Read e-book online A Collection of Dynamic Programming Interview Questions PDF

By Dr Antonio Gulli

ISBN-10: 1495320480

ISBN-13: 9781495320484

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

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Extra info for A Collection of Dynamic Programming Interview Questions Solved in C++

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This means that the solution can be then obtained recursively. Mathematically, we can define: In the remaining, we provide two different solutions: the first is top-down and recursive, while the second is based on dynamic programming and it is built bottom-up by storing partial results in a support array. Code unsigned int knapRecursive(const unsigned int C, const unsigned int w[], const unsigned int v[], const unsigned int n) { if (n == 0 || C == 0) return 0; if (w[n - 1] > C) return knapRecursive(C, w, v, n - 1); else return std::max(v[n - 1] + knapRecursive(C - w[n - 1], w, v, n - 1), knapRecursive(C, w, v, n - 1)); } unsigned int knapSack(const unsigned int C, const unsigned int w[], const unsigned int v[], const unsigned int n) { Matrix table(n + 1, C + 1); for (unsigned int i = 0; i <= n; ++i) for (unsigned int j = 0; j <= C; ++j) { if (i == 0 || j == 0) table(i, j) = 0; else if (w[i - 1] <= j) table(i, j) = std::max(v[i - 1] + table(i - 1, j - w[i - 1]), table(i - 1, j)); else table(i, j) = table(i - 1, j); } return table(n, C); } Complexity Pseudolinear in time and Pseudolinear in space 6.

Sum Subset -– Given an array of integers of sizen, partition it in such a way that the two subsets have equal sum s Solution Sum subset problem is and important problem in computer science with application in cryptography and complexity[5]. The problem is NP-Complete. The most naïve solution generates all the subsets and for each of them it checks whether the sum is the right number. The complexity is where the size of the array. We can use Dynamic programming for providing a pseudo-polynomial solution.

Scheduling – given n jobs, each one with a processing time ti a profit pi and a deadline di, maximize the profit Solution Suppose that each job has processing time profit and deadline for and that we get no profit, if the job is executed after its deadline. We want to maximize the profit for jobs executed at time. Recursively, Code Left as exercise Complexity If we assume that the processing time is bounded by, then we need to compute up to and we have jobs to consider. Therefore the total complexity is 36.

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A Collection of Dynamic Programming Interview Questions Solved in C++ by Dr Antonio Gulli

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