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New PDF release: A Collection of Dynamic Programming Interview Questions

By Dr Antonio Gulli

This publication offers a set of Dynamic programming difficulties, their resolution, and the C++ code concerning them.

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Solution This is a classical puzzle, frequently asked during interviews. Let be the minimum number of attempts given eggs and n floors. A dynamic solution can be computed by considering that when we drop an egg from floor f there are only two possible outcomes: a) If the egg breaks, then we have eggs and we need to check the floor b) If the egg does not break, then we have eggs and the remaining floors left Since we want to minimize the number of attempts, in the worst scenario we have to consider the maximum between a) and b).

DP pursues to solve each subproblem only once, as a result reducing the number of computations. After the solution to a given subproblem has been computed, it is stored in a table or "memoized". Next time the same solution is required, it is simply looked up. DP solves problems in either two methods: a) Top-down approach: This is a consequence of the recursive mathematical definition associated to many DP problems. b) Bottom-up approach: This requires a reformulation of the recursive mathematical definition where subproblems are solved first and their solutions used to build-on and achieve solutions for bigger subproblems In this book we will review a collection of Dynamic programming problems, their solution, and the C++ code related to them.

Reducing the space to is left as an exercise. 16. LCS – Given two strings, find the longest common subsequence Given the two strings, two subsequences are in common if they appear in the same order but not necessarily contiguous. The main difference with the previous problem is that here the terms are not consecutive. Solution A dynamic programming solution can be computed for the string and the string 1] by defining a recursive function on the prefixes and of length and A dynamic programming solution can be built by using a table where we store the partial results of the above computation (function).

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