package 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/
// Question Link : https://www.geeksforgeeks.org/maximum-profit-sale-wines/