2598. Smallest Missing Non-negative Integer After Operations

Problem Link

Description

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You are given a 0-indexed integer array nums and an integer value.

In one operation, you can add or subtract value from any element of nums.

• For example, if nums = [1,2,3] and value = 2, you can choose to subtract value from nums[0] to make nums = [-1,2,3].

The MEX (minimum excluded) of an array is the smallest missing non-negative integer in it.

• For example, the MEX of [-1,2,3] is 0 while the MEX of [1,0,3] is 2.

Return the maximum MEX of nums after applying the mentioned operation any number of times.

 

Example 1:

Input: nums = [1,-10,7,13,6,8], value = 5
Output: 4
Explanation: One can achieve this result by applying the following operations:
- Add value to nums[1] twice to make nums = [1,0,7,13,6,8]
- Subtract value from nums[2] once to make nums = [1,0,2,13,6,8]
- Subtract value from nums[3] twice to make nums = [1,0,2,3,6,8]
The MEX of nums is 4. It can be shown that 4 is the maximum MEX we can achieve.

Example 2:

Input: nums = [1,-10,7,13,6,8], value = 7
Output: 2
Explanation: One can achieve this result by applying the following operation:
- subtract value from nums[2] once to make nums = [1,-10,0,13,6,8]
The MEX of nums is 2. It can be shown that 2 is the maximum MEX we can achieve.

 

Constraints:

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

Solution

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Python3

class Solution:
    def findSmallestInteger(self, nums: List[int], value: int) -> int:
        N = len(nums)
        mod = [0] * value
        
        for x in nums:
            mod[x % value] += 1
        
        m = min(mod)
        
        for x in range(m * value, (m + 1) * value):
            index = x % value
            if mod[index] - m <= 0:
                return x
        
        return -1