88 lines
2.6 KiB
Java
88 lines
2.6 KiB
Java
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package 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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**/
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public class WineProblem {
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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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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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if (si == ei) {
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return arr[si] * year;
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}
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int start = WPRecursion(arr, si + 1, ei) + arr[si] * year;
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int end = WPRecursion(arr, si, ei - 1) + arr[ei] * year;
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int ans = Math.max(start, end);
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return ans;
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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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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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if (si == ei) {
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return arr[si] * year;
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}
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if (strg[si][ei] != 0) {
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return strg[si][ei];
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}
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int start = WPTD(arr, si + 1, ei, strg) + arr[si] * year;
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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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public static int WPBU(int[] arr) {
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int n = arr.length;
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int[][] strg = new int[n][n];
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for (int slide = 0; slide <= n - 1; slide++) {
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for (int si = 0; si <= n - slide - 1; si++) {
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int ei = si + slide;
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int year = (n - (ei - si + 1)) + 1;
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if (si == ei) {
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strg[si][ei] = arr[si] * year;
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} else {
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int start = strg[si + 1][ei] + arr[si] * year;
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int end = strg[si][ei - 1] + arr[ei] * year;
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strg[si][ei] = Math.max(start, end);
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}
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}
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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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