Recursion You will learn what is recursion as
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Recursion You will learn what is recursion as well as how and when to use it in your programs. James Tam
What Is Recursion? “the determination of a succession of elements by operation on one or more preceding elements according to a rule or formula involving a finite number of steps” (Merriam. Webster online) James Tam
What This Really Means Breaking a problem down into a series of steps. The final step is reached when some basic condition is satisfied. The solution for each step is used to solve the previous step. James Tam
Definition For Philosophy “…state of mind of the wise man; practical wisdom…” 1 See Metaphysics 1 The New Webster Encyclopedic Dictionary of the English Language James Tam
Metaphysics “…know the ultimate grounds of being or what it is that really exists, embracing both psychology and ontology. ” 2 2 The New Webster Encyclopedic Dictionary of the English Language James Tam
Result Of Lookup (Possibility One: Success) I know what Ontology means! James Tam
Result Of Lookup (Possibility One) Philosophy? ? ! Success! I’ll take a Philosophy option. Metaphysics? ! ? Ontology! James Tam
Result Of Lookup (Possibility Two: Failure) I don’t have a clue. James Tam
Result Of Lookup (Possibility Two) Philosophy? ? Metaphysics? ? Rats! I’m taking MGIS instead. ? Ontology? James Tam
Ontology “…equivalent to metaphysics. ” 3 3 The New Webster Encyclopedic Dictionary of the English Language James Tam
Looking Up A Word If (completely understand a definition) Return to previous definition (using definition that’s understood) Else lookup (unknown word(s)) James Tam
Recursion In Programming “A programming technique whereby a function or procedure calls itself either directly or indirectly. ” James Tam
Direct Call function James Tam
Indirect Call fun 1 fun 2 fun 3 … no. More. Fun James Tam
Requirements For Recursion 1) Base case 2) Progress is made (towards the base case) James Tam
Counting Example Write a program that will compute the sum of the first n positive integers. e. g. n = 3, sum = 3 + 2 + 1 = 6 sum (3) = 3 + sum (2) = 3 + 3 = 6 sum (2) = 2 + sum (1) = 2 + 1 = 3 sum (1) = 1 James Tam
Example Program program sum. Series (input, output); var last. Number : integer; total : integer; function sum (no : integer): integer; begin if (no = 1) then sum : = 1 else sum: = (no + sum (no - 1)); end; begin write('Enter the last number in the series : '); readln(last. Number); total : = sum(last. Number); writeln('Sum of the series from 1 - ', last. Number, ' is, ', total); end. sum. Series 6 total = sum(3) sum (3) if (3 = 1) then F sum : = 1 else 3 sum : = (3 +sum (3 – 1)); sum (2) if (2 = 1) then F sum : = 1 else 1 sum : = (2 +sum (2 – 1)); sum (1) if (1 = 1) then T sum : = 1 James Tam
Indirect Recursion In Pascal For full example look under /home/231/examples/functions/indirect. p Example Scenario: procedure proc 1 calls procedure proc 2 but procedure proc 2 calls procedure proc 1 Which one comes first? James Tam
Procedure Proc 1 First? procedure proc 1; begin : proc 2; : end; procedure proc 2; begin : proc 1; : end; What is proc 2? James Tam
Procedure Proc 2 First? procedure proc 2; begin : proc 1; : end; procedure proc 1; begin : proc 2; : end; What is proc 1? James Tam
Solution: Use A Dummy Definition A "placeholder" for the compiler (definition comes later) Example problem procedure proc 1; begin : proc 2; : end; procedure proc 2; begin : proc 1; : end; James Tam
Solution: Use A Dummy Definition A "placeholder" for the compiler (definition comes later) Example problem procedure proc 2; FORWARD; procedure proc 1; begin : proc 2; : end; procedure proc 2; begin : proc 1; : end; James Tam
When To Use Recursion When a problem can be divided into steps The result of one step can be used in a previous step All of the results together solve the problem James Tam
When To Consider Alternatives To Recursion When a loop will solve the problem just as well James Tam
Drawbacks Of Recursion Function calls can be costly • Uses up memory • Uses up time James Tam
Benefits Of Using Recursion Simpler solution that’s more elegant (for some problems) Easier to visualize solutions (for some people) James Tam
Common Pitfalls When Using Recursion No base case No progress towards the base case Using up too many resources (e. g. , variable declarations) for each function call James Tam
No Base Case function sum (no : integer): integer; begin sum : = (no + sum (no - 1)); end; James Tam
No Progress Towards Base Case function sum (no : integer): integer; begin if (no = 1) then sum : = 1 else sum : = (no + sum (no)); end; James Tam
Using Up Too Many Resources For full example look under /home/231/examples/functions/resource. Hog. p procedure proc; var arr : array [1. . 1000000] of char; begin proc; end; James Tam
Undergraduate Definition Of Recursion Word: re·cur·sion Pronunciation: ri-'k&r-zh&n Definition: See recursion James Tam
Summary Description of recursion Real world example Trace of a recursive Pascal program Benefits and drawbacks of using recursion When to use recursion and when to consider alternatives What are the potential pitfalls of using recursion Alternative definition of recursion James Tam
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