence = new Map();
+    
+    function findSetLeader(x) {
+        if (disjointSet[x] === x) return x;
+        disjointSet[x] = findSetLeader(disjointSet[x]);
+        return disjointSet[x];
+    }
+    
+    function unionSets(x, y) {
+        const xLeader = findSetLeader(x);
+        const yLeader = findSetLeader(y);
+        if (xLeader === yLeader) return;
+        if (setSize[xLeader] < setSize[yLeader]) {
+            disjointSet[xLeader] = yLeader;
+            setSize[yLeader] += setSize[xLeader];
+        } else {
+            disjointSet[yLeader] = xLeader;
+            setSize[xLeader] += setSize[yLeader];
+        }
+    }
+    
+    for (let i = 0; i < numElements; i++) {
+        let num = nums[i];
+        let divisor = 2;
+        while (divisor * divisor <= num) {
+            if (num % divisor === 0) {
+                if (factorFirstOccurrence.has(divisor)) {
+                    unionSets(i, factorFirstOccurrence.get(divisor));
+                } else {
+                    factorFirstOccurrence.set(divisor, i);
+                }
+                while (num % divisor === 0) {
+                    num /= divisor;
+                }
+            }
+            divisor++;
+        }
+        if (num > 1) {
+            if (factorFirstOccurrence.has(num)) {
+                unionSets(i, factorFirstOccurrence.get(num));
+            } else {
+                factorFirstOccurrence.set(num, i);
+            }
+        }
+    }
+    
+    return setSize[findSetLeader(0)] === numElements;
+};
\ No newline at end of file