Find Missing Observations

// https://leetcode.com/problems/find-missing-observations/description/

/*
You have observations of n + m 6-sided dice rolls with each face numbered from 1 to 6. 
n of the observations went missing, and you only have the observations of m rolls. 
Fortunately, you have also calculated the average value of the n + m rolls.
You are given an integer array rolls of length m where rolls[i] is the value of the ith observation. 
You are also given the two integers mean and n.
Return an array of length n containing the missing observations such that the average value of the n + m rolls is exactly mean.
If there are multiple valid answers, return any of them. If no such array exists, return an empty array.

The average value of a set of k numbers is the sum of the numbers divided by k.
Note that mean is an integer, so the sum of the n + m rolls should be divisible by n + m.

Ex1:
Input: rolls = [3,2,4,3], mean = 4, n = 2
Output: [6,6]
Explanation: The mean of all n + m rolls is (3 + 2 + 4 + 3 + 6 + 6) / 6 = 4.

Ex2:
Input: rolls = [1,5,6], mean = 3, n = 4
Output: [2,3,2,2]
Explanation: The mean of all n + m rolls is (1 + 5 + 6 + 2 + 3 + 2 + 2) / 7 = 3.

Ex3:
Input: rolls = [1,2,3,4], mean = 6, n = 4
Output: []
Explanation: It is impossible for the mean to be 6 no matter what the 4 missing rolls are.

*/

#include <vector>

using namespace std;

// Time: O(n), Space: O(n)
vector<int> missingRolls(vector<int>& rolls, int mean, int n) {
    int curSum = accumulate(rolls.begin(), rolls.end(), 0), m = rolls.size();
    int missingSum = mean * (n + m) - curSum;
    if (missingSum < n || missingSum > 6 * n) return {};

    int part = missingSum / n, rem = missingSum % n;
    vector<int> ans(n, part);
    for (int i = 0; i < rem; ++i)
        ++ans[i];
    return ans;
}```