1760. Minimum Limit of Balls in a Bag

https://leetcode.com/problems/minimum-limit-of-balls-in-a-bag

Description

You are given an integer array nums where the ith bag contains nums[i] balls. You are also given an integer maxOperations.

You can perform the following operation at most maxOperations times:

• Take any bag of balls and divide it into two new bags with a positive number of balls.

  • For example, a bag of 5 balls can become two new bags of 1 and 4 balls, or two new bags of 2 and 3 balls.

Your penalty is the maximum number of balls in a bag. You want to minimize your penalty after the operations.

Return the minimum possible penalty after performing the operations.

Example 1:

**Input:** nums = [9], maxOperations = 2
**Output:** 3
**Explanation:** 
- Divide the bag with 9 balls into two bags of sizes 6 and 3. [**9**] -> [6,3].
- Divide the bag with 6 balls into two bags of sizes 3 and 3. [**6**,3] -> [3,3,3].
The bag with the most number of balls has 3 balls, so your penalty is 3 and you should return 3.

Example 2:

**Input:** nums = [2,4,8,2], maxOperations = 4
**Output:** 2
**Explanation:**
- Divide the bag with 8 balls into two bags of sizes 4 and 4. [2,4,**8**,2] -> [2,4,4,4,2].
- Divide the bag with 4 balls into two bags of sizes 2 and 2. [2,**4**,4,4,2] -> [2,2,2,4,4,2].
- Divide the bag with 4 balls into two bags of sizes 2 and 2. [2,2,2,**4**,4,2] -> [2,2,2,2,2,4,2].
- Divide the bag with 4 balls into two bags of sizes 2 and 2. [2,2,2,2,2,**4**,2] -> [2,2,2,2,2,2,2,2].
The bag with the most number of balls has 2 balls, so your penalty is 2 an you should return 2.

Example 3:

**Input:** nums = [7,17], maxOperations = 2
**Output:** 7

Constraints:

• 1 <= nums.length <= 105

• 1 <= maxOperations, nums[i] <= 109

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