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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;
  if num = 1 then
    Summation := 1
    Summation := Summation(num-1) + num

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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