# Program to find minimum limit of balls in a bag in Python

PythonServer Side ProgrammingProgramming

Suppose we have an array nums where the ith element indicates a bag containing nums[i] number of balls. We also have another value called mx. We can perform the following operation at most mx times −

• Select any bag of balls and divide it into two new bags with at least one ball.

• Here penalty is the maximum number of balls in a bag.

We have to minimize the penalty after the operations. So finally, we have to find the minimum possible penalty after performing the operations.

So, if the input is like nums = [4,8,16,4], mx = 4, then the output will be 4 because we can perform following operations: Initially we have bags like [4,8,16,4], split bag with 16 balls like [4,8,8,8,4], then for each each bag with 8 balls, divide them into two bags with 4 balls each, so array will be like [4,4,4,8,8,4], then [4,4,4,4,4,8,4] and finally [4,4,4,4,4,4,4,4], so here minimum we have 4 balls, that is the penalty.

To solve this, we will follow these steps −

• Define a function helper() . This will take target, mx

• if target is same as 0, then

• return mx + 1

• count := 0

• for each num in nums, do

• count := count + quotient of (num - 1)/target

• return count <= mx

• From the main method, do the following

• left := maximum of the quotient of (sum of all elements of nums /(size of nums + mx)) and 1

• right := maximum of nums

• while left < right, do

• mid := quotient of (left + right)/2

• if helper(mid, mx) is non-zero, then

• right := mid

• otherwise,

• left := mid + 1

• return left

## Example

Let us see the following implementation to get better understanding −

def helper(target, mx):
if target == 0:
return mx + 1
count = 0
for num in nums:
count += (num - 1) // target
return count <= mx

def solve(nums, mx):
left, right = max(sum(nums) // (len(nums) + mx), 1), max(nums)
while left < right:
mid = (left + right) // 2
if helper(mid, mx):
right = mid
else:
left = mid + 1
return left

nums = [4,8,16,4]
mx = 4
print(solve(nums, mx))

## Input

[4,8,16,4], 4


## Output

4