LeetCode Python Dynamic Programming

Problem Statement: LeetCode 2064

This LeetCode problem focuses on distributing products to stores with the constraint of minimizing the maximum number of products received by any store. We'll tackle this using a Python solution, drawing inspiration from the NeetCode approach.

Understanding the Problem

The challenge revolves around distributing products to a set of stores. Each store has a different capacity, and the goal is to distribute the products in a way that minimizes the maximum number of products received by any single store.

We are given two lists: products (representing the total number of products) and stores (representing the capacity of each store).
The objective is to find the smallest possible maximum number of products that any store receives after the distribution.

Example: Visualizing the Problem

Imagine we have 10 products (products = [10]) and 2 stores, one with a capacity of 5 (stores = [5, 5]). Our goal is to distribute these products in a way that minimizes the maximum number of products at any store. We could distribute 5 products to each store, and the maximum would be 5.

Key Concepts: Binary Search and Dynamic Programming

To solve this problem effectively, we employ two essential concepts: binary search and dynamic programming.

Binary Search: This technique helps us efficiently search for the minimum maximum number of products. We start with a range of possible values and repeatedly narrow down the search space until we find the optimal solution.
Dynamic Programming: This technique helps us solve the problem by breaking it down into smaller subproblems, memoizing the solutions to avoid redundant calculations.

Python Solution: Code Breakdown

Here's a breakdown of the Python solution using a binary search and dynamic programming approach:

python
def minimizedMaximum(products, stores):
    left = 1  # Minimum possible product count per store
    right = max(products)  # Maximum possible product count per store
    
    while left < right:
        mid = (left + right) // 2  # Calculate the middle point
        if isPossible(products, stores, mid):  # Check if this mid value is feasible
            right = mid  # If possible, try even smaller values
        else:
            left = mid + 1  # If not possible, try larger values
    
    return left  # Return the final minimum maximum count

def isPossible(products, stores, maxCount):
    storesUsed = 0  # Keep track of stores used for distribution
    currentProducts = 0  # Track products distributed to the current store
    
    for product in products:
        if currentProducts + product > maxCount:  # Check if adding the current product exceeds maxCount
            storesUsed += 1  # Move to the next store
            currentProducts = 0  # Reset products for the new store
        currentProducts += product
    storesUsed += 1  # Account for the last store
    
    return storesUsed <= len(stores)  # Check if all products are distributed within the available stores

# Example usage:
products = [10]
stores = [5, 5]
result = minimizedMaximum(products, stores)
print(result)  # Output: 5

Explanation of the Python Code

The solution consists of two key functions:

minimizedMaximum: This function performs the binary search to find the optimal minimum maximum product count.
- It initializes left and right, representing the range of possible values.
- The while loop iterates until left and right converge.
- In each iteration, it calls the isPossible function to check if the current mid value is a feasible solution.
- If it's feasible, we narrow down the search by updating right to mid.
- If it's not feasible, we update left to mid + 1.
isPossible: This function determines whether it's possible to distribute all products to the stores with a maximum count not exceeding maxCount.
- It keeps track of the number of stores used storesUsed and the products allocated to the current store currentProducts.
- It iterates through the products, and for each product, checks if adding it to the current store would exceed maxCount.
- If so, it moves to the next store, resetting the currentProducts.
- Finally, it returns True if all products can be distributed within the available stores, and False otherwise.

Summary: Python Solution for LeetCode 2064

This Python solution effectively minimizes the maximum number of products distributed to any store using the NeetCode approach. It elegantly combines binary search for efficient exploration of the solution space and dynamic programming for optimization. By breaking down the problem into subproblems and memoizing solutions, the code ensures an efficient and optimized outcome. This problem demonstrates the power of these techniques for tackling coding challenges and preparing for interviews.

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