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Algorithm X is a recursive, nondeterministic, depth-first, backtracking algorithm that finds all solutions to the exact cover problem. Some of the better-known exact cover problems include tiling , the n queens problem , and Sudoku .
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 ...
Recursive drawing of a Sierpiński Triangle through turtle graphics. 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 ...
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 ...
This algorithm, also known as the "recursive backtracker" algorithm, is a randomized version of the depth-first search algorithm. Frequently implemented with a stack, this approach is one of the simplest ways to generate a maze using a computer. Consider the space for a maze being a large grid of cells (like a large chess board), each cell ...
These examples reduce easily to a single recursive function by inlining the forest function in the tree function, which is commonly done in practice: directly recursive functions that operate on trees sequentially process the value of the node and recurse on the children within one function, rather than dividing these into two separate functions.
A total recursive function is a partial recursive function that is defined for every input. Every primitive recursive function is total recursive, but not all total recursive functions are primitive recursive. The Ackermann function A(m,n) is a well-known example of a total recursive function (in fact, provable total), that is not primitive ...
Top-down approach: This is the direct fall-out of the recursive formulation of any problem. If the solution to any problem can be formulated recursively using the solution to its sub-problems, and if its sub-problems are overlapping, then one can easily memoize or store the solutions to the sub-problems in a table (often an array or hashtable ...