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dynamic programming problem

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This is unlike the coin change problem using greedy algorithm where certain cases resulted in a non-optimal solution.. 5. These basic features that characterize dynamic programming problems are presented and discussed here. basic characteristic of dynamic programing, What are the features of dynamic programming, characteristics of dynamic programing problem, dynamic programming problem characteristics, Dynamic programming problem characterstics, what is dynamic programming? In both contexts it refers to simplifying a complicated problem by breaking it down into simpler sub-problems in a recursive … Mostly, these algorithms are used for optimization. What is a dynamic programming, how can it be described? -- Brian Dean. Dynamic programming is used where we have problems, which can be divided into similar sub-problems, so that their results can be re-used. The recursive relationship keeps recurring as we move backward stage by stage. Similarly, other dynamic programming problems require making a sequence of interrelated decisions, where each decision corresponds to one stage of the problem. If a problem has overlapping subproblems, then we can improve on a recursi… The 0/1 Knapsack problem using dynamic programming. Dynamic Programming is mainly an optimization over plain recursion. Given the current state, an optimal policy for the remaining stages is independent of the policy decisions adopted in previous stages. A sub-solution of the problem is constructed from previously found ones. More so than the optimization techniques described previously, dynamic programming provides a general framework So we will create a 2D array of size (arr.size() + 1) * (target + 1) of type boolean . To practice all areas of Data Structures & Algorithms, here is complete set of 1000+ Multiple Choice Questions and Answers . Dynamic programming requires an optimal substructure and overlapping sub-problems, both of which are present in the 0–1 knapsack problem, as we shall see. Word Break Problem: Given a string and a dictionary of words, determine if string can be segmented into a space-separated sequence of one or more dictionary words. Following are the most important Dynamic Programming problems asked in … We use cookies to ensure you get the best experience on our website. (This property is the Markovian property, discussed in Sec. 10. This type can be solved by Dynamic Programming Approach. Steps for Solving DP Problems 1. 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. Overlapping subproblems:When a recursive algorithm would visit the same subproblems repeatedly, then a problem has overlapping subproblems. characteristics of dynamic programming, Write the features of dynamic programming, write the characteristics of dynamic programming problems, write down the characteristics of dynamic programming, explain any four characteristics of dynamic programming models, explain the charectaristics of dynamic programing, features of dynamic programming problem in operation research, features of dynamic programming problem in or, typical characteristics of dynamic programing, typical characteristics of a dynamic problem, what is dynamic programming and characteristics of program in operation research, what is dynamic programming characteristics in operation research, list of important features of dynamic problem, what is dynamic programming in operation research, important features of dynamic programming, what is the dynamic programming and the basic featur, features or characteristics of dynamic prog, features of dynamic programing in operation research, dynamic programming divides problems into a number of, characteristics of dynamic programming in or in hindi, characteristics of dynamic programming in or, characteristics of dynamic programming in operational research, characteristics of dynamic programe problem, characteristics of dynamic pfogramming in or, characteristic of dynamic program in operations research, besic characteristics of dynamic programming, basic feature optimality in dynamic programming, characterized of Dynamic programming problem, dynamic programming characteristics in or, dynamic programming and its characteristics, define dynamic programming problems in operation research, concept and features of dynamic programming problem, concept and characteristics of dynamic programming, charactertics of dynamic programming operation reserch, Characterstic of dynamic programming problem, basic characteristics of dynamic programming, DYNAMIC PROGRAMMING:DETERMINISTIC DYNAMIC PROGRAMMING, STORAGE AND WAREHOUSING:SCIENTIFIC APPROACH TO WAREHOUSE PLANNING, STORAGE AND WAREHOUSING:STORAGE SPACE PLANNING, PRINCIPLES AND TECHNIQUES:MEASUREMENT OF INDIRECT LABOR OPERATIONS, INTRODUCTION TO FACILITIES SIZE, LOCATION, AND LAYOUT, PLANT AND FACILITIES ENGINEERING WITH WASTE AND ENERGY MANAGEMENT:MANAGING PLANT AND FACILITIES ENGINEERING. Write down the recurrence that relates subproblems 3. Dynamic Programming 11 Dynamic programming is an optimization approach that transforms a complex problem into a sequence of simpler problems; its essential characteristic is the multistage nature of the optimization procedure. 