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A Collection of Dynamic Programming Interview Questions by Dr Antonio Gulli

By Dr Antonio Gulli

This e-book provides a suite of Dynamic programming difficulties, their resolution, and the C++ code with regards to them.

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We can sort the tuples by increasing indexes and then compute the longest increasing sequence (LIS) on the sequence of. Code Left as exercise Complexity Since we need to sort the complexity is 19. LBS – Given an array of integers, find the longest bitonic sequence Solution A sequence is bitonic, if it initially increases and then decreases. For an array we can compute the longest increasing sequence ending at position and the longest decreasing sequence starting at position. For each position we define: and Code Left as exercise Complexity Complexity is.

Here we provide an implementation where Fibonacci is computed at compile time leveraging the power of templates. template struct CTFibonacci { static constexpr int value() { return CTFibonacci::value() + CTFibonacci::value(); } }; template <> struct CTFibonacci<1> { static constexpr int value() { return 1; } }; template <> struct CTFibonacci<0> { static constexpr int value() { return 0; } }; Complexity Complexity is here exponential since . An alternative and more efficient solution memorizes the intermediate results and it avoids to recompute the same sub-problem for multiple times.

Leaving two positions in one same line should intuitively cost more than leaving a position in one and the other position in another line). This requirement can be fulfilled in multiple ways, for instance by defining or more conveniently for bitwise computation: . To summarize our goal is to find: such that. In the code the vector will contain final decreasing values containing the residuals for each word added to a given line. The values will increase again anytime that there is a need to change line.

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