Yukun Yao, Rutgers University

Abstract

In this talk we will talk about dynamic programming and combinatorial game theory. Dynamic Programming is a method for solving a complex problem by breaking it down into a collection of simpler subproblems, solving each of those subproblems just once, and storing their solutions using a memory-based data structure. We will see some problems that can be solved by dynamic programming. Then we will discuss impartial games, especially Nim and how we can use dynamic programming to find Sprague–Grundy function values so that we know where are winning positions and where are losing positions. A winning strategy follows. Sprague–Grundy theorem will also be mentioned.