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.
Example 1:
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.
Example 2:
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.
Example 3:
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.
Constraints:
m == rolls.length1 <= n, m <= 1051 <= rolls[i], mean <= 6class Solution {
public int[] missingRolls(int[] rolls, int mean, int n) {
int m = rolls.length, runningSum = 0, expectedSum = mean * (m + n);
for (int r : rolls)
runningSum += r;
int diff = expectedSum - runningSum;
if (diff < n || diff > 6 * n)
return new int[0];
int[] ans = new int[n];
Arrays.fill(ans, 1);
diff -= n;
int sixes = diff / 5;
for (int i = 0; i < sixes; i++)
ans[i] = 6;
ans[n - 1] += diff % 5;
return ans;
}
}