Fruit Into Baskets 🏆

Welcome to our detailed guide on Data Structures and Algorithms! Today, we're diving into a classic problem called "Fruit Into Baskets". This problem will help you understand and practice essential data structure concepts, particularly arrays and sliding windows. Let's get started!

Problem Statement 📝

You are given an array of integers representing the types of fruits in a market. Each fruit has a certain weight. You also have k baskets with limited capacity C. Your task is to distribute the fruits such that no basket exceeds its capacity, and you maximize the total weight of fruits in the baskets.

Pseudocode 💡

Initialize a variable totalWeight to store the total weight of fruits in the baskets.
Iterate through the fruit array using a sliding window approach: a. Initialize a variable currentWeight to store the weight of the current fruits in the basket. b. As long as the current weight is less than or equal to the basket capacity, add the weight of the current fruit to the currentWeight and move to the next fruit. c. When the current weight exceeds the basket capacity, subtract the weight of the first fruit in the basket (which was included in the previous iteration) from the currentWeight. Then, store the currentWeight in the total weight and reset currentWeight to the weight of the current fruit.
After iterating through the entire array, the totalWeight will hold the maximum total weight achievable within the constraints.

Code Example ✅

Here's a Python implementation of the solution:

python

def max_total_weight(fruits, baskets, capacity):
    total_weight = 0
    for i in range(len(fruits)):
        current_weight = 0
        for j in range(i, min(len(fruits), i + baskets)):
            current_weight += fruits[j]
            if current_weight > capacity:
                total_weight += current_weight - fruits[i - baskets]
                current_weight = fruits[j]
    return total_weight

# Example usage:
fruits = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
baskets = 3
capacity = 4
print(max_total_weight(fruits, baskets, capacity))  # Output: 22

Understanding the Code 💡

The max_total_weight function takes three arguments: fruits, baskets, and capacity.
We initialize total_weight to zero, indicating the total weight of the fruits in the baskets.
The outer loop iterates through the fruits array.
The inner loop, or sliding window, adds fruits to the current_weight variable, checks if the current_weight exceeds the basket capacity, and handles such cases by subtracting the weight of the first fruit in the current basket from the current_weight.
After iterating through the entire array, the total_weight variable holds the maximum total weight achievable.

Quiz 🎯

By now, you should have a good understanding of the Fruit Into Baskets problem and how to solve it using a sliding window approach. Keep practicing, and remember to always optimize your code for efficiency!

Happy coding! 🚀