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**NOV 2020**

Lecture 11: Dynamic Progamming CLRS Chapter 15 Outline of this section Introduction to Dynamic programming; a method for solving optimization problems. Chapter 4 pressed the reader to think seriously on each occasion about whether con-ditions ensuring the validity of the dynamic programming approach are met. Memoization is an optimization technique used to speed up programs by storing the results of expensive function calls and returning the cached result when the same inputs occur again. The dynamic programming is a linear optimization method that obtains optimum solution of a multivariable problem by decomposition of the problem into sub problems [2]. Each of the subproblem solutions is indexed in some way, typically based on the values of its input parameters, so as to facilitate its lookup. 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 (array, map,etc). Dynamic programming is â¦ 6.231 DYNAMIC PROGRAMMING LECTURE 4 LECTURE OUTLINE â¢ Examples of stochastic DP problems â¢ Linear-quadratic problems â¢ Inventory control. Consider the following dynamic programming of 0-1 knapsack problem. A dynamic programming algorithm solves a complex problem by dividing it into simpler subproblems, solving each of those just once, and storing their solutions. Tree DP Example Problem: given a tree, color nodes black as many as possible without coloring two adjacent nodes Subproblems: â First, we arbitrarily decide the root node r â B v: the optimal solution for a subtree having v as the root, where we color v black â W v: the optimal solution for a subtree having v as the root, where we donât color v â Answer is max{B (II) will present a graphical method of dynamic programming for handling the inventory problem â¦ and shortest paths in networks, an example of a continuous-state-space problem, and an introduction to dynamic programming under uncertainty. Specifically, EMGT 5130 W3 P4 Problem 3.12 Production and Inventory Planning Problem Model Formulation ... 0/1 Knapsack Problem Dynamic Programming - Duration: 15:50. Dynamic programming vs. Divide and Conquer A few examples of Dynamic programming â the 0-1 Knapsack Problem â Chain Matrix Multiplication â All Pairs Shortest Path application in this area is to inventory problems, but we also study problems of capital replacement and durable goods. Dynamic Programming A Network Problem An Inventory Problem Resource Allocation Problems Equipment Replacement Problems Characteristic of Dynamic Programming Knapsack Problems A Network Problem Example 1 (The Shortest Path Problem) Find the shortest path from node A to node G in the network shown in Figure 1. 11.1 AN ELEMENTARY EXAMPLE In order to introduce the dynamic-programming approach to solving multistage problems, in this section we analyze a simple example. 1 Dynamic programmingâs rules themselves are simple; the most difficult parts are reasoning whether a problem can be solved with dynamic programming and whatâre the subproblems. 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