If the egg doesn’t break after dropping from the ‘xth’ floor, then we only need to check for floors higher than ‘x’ so the problem reduces to ‘k-x’ floors and n eggs.If the egg breaks after dropping from ‘xth’ floor, then we only need to check for floors lower than ‘x’ with remaining eggs as some floor should exist lower than ‘x’ in which egg would not break so the problem reduces to x-1 floors and n-1 eggs.When we drop an egg from a floor x, there can be two cases (1) The egg breaks (2) The egg doesn’t break. For example- If we have ‘1’ egg and ‘k’ floors, we will start dropping the egg from the first floor till the egg breaks suppose on the ‘kth’ floor so the number of tries to give us surety is ‘k’. Meaning of a worst-case scenario: Worst case scenario gives the user the surety of the threshold floor.
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In the following solutions, we return the minimum number of trials in the worst case these solutions can be easily modified to print floor numbers of every trial also. The floor which gives the minimum value in the worst case is going to be part of the solution.
The solution is to try dropping an egg from every floor(from 1 to k) and recursively calculate the minimum number of droppings needed in the worst case. In this post, we will discuss a solution to a general problem with ‘n’ eggs and ‘k’ floors. The problem is not actually to find the critical floor, but merely to decide floors from which eggs should be dropped so that the total number of trials are minimized. What is the least number of egg-droppings that is guaranteed to work in all cases? In the worst case, this method may require 36 droppings. Drop the egg from the first-floor window if it survives, drop it from the second-floor window. If only one egg is available and we wish to be sure of obtaining the right result, the experiment can be carried out in only one way.
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….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. ….If an egg survives a fall then it would survive a shorter fall. ….If an egg breaks when dropped, then it would break if dropped from a higher floor. ….The effect of a fall is the same for all eggs. ….An egg that survives a fall can be used again. Suppose that we wish to know which stories in a 36-storey building are safe to drop eggs from, and which will cause the eggs to break on landing. The following is a description of the instance of this famous puzzle involving n=2 eggs and a building with k=36 floors.
Maximum subarray sum in O(n) using prefix sum.Count number of ways to partition a set into k subsets.Count number of ways to jump to reach end.Find all distinct subset (or subsequence) sums of an array.Longest Palindromic Subsequence | DP-12.Travelling Salesman Problem | Set 1 (Naive and Dynamic Programming).Intermediate problems of Dynamic programming ISRO CS Syllabus for Scientist/Engineer Exam.ISRO CS Original Papers and Official Keys.GATE CS Original Papers and Official Keys.
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