Difference between revisions of "Recursion"

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4E - Recursion (author: Tao Yue, state: unchanged)
 
4E - Recursion (author: Tao Yue, state: unchanged)
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The summation function, designated by an uppercase letter ''sigma'' (Σ) in mathematics, can be written recursively:
 
The summation function, designated by an uppercase letter ''sigma'' (Σ) in mathematics, can be written recursively:
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function Summation (num : integer) : integer;
 
function Summation (num : integer) : integer;
 
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Suppose you call <tt>Summation</tt> for <tt>3</tt>.
 
Suppose you call <tt>Summation</tt> for <tt>3</tt>.
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a := Summation(3);
 
a := Summation(3);
 
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In the example above, the base condition was <tt>if num = 1</tt>.  
 
In the example above, the base condition was <tt>if num = 1</tt>.  
  
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Latest revision as of 08:29, 25 February 2020

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

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

The summation function, designated by an uppercase letter sigma (Σ) in mathematics, can be written recursively:

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 a test to stop the recursion, the base condition. Under all other conditions, the recursion should go deeper. If there is no base condition, the recursion will either not take place at all, or become infinite.

In the example above, the base condition was if num = 1.

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