# Difference between revisions of "Recursion"

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The summation function, designated by an uppercase Sigma in mathematics, is a popular example of recursion: | The summation function, designated by an uppercase Sigma in mathematics, is a popular example of recursion: | ||

− | < | + | <syntaxhighlight> |

function Summation (num : integer) : integer; | function Summation (num : integer) : integer; | ||

begin | begin | ||

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Summation := Summation(num-1) + num | Summation := Summation(num-1) + num | ||

end; | end; | ||

− | </ | + | </syntaxhighlight> |

Suppose you call <tt>Summation</tt> for <tt>3</tt>. | Suppose you call <tt>Summation</tt> for <tt>3</tt>. | ||

− | < | + | <syntaxhighlight> |

a := Summation(3); | a := Summation(3); | ||

− | </ | + | </syntaxhighlight> |

* <tt>Summation(3)</tt> becomes <tt>Summation(2) + 3</tt>. | * <tt>Summation(3)</tt> becomes <tt>Summation(2) + 3</tt>. |

## Revision as of 15:54, 24 March 2012

4E - Recursion (author: Tao Yue, state: unchanged)

*Recursion* is a difficult topic to grasp. However, it's very easy to apply once you understand it. The programming assignment for this chapter will involve recursion.

Recursion means allowing a function or procedure to call itself. It keeps calling itself until some limit is reached.

The summation function, designated by an uppercase Sigma in mathematics, is a popular example of recursion:

```
function Summation (num : integer) : integer;
begin
if num = 1 then
Summation := 1
else
Summation := Summation(num-1) + num
end;
```

Suppose you call `Summation` for `3`.

`a := Summation(3);`

`Summation(3)`becomes`Summation(2) + 3`.`Summation(2)`becomes`Summation(1) + 2`.- At
`1`, the recursion stops and becomes`1`. `Summation(2)`becomes`1 + 2 = 3`.`Summation(3)`becomes`3 + 3 = 6`.`a`becomes`6`.

Recursion works backward until a given point is reached at which an answer is defined, and then works forward with that definition, solving the other definitions which rely upon that one.

All recursive procedures/functions should have some sort of test so stop the recursion. Under one condition, called the base condition, the recursion should stop. Under all other conditions, the recursion should go deeper. In the example above, the base condition was `if num = 1`. If you don't build in a base condition, the recursion will either not take place at all, or become infinite.

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