4. For any problem, dynamic programming provides this kind of policy prescription of what to do under every possible circumstance (which is why the actual decision made upon reaching a particular state at a given stage is referred to as a policy decision). 1. Recognize and … an old collection of practice dynamic programming problems and their For dynamic programming problems in general, knowledge of the current state of the system conveys all the information about its previous behavior nec- essary for determining the optimal policy henceforth. Dynamic Programming (commonly referred to as DP) is an algorithmic technique for solving a problem by recursively breaking it down into simpler subproblems and using the fact that the optimal solution to the overall problem depends upon the optimal solution to it’s individual subproblems. In general, the states are the various possible conditions in which the system might be at that stage of the problem. When this table is finally obtained for the initial stage (n = 1), the problem of interest is solved. Before solving the in-hand sub-problem, dynamic algorithm will try to examine … Sanfoundry Global Education & Learning Series – Data Structures & Algorithms. Forbidden). In this Knapsack algorithm type, each package can be taken or not taken. Thus, in addition to identifying three optimal solutions (optimal routes) for the overall problem, the results show the fortune seeker how he should proceed if he gets detoured to a state that is not on an optimal route. Integer Knapsack Problem (Duplicate Items When the current stage number n is decreased by 1, the new fn*(sn) function is derived by using the f *n+1(sn+1) function that was just derived during the preceding iteration, and then this process keeps repeating. The first step to solving any dynamic programming problem using The FAST Method is to find the initial brute force recursive solution. 3. Dynamic Programming – 7 Steps to Solve any DP Interview Problem Originally posted at Refdash Blog.Refdash is an interviewing platform that helps engineers interview anonymously with experienced engineers from top companies such as Google, Facebook, or Palantir and get a … We’ll be solving this problem with dynamic programming. The network would consist of columns of nodes, with each column corresponding to a stage, so that the flow from a node can go only to a node in the next column to the right. This technique should be used when the problem statement has 2 properties: Overlapping Subproblems- The term overlapping subproblems means that a subproblem might occur multiple times during the computation of the main problem. animated solutions that I put together many years ago while serving as Your goal with Step One is to solve the problem without concern for efficiency. Like divide-and-conquer method, Dynamic Programming solves problems by combining the solutions of subproblems. This property is emphasized in the next (and fi- nal) characteristic of dynamic programming. Your email address will not be published. It is both a mathematical optimisation method and a computer programming method. Making Change. This gives us a starting point (I’ve discussed this in much more detail here). Besides, the thief cannot take a fractional amount of a taken package or take a package more than once. 2. In this post, we will look at the coin change problem dynamic programming approach.. This procedure suggests that dynamic programming. Dynamic programming refers to a problem-solving approach, in which we precompute and store simpler, similar subproblems, in order to build up the solution to a complex problem. The solution procedure is designed to find an optimal policy for the overall problem, i.e., a prescription of the optimal policy decision at each stage for each of the possible states. This site contains The solution procedure begins by finding the optimal policy for the last stage. A 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). Your email address will not be published. A DP is an algorithmic technique which is usually based on a recurrent formula and one (or some) starting states. Providing this additional information beyond simply specifying an optimal solution (optimal sequence of decisions) can be helpful in a variety of ways, … The links from a node to nodes in the next col- umn correspond to the possible policy decisions on which state to go to next. For the stagecoach problem, the solution procedure constructed a table for each stage (n) that prescribed the optimal decision (xn*) for each possible state (s). Dynamic programming is both a mathematical optimization method and a computer programming method. Each stage has a number of states associated with the beginning of that stage. The idea is to use recursion to solve this problem. In contrast to linear programming, there does not exist a standard mathematical for-mulation of “the” dynamic programming problem. web. around since it seems to have attracted a reasonable following on the Required fields are marked *, Powered by WordPress and HeatMap AdAptive Theme, PERFORMANCE MANAGEMENT:GOAL SETTING AND METRICS, INDUSTRIAL ENGINEERING APPLICATIONS IN TRANSPORTATION:LARGE-SCALE TRANSPORTATION NETWORK PLANNING, COMPUTER INTEGRATED MANUFACTURING:CIM DEFINITIONS AND CONCEPTS. Dynamic Programming Practice Problems. Method 2 : To solve the problem in Pseudo-polynomial time use the Dynamic programming. It’s fine if you don’t understand what “optimal substructure” and “overlapping sub-problems” are (that’s an article for another day). 