Overlapping subproblem
Encyclopedia
In computer science
, a problem
is said to have overlapping subproblems if the problem can be broken down into subproblems which are reused several times or a recursive algorithm for the problem solves the same subproblem over and over rather than always generating new subproblem.
For example, the problem of computing the Fibonacci sequence exhibits overlapping subproblems. The problem of computing the nth Fibonacci number
F(n), can be broken down into the subproblems of computing F(n − 1) and F(n − 2), and then adding the two. The subproblem of computing F(n − 1) can itself be broken down into a subproblem that involves computing F(n − 2). Therefore the computation of F(n − 2) is reused, and the Fibonacci sequence thus exhibits overlapping subproblems.
Computer science
Computer science or computing science is the study of the theoretical foundations of information and computation and of practical techniques for their implementation and application in computer systems...
, a problem
Problem
A problem is an obstacle, impediment, difficulty or challenge, or any situation that invites resolution; the resolution of which is recognized as a solution or contribution toward a known purpose or goal...
is said to have overlapping subproblems if the problem can be broken down into subproblems which are reused several times or a recursive algorithm for the problem solves the same subproblem over and over rather than always generating new subproblem.
For example, the problem of computing the Fibonacci sequence exhibits overlapping subproblems. The problem of computing the nth Fibonacci number
Fibonacci number
In mathematics, the Fibonacci numbers are the numbers in the following integer sequence:0,\;1,\;1,\;2,\;3,\;5,\;8,\;13,\;21,\;34,\;55,\;89,\;144,\; \ldots\; ....
F(n), can be broken down into the subproblems of computing F(n − 1) and F(n − 2), and then adding the two. The subproblem of computing F(n − 1) can itself be broken down into a subproblem that involves computing F(n − 2). Therefore the computation of F(n − 2) is reused, and the Fibonacci sequence thus exhibits overlapping subproblems.