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 final class WineProblem {
private 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;
return Math.max(start, end);
}
// 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/
// Question Link : https://www.geeksforgeeks.org/maximum-profit-sale-wines/