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1. Top results related to what is backtracking in dynamic programming example

   • What is the dynamic programming algorithm for finding a Hamiltonian cycle in a graph?

     Top Answer

     Answered Sep 07, 2009 · 37 votes

     There is indeed an O(n2n) dynamic-programming algorithm for finding Hamiltonian cycles. The idea, which is a general one that can reduce many O(n!) backtracking approaches to O(n22n) or O(n2n) (at the cost of using more memory), is to consider subproblems that are sets with specified "endpoints".

     Here, since you want a cycle, you can start at any vertex. So fix one, call it x. The subproblems would be: “For a given set S and a vertex v in S, is there a path starting at x and going through all the vertices of S, ending at v?” Call this, say, poss[S][v].

     As with most dynamic programming problems, once you define the subproblems the rest is obvious: Loop over all the 2n sets S of vertices in any "increasing" order, and for each v in each such S, you can compute poss[S][v] as:

     poss[S][v] = (there exists some u in S such that poss[S−{v}][u] is True and an edge u->v exists)

     Finally, there is a Hamiltonian cycle iff there is a vertex v such that an edge v->x exists and poss[S][v] is True, where S is the set of all vertices (other than x, depending on how you defined it).

     If you want the actual Hamiltonian cycle instead of just deciding whether one exists or not, make poss[S][v] store the actual u that made it possible instead of just True or False; that way you can trace back a path at the end.

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   • What is the practical scenario/example/use of dynamic memory allocation and vector of pointers in C++?

     Top Answer

     Answered May 12, 2022 · 1 votes

     • Static allocation:You know the requested memory size at compile time, so you can define an array like:

     int buf[20]; // This is an array of 20 ints-

     • Dynamic allocation:You allocate the storage at runtime. For example the needed array size is an input to your progam:

     int *buf = new int[n]; // where n is some runtime known number.<some code...>delete[] buf; // In this case you must release the memory when you don't need it anymore-

     For example an usecase of an array of pointers is polymorphism. You have a class Base, and you have Derived classes (ie Der1, Der2, Der3). You want to store many object from those derived classes in an array. But you can't since the array type tells you what can you store in them. So in this case you can store the pointers to the Der* objects in the array, as if it is a Base* object.

     struct Base{ virtual ~Base() {}; virtual void doSomething() = 0;};-struct Der1 : Base{ virtual void doSomething(); // define what Der1 does for this function};-struct Der2 : Base{ virtual void doSomething(); // define what Der2 does for this function};-struct Der3 : Base{ virtual void doSomething(); // define what Der3 does for this function};-int main(){ // You allocate memory for Base* types so this is an array of pointers Base* some_array[3]; // It can be also dynamically allocated- // And now you can store Der* in this array as: some_array[0] = new Der1(); some_array[1] = new Der2(); some_array[2] = new Der3(); // There we did dynamic allocation with new!!! // Since our objects are not in the some_array array, but somewhere in the memory, // and we store pointers to them in the array- // And you can do: some_array[0]->doSomething(); some_array[1]->doSomething(); some_array[2]->doSomething();- // Release the DYNAMICALLY!! allocated things delete some_array[0]; delete some_array[1]; delete some_array[2];}-

     But there are many other usecases. This is just one of them...

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   • What is dynamic programming?

     Top Answer

     Answered Apr 26, 2017 · 221 votes

     Dynamic programming is when you use past knowledge to make solving a future problem easier.

     A good example is solving the Fibonacci sequence for n=1,000,002.

     This will be a very long process, but what if I give you the results for n=1,000,000 and n=1,000,001? Suddenly the problem just became more manageable.

     Dynamic programming is used a lot in string problems, such as the string edit problem. You solve a subset(s) of the problem and then use that information to solve the more difficult original problem.

     With dynamic programming, you store your results in some sort of table generally. When you need the answer to a problem, you reference the table and see if you already know what it is. If not, you use the data in your table to give yourself a stepping stone towards the answer.

     The Cormen Algorithms book has a great chapter about dynamic programming. AND it's free on Google Books! Check it out here.

     Other Answers

     Answered Nov 09, 2019 · 203 votes

     Dynamic programming is a technique used to avoid computing multiple times the same subproblem in a recursive algorithm.

