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Add tests, add IllegalArgumentException
, remove main
in `WineProb… (#5662)
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@ -1,21 +1,40 @@
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package com.thealgorithms.dynamicprogramming;
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/**
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* Imagine you have a collection of N wines placed next to each other on the
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* shelf. The price of ith wine is pi(Prices of different wines are different).
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* Because wine gets better every year supposing today is year 1, on year y the
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* price would be y*pi i.e y times the value of the initial year. You want to
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* sell all wines but you have to sell one wine per year. One more constraint on
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* each year you are allowed to sell either leftmost or rightmost wine on the
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* shelf. You are not allowed to reorder. You have to find the maximum profit
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* The WineProblem class provides a solution to the wine selling problem.
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* Given a collection of N wines with different prices, the objective is to maximize profit by selling
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* one wine each year, considering the constraint that only the leftmost or rightmost wine can be sold
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* at any given time.
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*
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* The price of the ith wine is pi, and the selling price increases by a factor of the year in which
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* it is sold. This class implements three approaches to solve the problem:
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*
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* 1. **Recursion**: A straightforward recursive method that computes the maximum profit.
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* - Time Complexity: O(2^N)
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* - Space Complexity: O(N) due to recursive calls.
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*
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* 2. **Top-Down Dynamic Programming (Memoization)**: This approach caches the results of subproblems
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* to avoid redundant computations.
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* - Time Complexity: O(N^2)
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* - Space Complexity: O(N^2) for the storage of results and O(N) for recursion stack.
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*
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* 3. **Bottom-Up Dynamic Programming (Tabulation)**: This method builds a table iteratively to
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* compute the maximum profit for all possible subproblems.
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* - Time Complexity: O(N^2)
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* - Space Complexity: O(N^2) for the table.
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*/
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public final class WineProblem {
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private WineProblem() {
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}
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// Method 1: Using Recursion
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// Time Complexity=0(2^N) Space Complexity=Recursion extra space
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/**
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* Calculate maximum profit using recursion.
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*
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* @param arr Array of wine prices.
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* @param si Start index of the wine to consider.
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* @param ei End index of the wine to consider.
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* @return Maximum profit obtainable by selling the wines.
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*/
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public static int wpRecursion(int[] arr, int si, int ei) {
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int n = arr.length;
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int year = (n - (ei - si + 1)) + 1;
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@ -29,8 +48,15 @@ public final class WineProblem {
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return Math.max(start, end);
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}
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// Method 2: Top-Down DP(Memoization)
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// Time Complexity=0(N*N) Space Complexity=0(N*N)+Recursion extra space
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/**
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* Calculate maximum profit using top-down dynamic programming with memoization.
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*
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* @param arr Array of wine prices.
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* @param si Start index of the wine to consider.
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* @param ei End index of the wine to consider.
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* @param strg 2D array to store results of subproblems.
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* @return Maximum profit obtainable by selling the wines.
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*/
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public static int wptd(int[] arr, int si, int ei, int[][] strg) {
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int n = arr.length;
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int year = (n - (ei - si + 1)) + 1;
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@ -45,15 +71,22 @@ public final class WineProblem {
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int end = wptd(arr, si, ei - 1, strg) + arr[ei] * year;
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int ans = Math.max(start, end);
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strg[si][ei] = ans;
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return ans;
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}
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// Method 3: Bottom-Up DP(Tabulation)
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// Time Complexity=0(N*N/2)->0(N*N) Space Complexity=0(N*N)
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/**
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* Calculate maximum profit using bottom-up dynamic programming with tabulation.
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*
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* @param arr Array of wine prices.
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* @throws IllegalArgumentException if the input array is null or empty.
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* @return Maximum profit obtainable by selling the wines.
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*/
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public static int wpbu(int[] arr) {
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if (arr == null || arr.length == 0) {
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throw new IllegalArgumentException("Input array cannot be null or empty.");
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}
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int n = arr.length;
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int[][] strg = new int[n][n];
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@ -73,13 +106,4 @@ public final class WineProblem {
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}
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return strg[0][n - 1];
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}
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public static void main(String[] args) {
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int[] arr = {2, 3, 5, 1, 4};
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System.out.println("Method 1: " + wpRecursion(arr, 0, arr.length - 1));
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System.out.println("Method 2: " + wptd(arr, 0, arr.length - 1, new int[arr.length][arr.length]));
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System.out.println("Method 3: " + wpbu(arr));
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}
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}
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// Memoization vs Tabulation : https://www.geeksforgeeks.org/tabulation-vs-memoization/
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// Question Link : https://www.geeksforgeeks.org/maximum-profit-sale-wines/
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