package DynamicProgramming;

/**
 * DynamicProgramming solution for the Egg Dropping Puzzle
 */
public class EggDropping {

 // min trials with n eggs and m floors 

 private static int minTrials(int n, int m) {

 int[][] eggFloor = new int[n + 1][m + 1];
 int result, x;

 for (int i = 1; i <= n; i++) {
 eggFloor[i][0] = 0; // Zero trial for zero floor.
 eggFloor[i][1] = 1; // One trial for one floor 
 }

 // j trials for only 1 egg

 for (int j = 1; j <= m; j++)
 eggFloor[1][j] = j;

 // Using bottom-up approach in DP

 for (int i = 2; i <= n; i++) {
 for (int j = 2; j <= m; j++) {
 eggFloor[i][j] = Integer.MAX_VALUE;
 for (x = 1; x <= j; x++) {
 result = 1 + Math.max(eggFloor[i - 1][x - 1], eggFloor[i][j - x]);

 // choose min of all values for particular x
 if (result < eggFloor[i][j])
 eggFloor[i][j] = result;
 }
 }
 }

 return eggFloor[n][m];
 }

 public static void main(String args[]) {
 int n = 2, m = 4;
 // result outputs min no. of trials in worst case for n eggs and m floors
 int result = minTrials(n, m);
 System.out.println(result);
 }
}