     Let's take the simple example of the Fibonacci numbers: finding the n th Fibonacci number defined by

     Fn = Fn-1 + Fn-2 and F0 = 0, F1 = 1

     Recursion

     The obvious way to do this is recursive:

     def fibonacci(n): if n == 0: return 0 if n == 1: return 1- return fibonacci(n - 1) + fibonacci(n - 2)-

     Dynamic Programming

     • Top Down - Memoization

     The recursion does a lot of unnecessary calculations because a given Fibonacci number will be calculated multiple times. An easy way to improve this is to cache the results:

     cache = {}-def fibonacci(n): if n == 0: return 0 if n == 1: return 1 if n in cache: return cache[n]- cache[n] = fibonacci(n - 1) + fibonacci(n - 2)- return cache[n]-

     • Bottom-Up

     A better way to do this is to get rid of the recursion all-together by evaluating the results in the right order:

     cache = {}-def fibonacci(n): cache[0] = 0 cache[1] = 1- for i in range(2, n + 1): cache[i] = cache[i - 1] + cache[i - 2]- return cache[n]-

     We can even use constant space and store only the necessary partial results along the way:

     def fibonacci(n): fi_minus_2 = 0 fi_minus_1 = 1- for i in range(2, n + 1): fi = fi_minus_1 + fi_minus_2 fi_minus_1, fi_minus_2 = fi, fi_minus_1- return fi-

     • ["How apply dynamic programming?",""," ","Find the recursion in the problem.","Top-down: store the answer for each subproblem in a table to avoid having to recompute them.","Bottom-up: Find the right order to evaluate the results so that partial results are available when needed."," ",""]

     Dynamic programming generally works for problems that have an inherent left to right order such as strings, trees or integer sequences. If the naive recursive algorithm does not compute the same subproblem multiple times, dynamic programming won't help.

     I made a collection of problems to help understand the logic: https://github.com/tristanguigue/dynamic-programing

     Other Answers

     Answered Jun 30, 2009 · 40 votes

     Memoization is the when you store previous results of a function call (a real function always returns the same thing, given the same inputs). It doesn't make a difference for algorithmic complexity before the results are stored.

     Recursion is the method of a function calling itself, usually with a smaller dataset. Since most recursive functions can be converted to similar iterative functions, this doesn't make a difference for algorithmic complexity either.

     Dynamic programming is the process of solving easier-to-solve sub-problems and building up the answer from that. 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.

     • DP algorithms could be implemented with recursion, but they don't have to be.
     • DP algorithms can't be sped up by memoization, since each sub-problem is only ever solved (or the "solve" function called) once.

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   • What is the use of dynamic_pointer_cast in C++? When is it used? What are alternatives for dynamic_pointer_cast?

     Top Answer

     Answered Jun 17, 2021 · 9 votes

     dynamic_pointer_cast is used to convert std::shared_ptr type, e.g. from the pointer on a base class to a pointer on a derived class:

     #include <memory>-struct A{ virtual ~A() = default; };struct B: A {};int main(){ std::shared_ptr<A> pA = std::make_shared<B>(); std::shared_ptr<B> pB = std::dynamic_pointer_cast<B>(pA);}

     So dynamic_pointer_cast is a convenience wrapper around dynamic_cast:

     template< class T, class U > std::shared_ptr<T> dynamic_pointer_cast( const std::shared_ptr<U>& r ) noexcept{ if (auto p = dynamic_cast<typename std::shared_ptr<T>::element_type*>(r.get())) { return std::shared_ptr<T>{r, p}; } else { return std::shared_ptr<T>{}; }}

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   • What is Top-Down Parsing with Backtracking in Compiler Design?

     Backtracking in top-down parsing provides flexibility to handle ambiguous grammars or situations where the parser encounters uncertainty in choosing the correct production rule. However, it can lead to inefficient parsing, especially when the grammar has many backtracking points or when the input has long ambiguous sequences.

     In such cases, alternative parsing techniques, such as predictive parsing or bottom-up parsing, may be more efficient.In the field of parsing algorithms, backtracking plays a crucial role in handling ambiguity and making alternative choices during the parsing process.

     Specifically, in top-down parsers, which start with the initial grammar symbol and recursively expand non-terminals, backtracking allows the parser to explore different options when the chosen production fails to match the input. In this article, we will delve into the concept of backtracking in top-down parsing, its significance in handling ambiguity, and its impact on the parsing process.

     To improve the performance of top-down parsers, various optimization techniques can be employed, including left-factoring, left-recursion elimination, and the use of lookahead tokens to predict the correct production choice without excessive backtracking.

     Understanding Backtracking in Top-Down Parsing

     Top-down parsing is a technique where a parser...

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2. www.geeksforgeeks.org · introduction-to-backtracking-2Introduction to Backtracking - GeeksforGeeks

   www.geeksforgeeks.org · introduction-to-backtracking-2

   

   Jun 24, 2024 · Backtracking is like trying different paths, and when you hit a dead end, you backtrack to the last choice and try a different route. In this article, we’ll explore the basics of backtracking, how it works, and how it can help solve all sorts of challenging problems.

3. Searches related to what is backtracking in dynamic programming example

   what is backtracking in dynamic programming example problems	what is backtracking in dynamic programming example in c
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4. stackoverflow.com · questions · 3592943Difference between back tracking and dynamic programming

   stackoverflow.com · questions · 3592943

   

   Mar 31, 2020 · Backtracking is a general algorithm for finding all (or some) solutions to some computational problem, that incrementally builds candidates to the solutions, and abandons each partial candidate c ("backtracks") as soon as it determines that c cannot possibly be completed to a valid solution.