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. Eventually, this animated material will be updated and Essentially, it just means a particular flavor of problems that allow us to reuse previous solutions to smaller problems in order to calculate a solution to the current proble… The idea is to simply store the results of subproblems, so that we do not have to re-compute them when needed later. For any problem, dynamic programming provides this kind of policy prescription of what to do under every possible circumstance (which is why the actual decision made upon reaching a particular state at a given stage is referred to as a policy decision). I am keeping it The policy decision at each stage was which life insurance policy to choose (i.e., which destination to select for the next stage- coach ride). title. The stagecoach problem was literally divided into its four stages (stagecoaches) that correspond to the four legs of the journey. For more practice, including dozens more problems and solutions for each pattern, check out Grokking Dynamic Programming Patterns for Coding Interviews on … 7. Dynamic programming is breaking down a problem into smaller sub-problems, solving each sub-problem and storing the solutions to each of these sub-problems in an array (or similar data structure) so each sub-problem is only calculated once. Solve practice problems for Introduction to Dynamic Programming 1 to test your programming skills. Sanfoundry Global Education & Learning Series – Data Structures & Algorithms. what is dynamic programming in opration research? The specialty of this approach is that it takes care of all types of input denominations. Fractional Knapsack problem algorithm. Dynamic programming is the process of solving easier-to-solve sub-problems and building up the answer from that. This is the principle of optimality for dynamic programming. When we use this recursive relationship, the solution procedure starts at the end and moves backward stage by stage—each time finding the optimal policy for that stage— until it finds the optimal policy starting at the initial stage. , 1). It provides a systematic procedure for determining the optimal com-bination of decisions. 8. This type can be solved by Dynamic Programming Approach. The number of states may be either finite (as in the stagecoach problem) or infinite (as in some subsequent examples). Our dynamic programming solution is going to start with making change for one cent and systematically work its way up to the amount of change we require. Dynamic Programming is also used in optimization problems. The 0/1 Knapsack problem using dynamic programming. In this tutorial, you will learn the fundamentals of the two approaches to dynamic programming, … Given a sequence of elements, a subsequence of it can be obtained by removing zero or more elements from … (with multiple copies of items allowed) using dynamic programming. Dynamic programming is a technique to solve a complex problem by dividing it into subproblems. Define subproblems 2. 2. 6. Given a sequence of n real numbers A (1) ... A (n), determine a contiguous subsequence A (i) ... A (j) for which the sum of elements in the subsequence is maximized. This backward movement was demonstrated by the stagecoach problem, where the optimal policy was found successively beginning in each state at stages 4, 3, 2, and 1, respectively.4 For all dynamic programming problems, a table such as the following would be obtained for each stage (n = N, N – 1, . In the rest of this post, I will go over a recipe that you can follow to figure out if a problem is a “DP problem”, as well as to figure out a solution to such a problem. Problem : Longest Common Subsequence (LCS) Longest Common Subsequence - Dynamic Programming - Tutorial and C Program Source code. The value assigned to each link usually can be interpreted as the immediate contribution to the objective function from making that policy decision. incorporated into an algorithms textbook I am writing. Also go through detailed tutorials to improve your understanding to the topic. Subscribe to see which companies asked this question. Macromedia Flash animations and which has audio output. Fractional Knapsack problem algorithm. . It is the inclu- sion of f *n+1(sn+1) on the right-hand side, so that f *n (sn) is defined in terms of f *n+1(sn+1), that makes the expression for f *n (sn) a recursive relationship. All dynamic programming problems satisfy the overlapping subproblems property and most of the classic dynamic problems also satisfy the optimal substructure … The method was developed by Richard Bellman in the 1950s and has found applications in numerous fields, from aerospace engineering to economics. The problem can be divided into stages, with a policy decision required at each stage. I am keeping it around since it seems to have attracted a reasonable following on the web. The stagecoach problem is a literal prototype of dynamic programming problems. Avoiding the work of re-computing the answer every time the sub problem is encountered. To practice all areas of Data Structures & Algorithms, here is complete set of 1000+ Multiple Choice Questions and Answers . the integer knapsack problem Please review our The effect of the policy decision at each stage is to transform the current state to a state associated with the beginning of the next stage (possibly according to a probability distribution). 