Create 2709-greatest-common-divisor-traversal.js

Author: everthis

2709-greatest-common-divisor-traversal.js

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+// max number in `nums` is 10^5. Only need primes up to sqrt(10^5) = 316
+const primes = [
+  2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71,
+  73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151,
+  157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233,
+  239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313,
+]
+
+/**
+ * @param {number[]} nums
+ * @return {boolean}
+ */
+const canTraverseAllPairs = function(nums) {
+  const n = nums.length
+  const uf = new Array(n).fill(-1)
+  const primeIdxs = {}
+
+  const find = (i) => (uf[i] < 0 ? i : find(uf[i]))
+
+  nums.forEach((num, i) => {
+    // find all prime factors of num
+    let primeFactors = []
+    for (let p of primes) {
+      if (num % p === 0) {
+        primeFactors.push(p)
+        while (num % p === 0) num = Math.floor(num / p)
+      }
+    }
+
+    if (num !== 1) primeFactors.push(num)
+
+    for (let factor of primeFactors) {
+      if (factor in primeIdxs) {
+        let pi = find(i)
+        let pj = find(primeIdxs[factor])
+        // union if not already merged
+        if (pi !== pj) {
+          if (uf[pi] > uf[pj]) [pi, pj] = [pj, pi]
+          uf[pi] += uf[pj]
+          uf[pj] = pi
+        }
+      } else primeIdxs[factor] = i
+    }
+  })
+
+  return Math.abs(Math.min(...uf)) === n
+};