#1819 - Number of Different Subsequences GCDs

Hard • View on LeetCode • View on GitHub

Problem Description

You are given an array nums that consists of positive integers.

The GCD of a sequence of numbers is defined as the greatest integer that divides all the numbers in the sequence evenly.

For example, the GCD of the sequence [4,6,16] is 2.

A subsequence of an array is a sequence that can be formed by removing some elements (possibly none) of the array.

For example, [2,5,10] is a subsequence of [1,2,1,2,4,1,5,10].

Return the number of different GCDs among all non-empty subsequences of nums.

Solution

/**
 * @param {number[]} nums
 * @return {number}
 */
var countDifferentSubsequenceGCDs = function(nums) {
  const maxNum = Math.max(...nums);
  const exists = new Array(maxNum + 1).fill(false);
  let result = 0;

  function gcd(a, b) {
    while (b) [a, b] = [b, a % b];
    return a;
  }

  for (const num of nums) {
    exists[num] = true;
  }

  for (let i = 1; i <= maxNum; i++) {
    let currentGcd = 0;
    for (let j = i; j <= maxNum; j += i) {
      if (exists[j]) {
        currentGcd = currentGcd ? gcd(currentGcd, j) : j;
      }
    }
    if (currentGcd === i) result++;
  }

  return result;
};