Super Washing Machines

The problem requires us to find the minimum number of moves to make all washing machines have the same number of dresses. If it’s not possible to do so, we have to return -1.

Here’s a method to accomplish this task:

  1. Calculate the Total Dresses: First, we need to find the total number of dresses in all washing machines. If this total number is not divisible evenly by the number of machines, it’s impossible to make all machines have the same number of dresses, and we return -1.

  2. Find the Target Number of Dresses: If the total number of dresses is divisible evenly by the number of machines, the target number of dresses for each machine is the total number of dresses divided by the number of machines.

  3. Calculate the Minimum Moves: We then calculate how many dresses each machine needs to gain or lose to reach the target number. We keep track of the current sum of differences from the target number and the maximum absolute value of the current sum and differences for each machine. The minimum number of moves required is the maximum of these values.

Here’s the code implementing the method:

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from typing import List

class Solution:
    def findMinMoves(self, machines: List[int]) -> int:
        total_dresses = sum(machines)
        n = len(machines)

        # Check if total dresses can be evenly distributed
        if total_dresses % n != 0:
            return -1

        target_dresses = total_dresses // n
        min_moves = 0
        current_sum = 0

        # Calculate the minimum moves
        for dresses in machines:
            difference = dresses - target_dresses
            current_sum += difference
            min_moves = max(min_moves, abs(current_sum), difference)

        return min_moves

The code first checks if the total number of dresses can be evenly distributed among the machines. If not, it returns -1. Otherwise, it calculates the minimum number of moves required to make all machines have the same number of dresses by following the method described above.

10 Prerequisite LeetCode Problems

“Super Washing Machines” focuses on array manipulation and the concept of load balancing. Here are 10 problems to solve problems like this:

  1. “53. Maximum Subarray”

    • This problem is fundamental for understanding how to deal with contiguous subarrays.

  2. “121. Best Time to Buy and Sell Stock”

    • This problem introduces the concept of tracking minimum and maximum values in an array, which is key for the main problem.

  3. “238. Product of Array Except Self”

    • This problem helps understand how to use prefix and suffix arrays, which could be used in the main problem.

  4. “41. First Missing Positive”

    • This problem is a tricky array problem that will help develop the problem-solving skills needed for the main problem.

  5. “189. Rotate Array”

    • This problem gets you comfortable with manipulating arrays.

  6. “325. Maximum Size Subarray Sum Equals k”

    • This problem involves finding a subarray with a certain sum, which is similar to distributing loads in the main problem.

  7. “209. Minimum Size Subarray Sum”

    • This problem again focuses on contiguous subarrays, which is useful for the main problem.

  8. “485. Max Consecutive Ones”

    • This problem helps in understanding how to deal with contiguous subarray problems.

  9. “713. Subarray Product Less Than K”

    • This problem introduces the concept of window sliding which could be used in the main problem.

  10. “560. Subarray Sum Equals K”

  • This problem again involves dealing with subarrays that sum to a certain value, which is a key part of the main problem.

These cover array manipulation, dealing with contiguous subarrays and understanding the concept of load balancing. After solving these problems, the “Super Washing Machines” problem should become more approachable.

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class Solution:
    def findMinMoves(self, machines: List[int]) -> int:
        ave, rem = divmod(sum(machines),len(machines))    
        if rem: return -1                                 

        machines = [m - ave for m in machines]            

        return max(max(machines),                         
                   max(map(abs,(accumulate(machines)))))

Problem Classification

Language Agnostic Coding Drills

  1. Understanding the Problem: The problem is about redistributing items (in this case, represented as integers in an array) evenly. We must find the minimum number of moves to do this.

  2. Array Manipulation: Arrays (lists in Python) are the primary data structure used here. You need to understand how to access and manipulate elements of an array.

  3. Accumulative Sum (Prefix Sum): accumulate function from itertools module is used to find cumulative sums. This function returns an iterator giving all the intermediate partial sums.

  4. Division and Remainders: The divmod function is used to calculate both the quotient and remainder when dividing the total number of items by the number of machines.

  5. Map Function: The map function is used to apply the absolute function to each item in the array.

  6. Conditional Statements: There’s a conditional statement that checks whether or not it’s possible to evenly distribute the items. If the remainder of the division operation is not zero, then it’s not possible to evenly distribute the items.

  7. Finding Maximum Values: There are two maximum values calculated here: the maximum value in the machines array (representing the maximum number of items a single machine needs to give or take), and the maximum cumulative movement of clothes needed, which is calculated by mapping the absolute function to the accumulative sum of the machines and getting the max value. The final result is the maximum of these two.

Understanding these concepts is crucial to understanding the problem and the solution. You can practice each of them separately in the language of your choice, and once you’re comfortable with each, you can combine them to solve the problem.

Targeted Drills in Python

1. Array Manipulation:

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# Create an array
arr = [1, 2, 3, 4, 5]
# Access elements of the array
print(arr[0])  # Output: 1
# Manipulate elements of the array
arr[0] = 6
print(arr)  # Output: [6, 2, 3, 4, 5]

2. Accumulative Sum (Prefix Sum):

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from itertools import accumulate

arr = [1, 2, 3, 4, 5]
# Find cumulative sums
cumulative_sums = list(accumulate(arr))
print(cumulative_sums)  # Output: [1, 3, 6, 10, 15]

3. Division and Remainders:

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# Calculate quotient and remainder
quotient, remainder = divmod(10, 3)
print(quotient, remainder)  # Output: 3 1

4. Map Function:

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# Create a list
numbers = [-1, 2, -3, 4, -5]
# Use map to get the absolute values
abs_values = list(map(abs, numbers))
print(abs_values)  # Output: [1, 2, 3, 4, 5]

5. Conditional Statements:

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# Using if-else statement
x = 10
if x > 5:
    print("x is greater than 5")
else:
    print("x is not greater than 5")

6. Finding Maximum Values:

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# Create a list
numbers = [1, 3, 7, 2, 5]
# Find the maximum value
max_value = max(numbers)
print(max_value)  # Output: 7

For each of these drills, you can create variations and try them out to get more practice. Once you’re comfortable with these, you can start working on the final problem.