You are given a 0-indexed integer array tasks, where tasks[i] represents the difficulty level of a task. In each round, you can complete either 2 or 3 tasks of the same difficulty level.

Return the minimum rounds required to complete all the tasks, or -1 if it is not possible to complete all the tasks.

Example 1:

Input: tasks = [2,2,3,3,2,4,4,4,4,4]
Output: 4
Explanation: To complete all the tasks, a possible plan is:
- In the first round, you complete 3 tasks of difficulty level 2.
- In the second round, you complete 2 tasks of difficulty level 3.
- In the third round, you complete 3 tasks of difficulty level 4.
- In the fourth round, you complete 2 tasks of difficulty level 4.
It can be shown that all the tasks cannot be completed in fewer than 4 rounds, so the answer is 4.


Example 2:

Input: tasks = [2,3,3]
Output: -1
Explanation: There is only 1 task of difficulty level 2, but in each round, you can only complete either 2 or 3 tasks of the same difficulty level. Hence, you cannot complete all the tasks, and the answer is -1.


Constraints:

• 1 <= tasks.length <= 105
• 1 <= tasks[i] <= 109

## Solution: Math

Count the frequency of each level. The only case that can not be finished is 1 task at some level. Otherwise we can always finish it by 2, 3 tasks at a time.

if n = 2: 2 => 1 round
if n = 3: 3 => 1 round
if n = 4: 2 + 2 => 2 rounds
if n = 5: 3 + 2 => 2 rounds

if n = 3k, n % 3 == 0 : 3 + 3 + … + 3 = k rounds
if n = 3k + 1, n % 3 == 1 : 3*(k – 1) + 2 + 2 = k + 1 rounds
if n = 3k + 2, n % 3 == 2 : 3*k + 2 = k + 1 rounds

We need (n + 2) / 3 rounds.

Time complexity: O(n)
Space complexity: O(n)

## C++

If you like my articles / videos, donations are welcome.

Buy anything from Amazon to support our website

Paypal
Venmo
huahualeetcode