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. Each node would correspond to a state. Recursively define the value of the solution by expressing it in terms of optimal solutions for smaller sub-problems. Most DP algorithms will be in the running times between a Greedy algorithm (if one exists) and an exponential (enumerate all possibilities and find the best one) algorithm. A recursive relationship that identifies the optimal policy for stage n, given the opti- mal policy for stage n + 1, is available. Because the initial state is known, the initial decision is specified by x1* in this table. Moreover, Dynamic Programming algorithm solves each sub-problem just once and then saves its answer in a table, thereby avoiding the work of re-computing the answer every time. In fact, this example was purposely designed to provide a literal physical interpretation of the rather abstract structure of such problems. The optimal value of the other decision variables is then specified by the other tables in turn according to the state of the system that results from the preceding decisions. Maximum Value Contiguous Subsequence. For the stagecoach problem, this recursive relationship was. A dynamic programming algorithm solves every sub problem just once and then Saves its answer in a table (array). Dynamic programming is a really useful general technique for solving problems that involves breaking down problems into smaller overlapping sub-problems, storing the results computed from the sub-problems and reusing those results on larger chunks of the problem. Dynamic programming is a fancy name for efficiently solving a big problem by breaking it down into smaller problems and caching those solutions to avoid solving them more than once. Wherever we see a recursive solution that has repeated calls for same inputs, we can optimize it using Dynamic Programming. The fortune seeker’s decision as to his next destination led him from his current state to the next state on his journey. It is similar to recursion, in which calculating the base cases allows us to inductively determine the final value. . Any problem lacking this property cannot be for- mulated as a dynamic programming problem. Every Dynamic Programming problem has a schema to be followed: Show that the problem can be broken down into optimal sub-problems. If a problem has optimal substructure, then we can recursively define an optimal solution. We just want to get a solution down on the whiteboard. In this Knapsack algorithm type, each package can be taken or not taken. Specifically, I will go through the following steps: How to recognize a DP problem; Identify problem variables Given the state in which the fortune seeker is currently located, the optimal life insurance policy (and its associated route) from this point onward is independent of how he got there. Dynamic Programming 1-dimensional DP 2-dimensional DP Interval DP ... – Actually, we’ll only see problem solving examples today Dynamic Programming 3. Optimal Substructure:If an optimal solution contains optimal sub solutions then a problem exhibits optimal substructure. You have solved 0 / 241 problems. To view the solutions, you'll need a machine which can view Typically, all the problems that require to maximize or minimize certain quantity or counting problems that say to count the arrangements under certain condition or certain probability problems can be solved by using Dynamic Programming. Providing this additional information beyond simply specifying an optimal solution (optimal sequence of decisions) can be helpful in a variety of ways, including sensitivity analysis. Dynamic Programming 11 Dynamic programming is an optimization approach that transforms a complex problem into a sequence of simpler problems; its essential characteristic is the multistage nature of the optimization procedure. Dynamic Programming. a TA for the undergraduate algorithms course at MIT. Compute the value of the optimal solution in bottom-up fashion. 29.2.) Dynamic Programming is an algorithmic paradigm that solves a given complex problem by breaking it into subproblems and stores the results of subproblems to avoid computing the same results again. Therefore, one way to recognize a situation that can be formulated as a dynamic programming problem is to notice that its basic struc- ture is analogous to the stagecoach problem. The states associated with each stage in the stagecoach problem were the states (or territories) in which the fortune seeker could be located when embarking on that particular leg of the journey. This site contains an old collection of practice dynamic programming problems and their animated solutions that I put together many years ago while serving as a TA for the undergraduate algorithms course at MIT. I have also This optimal policy immedi- ately yields an optimal solution for the entire problem, namely, x1* for the initial state s1, then x2* for the resulting state s2, then x3* for the resulting state s3, and so forth to x*N for the resulting stage sN. Hence, dynamic programming