C# Program for Egg Dropping Puzzle | DP-11

The following is a description of the instance of this famous puzzle involving n=2 eggs and a building with k=36 floors.

Suppose that we wish to know which stories in a 36-story building are safe to drop eggs from, and which will cause the eggs to break on landing. We make a few assumptions:

…..An egg that survives a fall can be used again.
…..A broken egg must be discarded.
…..The effect of a fall is the same for all eggs.
…..If an egg breaks when dropped, then it would break if dropped from a higher floor.
…..If an egg survives a fall then it would survive a shorter fall.
…..It is not ruled out that the first-floor windows break eggs, nor is it ruled out that the 36th-floor do not cause an egg to break.

The problem is not actually to find the critical floor, but merely to decide floors from which eggs should be dropped so that total number of trials are minimized.

Source: Wiki for Dynamic Programming


Dynamic Programming Solution






// A Dynamic Programming based C# Program
// for the Egg Dropping Puzzle
using System;
class GFG {
    // A utility function to get maximum of
    // two integers
    static int max(int a, int b)
        return (a > b) ? a : b;
    /* Function to get minimum number of 
    trials needed in worst case with n
    eggs and k floors */
    static int eggDrop(int n, int k)
        /* A 2D table where entery eggFloor[i][j]
        will represent minimum number of trials
        needed for i eggs and j floors. */
        int[, ] eggFloor = new int[n + 1, k + 1];
        int res;
        int i, j, x;
        // We need one trial for one floor and0
        // trials for 0 floors
            eggFloor[i, 1] = 1;
            eggFloor[i, 0] = 0;
        // We always need j trials for one egg
        // and j floors.
            eggFloor[1, j] = j;
        // Fill rest of the entries in table
        // using optimal substructure property
            for (j = 2; j <= k; j++) {
                eggFloor[i, j] = int.MaxValue;
                for (x = 1; x <= j; x++) {
                    res = 1 + max(eggFloor[i - 1, x - 1],
                                  eggFloor[i, j - x]);
                    if (res < eggFloor[i, j])
                        eggFloor[i, j] = res;
        // eggFloor[n][k] holds the result
        return eggFloor[n, k];
    // Driver function
    public static void Main()
        int n = 2, k = 36;
        Console.WriteLine("Minimum number of trials "
                          + "in worst case with " + n + " eggs and "
                          + k + "floors is " + eggDrop(n, k));
// This code is contributed by Sam007.



Minimum number of trials in worst case with 2 eggs and 36floors is 8

Please refer complete article on Egg Dropping Puzzle | DP-11 for more details!

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