Create 1998-gcd-sort-of-an-array.js

Author: everthis

1998-gcd-sort-of-an-array.js

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+/**
+ * @param {number[]} nums
+ * @return {boolean}
+ */
+const gcdSort = function(nums) {
+  const spf = Array(nums.length).fill(0)
+         let maxNum = Math.max(...nums);
+        sieve(maxNum);
+
+        const uf = new UnionFind(maxNum+1);
+        for (let x of nums) {
+            for (let f of getFactors(x)) uf.union(f, x);          
+        }
+
+
+        const sortedArr = nums.slice();
+        sortedArr.sort((a, b) => a - b)
+
+        for (let i = 0; i < nums.length; ++i) {
+            let pu = uf.find(sortedArr[i]);
+            let pv = uf.find(nums[i]);
+            if (pu != pv) return false; // can't swap nums[i] with sortedArr[i]
+        }
+        return true;
+  
+  function sieve( n) { // O(Nlog(logN)) ~ O(N)
+    for (let i = 2; i <= n; ++i) spf[i] = i;
+    for (let i = 2; i * i <= n; i++) {
+      if (spf[i] != i) continue; // skip if `i` is not a prime number
+      for (let j = i * i; j <= n; j += i) {
+        if (spf[j] == j) { // marking spf[j] if it is not previously marked
+          spf[j] = i;
+        }
+      }
+    }
+  }
+  
+  function getFactors(n) { // O(logN)
+    const factors = [];
+    while (n > 1) {
+      factors.push(spf[n]);
+      n = ~~(n /spf[n]);
+    }
+    return factors;
+  }
+};
+
+function gcd( x,  y) {
+    return y == 0 ? x : gcd(y, x % y);
+}
+
+class UnionFind {
+    constructor(n) {
+        this.parent = [];
+        for (let i = 0; i < n; i++) this.parent[i] = i;
+    }
+    find(x) {
+        if (x == this.parent[x]) return x;
+        return this.parent[x] = this.find(this.parent[x]); // Path compression
+    }
+    union( u,  v) {
+        let pu = this.find(u), pv = this.find(v);
+        if (pu != pv) this.parent[pu] = pv;
+    }
+};
+