C++ Chapter 15: Recursion

Rules for recursive cases

1) Every recursive definition must have one (or more) base cases. 2) the general case must eventually reduce to the base case. 3) the base case stops the recursion.

two ways of repeating statements in C++

1) looping structures (for, while, do...while) 2) recursive functions

First step in developing a recursive function

Define the problem and find the limiting (base case) solution

recursive algorithm

an algorithm that finds the solution to a problem by reducing the problem to smaller versions of itself; It must have one or more base cases, and the general case must eventually be reduced to a base case

directly recursive

refers to functions that explicitly call themselves

In order to decide whether to call recursively again, a recursive function uses a...

selections structure ("if" or "switch" statement)

recursive definition

statement of a problem solution in which the problem is reduced to smaller versions of itself

Rightmost bit

the binary representation of the remainder after division by 2

base case

the case for which the solution is obtained directly

general case

the case that is recursively defined and eventually reduces to the base case.

Recursion

the process of solving a problem with a self-referencing process or the process of solving a problem by reducing it to smaller versions of itself

rightmost bit (of x )

the remainder of x after division by 2

Why are base cases necessary in recursive solutions?

A recursive solution will call itself, simplifying the problem each time until it reaches a base case. If there is no base case, then infinite recursion will occur

Why can you think of a recursive function as having an unlimited number of copies of itself?

Because every call to the recursive function has its own code and its own set of parameters and local variables

Which is faster, iteration or recursion?

Iteration. Recursion requires a constant allocation and deallocation of memory that makes it slower

Can main be called recursively?

NO

Recursion

The process of solving a problem by reducing it to smaller versions of itself

infinite recursion

When no base case is offered, and the function continues to call upon itself infinitely.

When does recursion terminate?

When the base case is recognized.

recursive definition

a definition in which something is defined in terms of a smaller version of itself

tail recursive function

a function in which the last statement executed is the recursive call.

recursive function

a function that calls itself in its body.

recursive function

a function that calls itself, either directly or indirectly

tail recursive function

a recursive function in which the last statement executed is the recursive call

indirectly recursive

a recursive function that calls another function that results in the original function call

directly recursive

a recursive function that calls itself

recursive algorithm

a solution that solves the problem by breaking it into smaller versions of itself, then using the necessary code to solve.

general case

case In a recursive algorithm, the case where the solution is obtained recursively by simplification on each call

base case

in a recursive algorithm, the case for which the solution is obtained directly

iterative control structures

use a looping structure, such as while, for, or do...while, to repeat a set of statements

indirectly recursive

when a function calls another function that calls upon the first function.

Can a recursive function have more than one base case?

yes