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

Author: everthis

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

@@ -3,25 +3,92 @@
  * @return {boolean}
  */
 const gcdSort = function(nums) {
-  const spf = Array(nums.length).fill(0)
-         let maxNum = Math.max(...nums);
-        sieve(maxNum);
+  const n = nums.length
+  const maxNum = Math.max(...nums);
+  const spf = sieve(maxNum);
+
+  const uf = new UnionFind(maxNum + 1)
+  for(const e of nums) {
+    for(const f of getFactors(e)) uf.union(e, f)
+  }
+  const clone = nums.slice()
+  clone.sort((a, b) => a - b)
 
-        const uf = new UnionFind(maxNum+1);
-        for (let x of nums) {
-            for (let f of getFactors(x)) uf.union(f, x);          
+  for(let i = 0; i < n; i++) {
+    if(uf.find(nums[i]) !== uf.find(clone[i])) return false
+  }
+  
+  return true
+
+  function sieve(n) { // O(Nlog(logN)) ~ O(N)
+    const res = [0, 0]
+    for (let i = 2; i <= n; ++i) res[i] = i;
+    for (let i = 2; i * i <= n; i++) {
+      if (res[i] != i) continue; // skip if `i` is not a prime number
+      for (let j = i * i; j <= n; j += i) {
+        if (res[j] == j) { // marking spf[j] if it is not previously marked
+          res[j] = i;
         }
+      }
+    }
+    return res
+  }
+  
+  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);
+}
 
-        const sortedArr = nums.slice();
-        sortedArr.sort((a, b) => a - b)
+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;
+    }
+};
 
-        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;
+// another
+
+/**
+ * @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;