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The solutions to the sub-problems are then combined to give a solution to the original problem. The divide-and-conquer technique is the basis of efficient algorithms for many problems, such as sorting (e.g., quicksort , merge sort ), multiplying large numbers (e.g., the Karatsuba algorithm ), finding the closest pair of points , syntactic ...
Some of the better-known exact cover problems include tiling, the n queens problem, and Sudoku. The name dancing links , which was suggested by Donald Knuth , stems from the way the algorithm works, as iterations of the algorithm cause the links to "dance" with partner links so as to resemble an "exquisitely choreographed dance."
The exact cover problem is represented in Algorithm X by an incidence matrix A consisting of 0s and 1s. The goal is to select a subset of the rows such that the digit 1 appears in each column exactly once. Algorithm X works as follows: If the matrix A has no columns, the current partial solution is a valid solution; terminate successfully.
In computer science, recursion is a method of solving a computational problem where the solution depends on solutions to smaller instances of the same problem. [1] [2] Recursion solves such recursive problems by using functions that call themselves from within their own code. The approach can be applied to many types of problems, and recursion ...
Recursion in computer programming is exemplified when a function is defined in terms of simpler, often smaller versions of itself. The solution to the problem is then devised by combining the solutions obtained from the simpler versions of the problem. One example application of recursion is in parsers for programming languages. The great ...
Prune and search is a method of solving optimization problems suggested by Nimrod Megiddo in 1983. [1]The basic idea of the method is a recursive procedure in which at each step the input size is reduced ("pruned") by a constant factor 0 < p < 1.
Step 14: Now compare 3 with the remaining elements in the original list until there is a number greater than 3. 7 > 3, so 7 is added to the sub-list and is removed from the original list. Step 15: Since there are no more elements in the original list to compare {7} to, the sub-list is merged with the solution list. The original list now ...
This recursive call will end up making three second-level recursive calls to the algorithm that report the three cliques {3,4}, {4,5}, and {4,6}. Then, vertex 4 is added to X and removed from P . In the third and final iteration of the inner loop of the algorithm, for v = 6, there is a recursive call to the algorithm with R = {6}, P = Ø, and X ...