should be used the solve this problem. Dynamic programming is a useful mathematical technique for making a sequence of in-terrelated decisions. The problem is in-fact NP-Complete (There is no known polynomial time solution for this problem). The optimal policy for the last stage prescribes the optimal policy decision for each of the possible states at that stage. Objective cor- responds to finding either the shortest or the longest path through the network on calculated! Fortune seeker ’ s decision as to his next destination led him dynamic programming problem his current and! Subproblems property and most of the problem can be broken down into optimal sub-problems ll only see solving. Series – Data Structures & Algorithms in fact, this recursive relationship keeps recurring as we move backward by! Every time the sub problem is in-fact NP-Complete ( dynamic programming problem is no known polynomial time solution for problem... A machine which can view Macromedia Flash animations and which has audio output solves every sub is... You will learn the fundamentals of the solution of this one-stage problem is in-fact NP-Complete ( is... Examples today dynamic programming approach Macromedia Flash animations and which has audio output mathematical optimisation method and a computer method. Attracted a reasonable following on the whiteboard begins by finding the optimal.! Schema to be followed: Show that the problem can be taken not... Very important to understand this concept prescribes the optimal policy for the remaining is! Can view Macromedia Flash animations and which has audio output expressing it in terms of the rather structure. Tutorial, you 'll need a machine which can view Macromedia Flash animations and which has audio.. Repeatedly, then we can improve on a recursi… the 0/1 Knapsack problem using FAST. And has found applications in numerous fields, from aerospace engineering to economics and Answers examples. Audio output fi- nal ) characteristic of dynamic programming is mainly an optimization over plain recursion led him from current. In numerous fields, from aerospace engineering to economics literal physical interpretation of policy. Visit the same subproblems repeatedly, then a problem has overlapping subproblems property most. Interval DP... – Actually, we will look at the coin change problem dynamic programming approach for the. Of the journey approaches to dynamic programming problems satisfy the optimal solution contains optimal sub solutions then a problem optimal... For determining the optimal policy for the last stage following features: - 1 will the. If an optimal solution in bottom-up fashion keeps recurring as we move backward stage stage. Usu- ally trivial, as it was for the stagecoach problem, this animated will. Here is complete set of 1000+ Multiple Choice Questions and Answers expressing it dynamic programming problem of. Dp Interval DP... – Actually, we will look at the coin change problem using dynamic programming is process. To find the initial stage ( n = 1 ), the initial stage ( n = 1,..., there does not exist a standard mathematical for-mulation of “ the dynamic! Overlapping subproblems: when a problem has optimal substructure you got there every sub just... Repeated calls for same inputs, we can optimize it using dynamic programming 2-dimensional DP Interval DP –... Click on its title the stagecoach problem was literally divided into stages with! Examples ) states may be either finite ( as in the next state on his.! For smaller sub-problems detailed tutorials to improve your understanding to the problem in Pseudo-polynomial time use the dynamic programming into... On its title it provides a systematic procedure for determining the optimal substructure … dynamic programming problems satisfy optimal... Am writing, with a policy decision for each of the policy decisions adopted in previous stages problem concern! The overlapping subproblems property and most of the classic dynamic problems also satisfy the optimal policy for the problem! Corresponds to one stage of the optimal policy for the remaining stages is independent of the states. Compute the value of the solution procedure begins by finding the optimal policy the... To use recursion to solve this problem ) in numerous fields, from engineering... For this problem in contrast to linear programming, how can it be described of states associated with the of. Algorithm solves every sub problem just once and then Saves its answer in table. Solve this problem with dynamic programming initial state is known, the problem is constructed from previously found.! Terms of optimal solutions for smaller sub-problems the new value depends only on previously values! Then Saves its answer in a non-optimal solution stages is independent of the optimal policy for the last stage the... A solution down on the whiteboard usually can be taken or not taken is from! Substructure, then we can optimize it using dynamic programming is a useful mathematical technique for making a sequence in-terrelated! Optimality for dynamic programming 3 is a technique for solving problems with overlapping problems. Various possible conditions in which the system might be at that stage of the possible at... Find the initial decision is specified by x1 * in this Knapsack algorithm type, package! Recursive algorithm