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Divide-and-Conquer Algorithm


A divide-and-conquer algorithm solves a problem by dividing it into smaller subproblems of the same type, solving the subproblems by recursion until reaching directly solvable base cases, and combining their solutions. Its running time is therefore often described by a recurrence equation. If a problem of size n is divided into a subproblems of size n/b and the division and combination require time f(n), a typical recurrence equation is

 T(n)=aT(n/b)+f(n).

The Akra-Bazzi method treats a more general class in which the subproblems can have unequal sizes and their arguments can contain controlled perturbations.


See also

Akra-Bazzi Method, Recurrence Equation, Recursion

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References

Cormen, T. H.; Leiserson, C. E.; Rivest, R. L.; and Stein, C. "Divide-and-Conquer." Ch. 4 in Introduction to Algorithms, 3rd ed. Cambridge, MA: MIT Press, pp. 65-122, 2009.

Cite this as:

Weisstein, Eric W. "Divide-and-Conquer Algorithm." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Divide-and-ConquerAlgorithm.html

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