Question

2344. Minimum Deletions to Make Array Divisible

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Description

You are given two positive integer arrays nums and numsDivide. You can delete any number of elements from nums.

Return _the minimum number of deletions such that the smallest element in _nums_ divides all the elements of _numsDivide. If this is not possible, return -1.

Note that an integer x divides y if y % x == 0.

 

Example 1:

Input: nums = [2,3,2,4,3], numsDivide = [9,6,9,3,15]
Output: 2
Explanation: 
The smallest element in [2,3,2,4,3] is 2, which does not divide all the elements of numsDivide.
We use 2 deletions to delete the elements in nums that are equal to 2 which makes nums = [3,4,3].
The smallest element in [3,4,3] is 3, which divides all the elements of numsDivide.
It can be shown that 2 is the minimum number of deletions needed.

Example 2:

Input: nums = [4,3,6], numsDivide = [8,2,6,10]
Output: -1
Explanation: 
We want the smallest element in nums to divide all the elements of numsDivide.
There is no way to delete elements from nums to allow this.

 

Constraints:

• 1 <= nums.length, numsDivide.length <= 105
• 1 <= nums[i], numsDivide[i] <= 109

Solutions

Solution 1

class Solution:
  def minOperations(self, nums: List[int], numsDivide: List[int]) -> int:
    x = numsDivide[0]
    for v in numsDivide[1:]:
      x = gcd(x, v)
    nums.sort()
    for i, v in enumerate(nums):
      if x % v == 0:
        return i
    return -1

class Solution {
  public int minOperations(int[] nums, int[] numsDivide) {
    int x = 0;
    for (int v : numsDivide) {
      x = gcd(x, v);
    }
    Arrays.sort(nums);
    for (int i = 0; i < nums.length; ++i) {
      if (x % nums[i] == 0) {
        return i;
      }
    }
    return -1;
  }

  private int gcd(int a, int b) {
    return b == 0 ? a : gcd(b, a % b);
  }
}

class Solution {
public:
  int minOperations(vector<int>& nums, vector<int>& numsDivide) {
    int x = 0;
    for (int& v : numsDivide) {
      x = gcd(x, v);
    }
    sort(nums.begin(), nums.end());
    for (int i = 0; i < nums.size(); ++i) {
      if (x % nums[i] == 0) {
        return i;
      }
    }
    return -1;
  }
};

func minOperations(nums []int, numsDivide []int) int {
  x := 0
  for _, v := range numsDivide {
    x = gcd(x, v)
  }
  sort.Ints(nums)
  for i, v := range nums {
    if x%v == 0 {
      return i
    }
  }
  return -1
}

func gcd(a, b int) int {
  if b == 0 {
    return a
  }
  return gcd(b, a%b)
}

Solution 2

class Solution:
  def minOperations(self, nums: List[int], numsDivide: List[int]) -> int:
    x = gcd(*numsDivide)
    nums.sort()
    return next((i for i, v in enumerate(nums) if x % v == 0), -1)

class Solution {
  public int minOperations(int[] nums, int[] numsDivide) {
    int x = 0;
    for (int v : numsDivide) {
      x = gcd(x, v);
    }
    int y = 1 << 30;
    for (int v : nums) {
      if (x % v == 0) {
        y = Math.min(y, v);
      }
    }
    if (y == 1 << 30) {
      return -1;
    }
    int ans = 0;
    for (int v : nums) {
      if (v < y) {
        ++ans;
      }
    }
    return ans;
  }

  private int gcd(int a, int b) {
    return b == 0 ? a : gcd(b, a % b);
  }
}

class Solution {
public:
  int minOperations(vector<int>& nums, vector<int>& numsDivide) {
    int x = 0;
    for (int& v : numsDivide) {
      x = gcd(x, v);
    }
    int y = 1 << 30;
    for (int& v : nums) {
      if (x % v == 0) {
        y = min(y, v);
      }
    }
    if (y == 1 << 30) {
      return -1;
    }
    int ans = 0;
    for (int& v : nums) {
      ans += v < y;
    }
    return ans;
  }
};

func minOperations(nums []int, numsDivide []int) int {
  x := 0
  for _, v := range numsDivide {
    x = gcd(x, v)
  }
  y := 1 << 30
  for _, v := range nums {
    if x%v == 0 {
      y = min(y, v)
    }
  }
  if y == 1<<30 {
    return -1
  }
  ans := 0
  for _, v := range nums {
    if v < y {
      ans++
    }
  }
  return ans
}

func gcd(a, b int) int {
  if b == 0 {
    return a
  }
  return gcd(b, a%b)
}

Solution 3

class Solution:
  def minOperations(self, nums: List[int], numsDivide: List[int]) -> int:
    x = gcd(*numsDivide)
    y = min((v for v in nums if x % v == 0), default=0)
    return sum(v < y for v in nums) if y else -1