2028. Find Missing Observations - Explanation

1. Math - I

class Solution:
    def missingRolls(self, rolls: List[int], mean: int, n: int) -> List[int]:
        m = len(rolls)
        nTotal = (mean * (n + m)) - sum(rolls)

        if nTotal < n or nTotal > n * 6:
            return []

        res = []
        while nTotal:
            dice = min(nTotal - n + 1, 6)
            res.append(dice)
            nTotal -= dice
            n -= 1
        return res

Time & Space Complexity

Time complexity: $O(m + n)$
Space complexity:
- $O(1)$ extra space.
- $O(n)$ space for the output array.

Where $m$ is the size of the array $rolls$ and $n$ is the number of missing observations.

2. Math - II

class Solution:
    def missingRolls(self, rolls: List[int], mean: int, n: int) -> List[int]:
        m = len(rolls)
        nTotal = (mean * (n + m)) - sum(rolls)

        if nTotal < n or nTotal > n * 6:
            return []

        avg = nTotal // n
        rem = nTotal - (avg * n)
        return [avg] * (n - rem) + [avg + 1] * rem

Time & Space Complexity

Time complexity: $O(m + n)$
Space complexity:
- $O(1)$ extra space.
- $O(n)$ space for the output array.

Where $m$ is the size of the array $rolls$ and $n$ is the number of missing observations.