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2644. Find the Maximum Divisibility Score

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Description

You are given two 0-indexed 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 there is more than one integer with the maximum score, return the minimum of them.

 

Example 1:

Input: nums = [4,7,9,3,9], divisors = [5,2,3]
Output: 3
Explanation: The divisibility score for every element in divisors is:
The divisibility score of divisors[0] is 0 since no number in nums is divisible by 5.
The divisibility score of divisors[1] is 1 since 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.
Since divisors[2] has the maximum divisibility score, we return it.

Example 2:

Input: nums = [20,14,21,10], divisors = [5,7,5]
Output: 5
Explanation: The divisibility score for every element in divisors is:
The divisibility score of divisors[0] is 2 since nums[0] and nums[3] are divisible by 5.
The divisibility score of divisors[1] is 2 since nums[1] and nums[2] are divisible by 7.
The divisibility score of divisors[2] is 2 since nums[0] and nums[3] are divisible by 5.
Since divisors[0], divisors[1], and divisors[2] all have the maximum divisibility score, we return the minimum of them (i.e., divisors[2]).

Example 3:

Input: nums = [12], divisors = [10,16]
Output: 10
Explanation: The divisibility score for every element in divisors is:
The divisibility score of divisors[0] is 0 since no number in nums is divisible by 10.
The divisibility score of divisors[1] is 0 since no number in nums is divisible by 16.
Since divisors[0] and divisors[1] both have the maximum divisibility score, we return the minimum of them (i.e., divisors[0]).

 

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 $O(1)$.

class Solution:
    def maxDivScore(self, nums: List[int], divisors: List[int]) -> int:
        ans, mx = divisors[0], 0
        for div in divisors:
            cnt = sum(x % div == 0 for x in nums)
            if mx < cnt:
                mx, ans = cnt, div
            elif mx == cnt and ans > div:
                ans = div
        return ans

class Solution {
    public int maxDivScore(int[] nums, int[] divisors) {
        int ans = divisors[0];
        int mx = 0;
        for (int div : divisors) {
            int cnt = 0;
            for (int x : nums) {
                if (x % div == 0) {
                    ++cnt;
                }
            }
            if (mx < cnt) {
                mx = cnt;
                ans = div;
            } else if (mx == cnt) {
                ans = Math.min(ans, div);
            }
        }
        return ans;
    }
}

class Solution {
public:
    int maxDivScore(vector<int>& nums, vector<int>& divisors) {
        int ans = divisors[0];
        int mx = 0;
        for (int div : divisors) {
            int cnt = 0;
            for (int x : nums) {
                cnt += x % div == 0;
            }
            if (mx < cnt) {
                mx = cnt;
                ans = div;
            } else if (mx == cnt) {
                ans = min(ans, div);
            }
        }
        return ans;
    }
};

func maxDivScore(nums []int, divisors []int) int {
	ans, mx := divisors[0], 0
	for _, div := range divisors {
		cnt := 0
		for _, x := range nums {
			if x%div == 0 {
				cnt++
			}
		}
		if mx < cnt {
			ans, mx = div, cnt
		} else if mx == cnt && ans > div {
			ans = div
		}
	}
	return ans
}

function maxDivScore(nums: number[], divisors: number[]): number {
    let ans: number = divisors[0];
    let mx: number = 0;
    for (const div of divisors) {
        const cnt = nums.reduce((a, b) => a + (b % div == 0 ? 1 : 0), 0);
        if (mx < cnt) {
            mx = cnt;
            ans = div;
        } else if (mx === cnt && ans > div) {
            ans = div;
        }
    }
    return ans;
}

impl Solution {
    pub fn max_div_score(nums: Vec<i32>, divisors: Vec<i32>) -> i32 {
        let mut ans = divisors[0];
        let mut mx = 0;

        for &div in &divisors {
            let mut cnt = 0;

            for &n in &nums {
                if n % div == 0 {
                    cnt += 1;
                }
            }

            if cnt > mx || (cnt >= mx && div < ans) {
                mx = cnt;
                ans = div;
            }
        }

        ans
    }
}