#### Wine Problem

A
a
N
```package com.thealgorithms.dynamicprogramming;

/**
* Imagine you have a collection of N wines placed next to each other on the
* shelf. The price of ith wine is pi(Prices of different wines are different).
* Because wine gets better every year supposing today is year 1, on year y the
* price would be y*pi i.e y times the value of the initial year. You want to
* sell all wines but you have to sell one wine per year. One more constraint on
* each year you are allowed to sell either leftmost or rightmost wine on the
* shelf. You are not allowed to reorder. You have to find the maximum profit
*
*/
public class WineProblem {

// Method 1: Using Recursion
// Time Complexity=0(2^N) Space Complexity=Recursion extra space
public static int WPRecursion(int[] arr, int si, int ei) {
int n = arr.length;
int year = (n - (ei - si + 1)) + 1;
if (si == ei) {
return arr[si] * year;
}

int start = WPRecursion(arr, si + 1, ei) + arr[si] * year;
int end = WPRecursion(arr, si, ei - 1) + arr[ei] * year;

int ans = Math.max(start, end);

return ans;
}

// Method 2: Top-Down DP(Memoization)
// Time Complexity=0(N*N) Space Complexity=0(N*N)+Recursion extra space
public static int WPTD(int[] arr, int si, int ei, int[][] strg) {
int n = arr.length;
int year = (n - (ei - si + 1)) + 1;
if (si == ei) {
return arr[si] * year;
}

if (strg[si][ei] != 0) {
return strg[si][ei];
}
int start = WPTD(arr, si + 1, ei, strg) + arr[si] * year;
int end = WPTD(arr, si, ei - 1, strg) + arr[ei] * year;

int ans = Math.max(start, end);

strg[si][ei] = ans;

return ans;
}

// Method 3: Bottom-Up DP(Tabulation)
// Time Complexity=0(N*N/2)->0(N*N) Space Complexity=0(N*N)
public static int WPBU(int[] arr) {
int n = arr.length;
int[][] strg = new int[n][n];

for (int slide = 0; slide <= n - 1; slide++) {
for (int si = 0; si <= n - slide - 1; si++) {
int ei = si + slide;
int year = (n - (ei - si + 1)) + 1;
if (si == ei) {
strg[si][ei] = arr[si] * year;
} else {
int start = strg[si + 1][ei] + arr[si] * year;
int end = strg[si][ei - 1] + arr[ei] * year;

strg[si][ei] = Math.max(start, end);
}
}
}
return strg[0][n - 1];
}

public static void main(String[] args) {
int[] arr = { 2, 3, 5, 1, 4 };
System.out.println("Method 1: " + WPRecursion(arr, 0, arr.length - 1));
System.out.println(
"Method 2: " +
WPTD(arr, 0, arr.length - 1, new int[arr.length][arr.length])
);
System.out.println("Method 3: " + WPBU(arr));
}
}
// Memoization vs Tabulation : https://www.geeksforgeeks.org/tabulation-vs-memoization/