2644. Find the Maximum Divisibility Score
Description
You are given two integer arrays nums
and divisors
.
The divisibility score of divisors[i]
is the number of indices j
such that nums[j]
is divisible by divisors[i]
.
Return the integer divisors[i]
with the maximum divisibility score. If multiple integers have the maximum score, return the smallest one.
Example 1:
Input: nums = [2,9,15,50], divisors = [5,3,7,2]
Output: 2
Explanation:
The divisibility score of divisors[0]
is 2 since nums[2]
and nums[3]
are divisible by 5.
The divisibility score of divisors[1]
is 2 since nums[1]
and nums[2]
are divisible by 3.
The divisibility score of divisors[2]
is 0 since none of the numbers in nums
is divisible by 7.
The divisibility score of divisors[3]
is 2 since nums[0]
and nums[3]
are divisible by 2.
As divisors[0]
, divisors[1]
, and divisors[3]
have the same divisibility score, we return the smaller one which is divisors[3]
.
Example 2:
Input: nums = [4,7,9,3,9], divisors = [5,2,3]
Output: 3
Explanation:
The divisibility score of divisors[0]
is 0 since none of numbers in nums
is divisible by 5.
The divisibility score of divisors[1]
is 1 since only nums[0]
is divisible by 2.
The divisibility score of divisors[2]
is 3 since nums[2]
, nums[3]
and nums[4]
are divisible by 3.
Example 3:
Input: nums = [20,14,21,10], divisors = [10,16,20]
Output: 10
Explanation:
The divisibility score of divisors[0]
is 2 since nums[0]
and nums[3]
are divisible by 10.
The divisibility score of divisors[1]
is 0 since none of the numbers in nums
is divisible by 16.
The divisibility score of divisors[2]
is 1 since nums[0]
is divisible by 20.
Constraints:
1 <= nums.length, divisors.length <= 1000
1 <= nums[i], divisors[i] <= 109
Solutions
Solution 1: Enumeration
We can enumerate each element $div$ in $divisors$, and calculate how many elements in $nums$ can be divided by $div$, denoted as $cnt$.
- If $cnt$ is greater than the current maximum divisibility score $mx$, then update $mx = cnt$, and update $ans = div$.
- If $cnt$ equals $mx$ and $div$ is less than $ans$, then update $ans = div$.
Finally, return $ans$.
The time complexity is $O(m \times n)$, where $m$ and $n$ are the lengths of $nums$ and $divisors$ respectively. The space complexity is $O(1)$.
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