Elements of Competitive Programming : Dynamic Programming (88 Problems with Solutions) : A Functional Approach

This book was planned as an aid to students preparing for competitive programming. Written in a problem-solution format, this is exceptionally convenient for analyzing common errors made by the coder in competitive coding sports, for reviewing different methods of solving the same problems and for discussing difficult questions of fundamentals of algorithms with focus on dynamic programming. Attention can be drawn to various aspects of the problem, certain fine points can be made, and a more thorough understanding of the fundamentals can be reached. The art of formulating and solving problems using dynamic programming can be learned only through active participation by the student.

Infused with the wisdom of Richard Bellman, the father of Dynamic Programming, this tiny book distills the inherent concepts and techniques in a problem-solution format with focus on :

• to convey the art of formulating the solution of problems in terms of dynamic-programming recurrence relations
• how to define and characterize the optimal value function
• evaluation of the feasibility and computational magnitude of the solution, based on the recurrence relation
• to show how dynamic programming can be used analytically to establish the structure of the optimal solution, or conditions necessarily satisfied by the optimal solution, both for their own interest and as means of reducing computation.

The student must first discover, by experience, that proper formulation is not quite as trivial as it appears when reading a solution. Then, by considerable practice with solving problems on his own, he will acquire the feel for the subject that ultimately renders proper formulation easy and natural. For this reason, this book contains a large number (88) of instructional problems in a graded way, carefully chosen to allow the student to acquire the art that I seek to convey. The student must do these problems on his own. Solutions are given next to the problem because the reader needs feedback on the correctness of his procedures in order to learn, but any student who reads the solution before seriously attempting the problem does so at this own peril.

This book provides a functional approach to solving problems using dynamic programming. Written in an extremely lively form of problems and solutions (including code in modern C++ and pseudo style), this leads to extreme simplification of optimal coding with great emphasis on unconventional and integrated science of dynamic Programming. Though aimed primarily at serious programmers, it imparts the knowledge of deep internals of underlying concepts and beyond to computer scientists alike.