Backtracking Flashcards
What is the city road trip problem?
The city road trip problem involves finding the shortest route that visits all specified places exactly once and returns to the starting point, ensuring that no place is revisited.
Why is the brute-force approach impractical for solving the city road trip problem?
The brute-force approach is impractical because it requires generating and evaluating all possible permutations of the places, which grows factorially (n!) as the number of places increases, making it computationally infeasible for large numbers of places.
What is backtracking?
Backtracking is an algorithmic technique for solving problems by incrementally building solutions, abandoning choices as soon as it is determined that they cannot lead to a feasible solution, and exploring alternatives.
How does the backtracking approach solve the city road trip problem?
The backtracking approach solves the problem by starting from an initial place, recursively visiting unvisited places while keeping track of the total distance, and backtracking when a place has been revisited or no further progress can be made, ensuring that the shortest route is found.
What is the base case in the backtracking algorithm for the city road trip problem?
The base case occurs when all places have been visited. At this point, the algorithm checks the total distance including the return to the starting point and updates the minimum distance if the current route is shorter than previously recorded routes.
What is the main advantage of the backtracking approach over the brute-force method?
The main advantage of the backtracking approach is its efficiency. By applying constraints and pruning non-viable paths at each step, backtracking reduces the number of routes that need to be evaluated, making it more feasible for larger problems compared to the brute-force method.
How is the backtracking algorithm implemented in the context of the city road trip problem?
The backtracking algorithm is implemented using recursion. It starts from the initial place, marks it as visited, and recursively visits unvisited places, backtracking when necessary. It keeps track of the total distance and updates the minimum distance when a complete route is found.
Can you give an example of a real-world problem that can be solved using backtracking?
Real-world problems that can be solved using backtracking include pathfinding in mazes, solving puzzles like Sudoku, generating permutations and combinations, and syntax analysis in compilers.
In the context of backtracking, what does it mean to “prune non-viable paths”?
Pruning non-viable paths means stopping the exploration of a route as soon as it is determined that continuing down that path cannot lead to a feasible solution, thus saving computational effort by not considering unnecessary possibilities.
What are some characteristics of problems that are well-suited for a backtracking approach?
Problems well-suited for backtracking typically require exploring all potential solutions incrementally, need to find the best feasible solution, and benefit from pruning non-viable paths early to avoid unnecessary computations.
