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1760. Minimum Limit of Balls in a Bag

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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

Solutions

Binary search.

Python3

class Solution:
    def minimumSize(self, nums: List[int], maxOperations: int) -> int:
        left, right = 1, max(nums)
        while left < right:
            mid = (left + right) >> 1
            ops = sum((num - 1) // mid for num in nums)
            if ops <= maxOperations:
                right = mid
            else:
                left = mid + 1
        return left

Java

class Solution {
    public int minimumSize(int[] nums, int maxOperations) {
        int left = 1, right = (int) 1e9;
        while (left < right) {
            int mid = (left + right) >>> 1;
            long ops = 0;
            for (int num : nums) {
                ops += (num - 1) / mid;
            }
            if (ops <= maxOperations) {
                right = mid;
            } else {
                left = mid + 1;
            }
        }
        return left;
    }
}

C++

class Solution {
public:
    int minimumSize(vector<int>& nums, int maxOperations) {
        int left = 1, right = 1e9;
        while (left < right)
        {
            int mid = left + ((right - left) >> 1);
            long long ops = 0;
            for (int num : nums) ops += (num - 1) / mid;
            if (ops <= maxOperations) right = mid;
            else left = mid + 1;
        }
        return left;
    }
};

Go

func minimumSize(nums []int, maxOperations int) int {
	left, right := 1, int(1e9)
	for left < right {
		mid := (left + right) >> 1
		var ops int
		for _, num := range nums {
			ops += (num - 1) / mid
		}
		if ops <= maxOperations {
			right = mid
		} else {
			left = mid + 1
		}
	}
	return left
}

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