Backtracking - Wikipedia, the free encyclopedia
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.
Backtracking can be applied only for problems which admit the concept of a "partial candidate solution" and a relatively quick test of whether it can possibly be completed to a valid solution
Backtracking algorithms use recursion to search for the best solution to complicated problems. These algorithms recursively build partial test solutions to solve the problem. When they find that a test solution cannot lead to a usable final solution, they backtrack, discarding that test solution and continuing the search from farther up the call stack.
Backtracking is useful when you can incrementally build partial solutions and you can sometimes quickly determine that a partial solution cannot lead to a complete solution. In that case, you can stop improving that partial solution, backtrack to the previous partial solution, and continue the search from there.
The general form of a Backtracking algorithm:
The easiest way to implement a backtracking algorithm is by using recursion.
First, We need to define three cases:
Find any solution:
Find the best solution:
First, you should always check all the possible paths! Even if you find a solution, you should continue looking for a better one. The trick here is to have a dynamic Reject case. At the beginning of the algorithm you set somebest_solution variable to a maximal value. During the runtime of the algorithm, every time you find a better solution you update this variable. This variable gives you the ability to drop possible solutions without completely checking them.
Don’t use Backtracking to solve a problem that already has a known solution
Use Backtracking to solve problems with a small input or with a small set of possible solutions, otherwise your CPU will really hate you!
Trade-off – This is the most important one for me. Sometimes there is a known solution for a problem, but implementing & QA it may take a long time.
Print all permutations of a given string
http://www.geeksforgeeks.org/write-a-c-program-to-print-all-permutations-of-a-given-string/
Read full article from Practicing Backtracking | The Tokenizer
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.
Backtracking can be applied only for problems which admit the concept of a "partial candidate solution" and a relatively quick test of whether it can possibly be completed to a valid solution
Backtracking algorithms use recursion to search for the best solution to complicated problems. These algorithms recursively build partial test solutions to solve the problem. When they find that a test solution cannot lead to a usable final solution, they backtrack, discarding that test solution and continuing the search from farther up the call stack.
Backtracking is useful when you can incrementally build partial solutions and you can sometimes quickly determine that a partial solution cannot lead to a complete solution. In that case, you can stop improving that partial solution, backtrack to the previous partial solution, and continue the search from there.
The general form of a Backtracking algorithm:
The easiest way to implement a backtracking algorithm is by using recursion.
First, We need to define three cases:
- Reject: We are in the wrong way → this path can't lead us to the solution.
- Accept: We find a solution for the problem.
- Step: We are at some point between A to B, continue to the next step.
Find any solution:
Find the best solution:
First, you should always check all the possible paths! Even if you find a solution, you should continue looking for a better one. The trick here is to have a dynamic Reject case. At the beginning of the algorithm you set somebest_solution variable to a maximal value. During the runtime of the algorithm, every time you find a better solution you update this variable. This variable gives you the ability to drop possible solutions without completely checking them.
Don’t use Backtracking to solve a problem that already has a known solution
Use Backtracking to solve problems with a small input or with a small set of possible solutions, otherwise your CPU will really hate you!
Trade-off – This is the most important one for me. Sometimes there is a known solution for a problem, but implementing & QA it may take a long time.
Print all permutations of a given string
http://www.geeksforgeeks.org/write-a-c-program-to-print-all-permutations-of-a-given-string/
Time Complexity: O(n*n!)
void permute(char *a, int i, int n) { int j; if (i == n) printf("%s\n", a); else { for (j = i; j <= n; j++) { swap((a+i), (a+j)); permute(a, i+1, n); swap((a+i), (a+j)); //backtrack } }} public static void digitSumBacktracking (ArrayList input_list, ArrayList output_list, int sum, int level) { counter++; // Reject – this path doesn't lead to any solution if (sum > MATCH) { return; } // Accept – We find a solution! if (sum == MATCH) { System.out.println("Solution: " + output_list); return; } // Step – go over all the possible options in the input for (Integer n : input_list) { ArrayList clone_input_list = (ArrayList) input_list.clone(); clone_input_list.remove(n); ArrayList clone_output_list = (ArrayList) output_list.clone(); clone_output_list.add(n); digitSumBacktracking(clone_input_list , clone_output_list, sum + n,level + 1); } }Read full article from Practicing Backtracking | The Tokenizer
