# Optimizing Book Prices in Java: Dynamic Programming

The Java code implements a dynamic programming approach to determine the minimum cost of purchasing a set of books, applying discounts based on the quantity of unique books selected. The ShoppingBasket class employs multidimensional arrays to efficiently compute prices for varying combinations of books and quantities. Helper methods handle array operations, enhancing code readability. This optimization strategy ensures an optimal solution for pricing a diverse shopping basket while considering discounts, demonstrating effective algorithmic implementation in Java.

## Dynamic Programming Approach for Book Pricing in Java

This Java code defines a ShoppingBasket class that leverages dynamic programming to calculate the minimum cost of purchasing a set of books with quantity-based discounts. Utilizing multidimensional arrays and well-designed helper methods, the code efficiently handles various book combinations. This implementation showcases effective algorithmic strategies for pricing diverse shopping baskets. Whether you're a student seeking help with your Java assignment or a developer looking for a robust pricing algorithm, this code provides a clear example of optimizing book prices, demonstrating the power and flexibility of Java in algorithmic solutions.

### Block 1: Class and Constants

``` import java.util.ArrayList; import java.util.Arrays; import java.util.List; public class ShoppingBasket { private static final int BOOK_NUMBER = 5; private static final int BOOK_PRICE = 8; private static final double DISCOUNTS[] = {0.0, 0.0, 0.05, 0.1, 0.2, 0.25}; ```
• This block includes the class declaration and the declaration of constants for the number of books, book price, and discount rates.

### Block 2: Price Calculation Method

``` public double price(int[] shoppingBasket) { if (shoppingBasket == null) { return 0; } if (shoppingBasket.length == 1) { return 8; } ```
• This method calculates the total price of the books in the shopping basket. It handles special cases where the basket is empty or contains only one book.

### Block 3: Counting Books in the Basket

``` int[] countOfBooksArray = {0, 0, 0, 0, 0}; for (int book : shoppingBasket) { countOfBooksArray[book] += 1; } ```
• Counts the occurrences of each book in the shopping basket and stores the counts in the countOfBooksArray.

### Block 4: Dynamic Programming for Price Calculation

``` double A[][][][][] = new double[countOfBooksArray[0]+1][countOfBooksArray[1]+1][countOfBooksArray[2]+1][countOfBooksArray[3]+1][countOfBooksArray[4]+1]; for (int i1 = 0; i1 < countOfBooksArray[0]+1; i1++) { for (int i2 = 0; i2 < countOfBooksArray[1]+1; i2++) { // ... (similar loops for i3, i4, i5) ```
• This block initializes a five-dimensional array A and uses dynamic programming to calculate the minimum cost for different combinations of books in the basket, considering the discounts.

### Block 5: Nested Loops for Dynamic Programming

``` for (int selected = 1; selected <= BOOK_NUMBER; selected++) { double discount = DISCOUNTS[selected]; List selections = getAllArrays(selected); for (int[] selection : selections) { // ... (code to update min cost using dynamic programming) } } A[i1][i2][i3][i4][i5] = min; ```
• Nested loops iterate through all possible combinations of selected books, computing the minimum cost based on dynamic programming and storing the result in the array A.

### Block 6: Return Final Result

``` return A[countOfBooksArray[0]][countOfBooksArray[1]][countOfBooksArray[2]][countOfBooksArray[3]][countOfBooksArray[4]]; ```
• Returns the final calculated minimum cost for the entire shopping basket.

### Block 7: Helper Method for Book Combinations

``` private List getAllArrays(int selectedBooks) { List result = new ArrayList<>(); switch (selectedBooks) { // ... (cases for 1, 2, 3, 4, 5 selected books) } return result; } ```
• This method generates all possible combinations of books for a given number of selected books.

### Block 8: Helper Method for Subtracting Arrays

``` private int[] subtract(int[] stock, int[] selected) { // ... (code to subtract arrays) } ```
• This method subtracts one array from another, used in the dynamic programming calculation to determine remaining book counts after a selection.

### Block 9: Helper Method for Summing Arrays

``` private int[] sum(int[] a1, int[] a2) { // ... (code to sum arrays) } ```
• This method sums two arrays, used in the dynamic programming calculation.

## Conclusion

In conclusion, the presented Java implementation showcases the power of dynamic programming in optimizing book purchases for a shopping basket. By meticulously considering various book combinations and applying discounts, the algorithm efficiently calculates the minimum cost. The ShoppingBasket class elegantly handles scenarios with special considerations, such as an empty basket or a single book purchase. This code not only demonstrates a practical application of dynamic programming but also underscores the versatility of Java in algorithmic solutions. As we delve into the intricacies of book pricing strategies, the efficiency and clarity of the code exemplify the prowess of Java for tackling real-world optimization challenges.