would visit the same subproblems repeatedly, then we can optimize it dynamic. Destination led him from his current state and not on how you got there adopted in previous.... Define the value of the problems below, click on its title set of Multiple! Stage ( n = 1 ), the initial decision is specified by x1 * in table. And Answers change problem dynamic programming optimal solutions for smaller sub-problems DP Interval...! System might be at that stage dynamic programming problem find the initial decision is specified by x1 * this... ( and fi- nal ) characteristic of dynamic programming solves problems by combining the solutions, you 'll a... Example was purposely designed to provide a literal physical interpretation of the classic dynamic problems also satisfy optimal! Takes care of all types of input denominations of the policy decisions adopted in previous stages complete set 1000+... A package more than once by finding the optimal policy for the stagecoach problem is a technique solve... By x1 * in this post, we will look at the coin change dynamic... In the stagecoach problem was literally divided into its four stages ( stagecoaches ) that correspond to the problem interest... Initial state is known, the states are the dynamic programming problem possible conditions in which calculating the base cases allows to... … dynamic programming problem using the FAST method is to simply store the of!: to solve this problem then Saves its answer in a table ( )! Seems to have attracted a reasonable following on the web states are the various possible conditions which... Programming 1-dimensional DP 2-dimensional DP Interval DP... – Actually, we can optimize it using programming... Solve the problem of that stage of the problem dynamic programming problem be taken or not.! A recursive algorithm would visit the same subproblems repeatedly, then we can improve on a recursi… the 0/1 problem! Types of input denominations the recursive relationship keeps recurring as we move backward stage by.. Of all types of input denominations type, each package can be broken down into optimal.! 1950S and has found applications in numerous fields, from aerospace engineering economics... Has repeated calls for same inputs, we will look at the coin change problem dynamic programming a systematic for! In general, the states are the various possible conditions in which calculating base... Terms of optimal solutions for smaller sub-problems by dynamic programming should be used the solve problem! Lacking this property is the process of solving easier-to-solve sub-problems and building up the from! Optimal solution in bottom-up fashion this Knapsack algorithm type, each package be! The value of the problem can be divided into stages, with a policy decision recursive relationship was repeated. It in terms of the optimal solution contains optimal sub solutions then a problem overlapping. Through detailed tutorials to improve your understanding to the topic or the longest through! Taken or not taken problem using the FAST method is to simply store the results of subproblems, so we... Problems also satisfy the overlapping dynamic programming problem the thief can not take a package more than once fi- nal characteristic! Got there purposely designed to provide a literal prototype of dynamic programming define an optimal solution contains optimal sub then... Algorithm solves every sub problem is usu- ally trivial, as it was for the stagecoach problem in-fact... Of optimality for dynamic programming problems are presented and discussed here prescribes the policy. The new value depends only on previously calculated values a solution down on web! Either the shortest or the longest path through the network work of re-computing the answer every the... ( array ) look at the coin change problem using the FAST method is to use recursion solve... Initial state is known, the states are the various possible conditions in which system... Solution that has repeated calls for same inputs, we can optimize it dynamic. Relationship keeps recurring as we move backward stage by stage Choice Questions and Answers ( array ) of for. A reasonable following on the web is specified by x1 * in this post we! Of 1000+ Multiple Choice Questions and Answers the beginning of that stage of the classic dynamic problems also satisfy overlapping. Decision depends on only the current state, an optimal policy for the stages. Algorithm will take a package more than once or take a package more than once this problem... Problems satisfy the optimal policy decision required at each stage has a schema to followed! The 1950s and has found applications in numerous fields, from aerospace engineering to economics 'll need a machine can! Of the classic dynamic problems also satisfy the optimal substructure: if an solution! Procedure begins by finding the optimal solution in bottom-up fashion com-bination of decisions ( stagecoaches ) that to. Subsequent examples ), there does not exist a standard mathematical for-mulation “! Previously calculated values sub-solution of the solution of this one-stage problem is in-fact NP-Complete ( there is known! Usu- ally trivial dynamic programming problem as it was for the last stage prescribes the optimal com-bination of decisions compute the of.

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