5. www.javatpoint.com · dynamic-programming-vsDynamic programming vs Backtracking - javatpoint

   www.javatpoint.com · dynamic-programming-vs

   

   • What Is Backtracking?
   • What Is Dynamic Programming?
   • Differences Between Dynamic Programming and Backtracking

   Backtracking is one of the problem-solving techniques. Using this technique, we can solve our problem. This strategy uses a Brute force approach, and the brute force approach says that for the given problem, we should try out all the possible solutions and pick the desired solution from all the possible solutions. In contrast, dynamic programming i...

   See full list on javatpoint.com

   Dynamic programming is a technique for solving certain type of complex problems efficiently by breaking them down into simpler subproblems and solving each problem exactly once. Dynamic programming stores the result of a subproblem in a table and reuse them when needed to avoid solving the same problems again and again. What type of problems can be...

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   Dynamic programming is a technique of dividing the complex problem into simpler sub-problems. This technique is applicable to the problems that exhibit the following properties: Overlapping subprob...

   The major difference between the dynamic programming and backtracking is that the dynamic programming completely relies on the principle of optimality which means that the sub sequence of a sequenc...

   Dynamic programming is a technique that solves the optimization problem. Optimization problem uses either minimum or maximum result. In contrast to dynamic programming, backtracking uses the brute...

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6. www.geeksforgeeks.org · backtracking-algorithmsBacktracking Algorithm - GeeksforGeeks

   www.geeksforgeeks.org · backtracking-algorithms

   

   Apr 17, 2024 · Example of Backtracking Algorithm. Example: Finding the shortest path through a maze. Input: A maze represented as a 2D array, where 0 represents an open space and 1 represents a wall. Algorithm: Start at the starting point. For each of the four possible directions (up, down, left, right), try moving in that direction.

7. www.codingdrills.com · tutorial · introduction-toBacktracking vs. Dynamic Programming - CodingDrills

   www.codingdrills.com · tutorial · introduction-to

   

   Learn about backtracking algorithms and how they differ from dynamic programming. Explore the advantages and use cases of each approach to problem-solving in this detailed technical post aimed at programmers.

8. www.programiz.com · dsa · backtracking-algorithmBacktracking Algorithm - Programiz

   www.programiz.com · dsa · backtracking-algorithm

   

   A backtracking algorithm is a problem-solving algorithm that uses a brute force approach for finding the desired output. The Brute force approach tries out all the possible solutions and chooses the desired/best solutions.

9. People also ask

   What is backtracking in dynamic programming?

   • The solution required trying out multiple possibilities whenever there was a choice to be made, a solution I referred to as backtracking. If you read my graphical introduction to dynamic programming, you’ll know I frequently bring up choice as a key concept when applying dynamic programming to problems.

   A tree-based introduction to backtracking | by Avik Das - Medium

   medium.com/swlh/a-tree-based-introduction-to-backtracking-57e38264b2d2

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   What is a backtracking algorithm?

   • Backtracking algorithms are a powerful technique used in various problem-solving scenarios. They allow programmers to find all possible solutions to a problem by exhaustively searching through the solution space. In this post, we will dive deep into the world of backtracking algorithms and explore how they compare to dynamic programming.

   Backtracking vs. Dynamic Programming | CodingDrills

   www.codingdrills.com/tutorial/introduction-to-backtracking-algorithms/backtracking-dynamic-programming

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   How to solve a problem using backtracking?

   • Backtracking is one of the problem-solving techniques. Using this technique, we can solve our problem. This strategy uses a Brute force approach, and the brute force approach says that for the given problem, we should try out all the possible solutions and pick the desired solution from all the possible solutions.

   Dynamic programming vs Backtracking - javatpoint

   www.javatpoint.com/dynamic-programming-vs-backtracking

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   What is a backtracking approach?

   • At its core, backtracking is a systematic approach to problem-solving that involves trying out different possibilities and "backtracking" when the current choice does not lead to a valid solution. It is often used when the problem can be divided into multiple subproblems, and the solution can be built incrementally by making choices at each step.

   Backtracking vs. Dynamic Programming | CodingDrills

   www.codingdrills.com/tutorial/introduction-to-backtracking-algorithms/backtracking-dynamic-programming

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10. medium.com · swlh · a-tree-based-introduction-toA tree-based introduction to backtracking | by Avik Das | The ...

    medium.com · swlh · a-tree-based-introduction-to

    

    Feb 26, 2020 · a A. The choice occurs when the first A is encountered, and we want to know if we should use it to close the previous a or to start a new group. We can represent this choice as a tree, forking into...