Preparation Data Structures 02 recursion
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The document discusses recursion as a programming concept, defining recursive methods and their components, including base cases and recursive calls. It outlines design guidelines for creating effective recursive functions and highlights the importance of proper handling to avoid infinite recursion. Additionally, the document provides examples of recursive methods and debugging strategies.
![Images/cinvestav-
Base Code so you can start
Base Code
c l a s s C o m b i n a ti o n s {
p u b l i c s t a t i c i n t Co m b i n a t io n s ( i n t n , i n t k )
{
}
p u b l i c s t a t i c v o i d main ( S t r i n g [ ] a r g s )
{
}
}
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Preparation Data Structures 02 recursion
- 1. Data Structures Recursion Andres Mendez-Vazquez May 6, 2015 1 / 19
- 2. Images/cinvestav- Outline 1 Introduction 2 Recursive Method Questions to Answer When Designing a Recursion 3 Design guidelines for successful recursion Examples of Code with Innite Recursion Example 2 / 19
- 3. Images/cinvestav- What is recursion? Fact Sometimes, the best way to solve a problem is by solving a smaller version of the exact same problem rst Example You can build a house by hiring a contractor. The contractor in turn hires several subcontractors to complete portions of the house. Each subcontractor might hire other subcontractors to help. 3 / 19
- 4. Images/cinvestav- What is recursion? Fact Sometimes, the best way to solve a problem is by solving a smaller version of the exact same problem rst Example You can build a house by hiring a contractor. The contractor in turn hires several subcontractors to complete portions of the house. Each subcontractor might hire other subcontractors to help. 3 / 19
- 5. Images/cinvestav- Another Example Example: Principal Idea You do your part until your friend nishes and tells you 4 / 19
- 6. Images/cinvestav- Recursive Method Denition A method that calls itself is a recursive method. The invocation is a recursive call or recursive invocation. The previous example can be seen in code as follow 5 / 19
- 7. Images/cinvestav- Recursive Method Denition A method that calls itself is a recursive method. The invocation is a recursive call or recursive invocation. The previous example can be seen in code as follow /∗∗ Counts down from a given positive integer . @param integer an integer 0 ∗/ p u b l i c s t a t i c v o i d countDown ( i n t i n t e g e r ) { System . out . p r i n t l n ( i n t e g e r ) ; i f ( i n t e g e r 1) countDown ( i n t e g e r − 1 ) ; } // end countDown 5 / 19
- 8. Images/cinvestav- Example with 3 Tracing the recursive call countDown(3) //Client public static void main(...) { countDown(3); ... } public static void countDown(3) { System.out.println(3); countDown(3 – 1); } if (3 1) public static void countDown(2) { System.out.println(2); countDown(2 – 1); } if (2 1) public static void countDown(1) { System.out.println(1); } if (1 1) 6 / 19
- 9. Images/cinvestav- Outline 1 Introduction 2 Recursive Method Questions to Answer When Designing a Recursion 3 Design guidelines for successful recursion Examples of Code with Innite Recursion Example 7 / 19
- 10. Images/cinvestav- Questions to answer when designing a recursive solution First What part of the solution can you contribute directly? Second What smaller but identical problem has a solution that, when taken with your contribution, provides the solution to the original problem? Third When does the process end? That is, what smaller but identical problem has a known solution, and have you reached this problem, or base case? 8 / 19
- 11. Images/cinvestav- Questions to answer when designing a recursive solution First What part of the solution can you contribute directly? Second What smaller but identical problem has a solution that, when taken with your contribution, provides the solution to the original problem? Third When does the process end? That is, what smaller but identical problem has a known solution, and have you reached this problem, or base case? 8 / 19
- 12. Images/cinvestav- Questions to answer when designing a recursive solution First What part of the solution can you contribute directly? Second What smaller but identical problem has a solution that, when taken with your contribution, provides the solution to the original problem? Third When does the process end? That is, what smaller but identical problem has a known solution, and have you reached this problem, or base case? 8 / 19
- 13. Images/cinvestav- For countDown Answer 1 The method countDown displays the given integer rst. Answer 2 The smaller problem is counting down from integer - 1. Answer 3 The if statement asks if the process has reached the base case. In our case integer = 1. 9 / 19
- 14. Images/cinvestav- For countDown Answer 1 The method countDown displays the given integer rst. Answer 2 The smaller problem is counting down from integer - 1. Answer 3 The if statement asks if the process has reached the base case. In our case integer = 1. 9 / 19
- 15. Images/cinvestav- For countDown Answer 1 The method countDown displays the given integer rst. Answer 2 The smaller problem is counting down from integer - 1. Answer 3 The if statement asks if the process has reached the base case. In our case integer = 1. 9 / 19
- 16. Images/cinvestav- Design guidelines for successful recursion First The method must be given an input value. Second The method denition must contain logic that involves this input value and leads to dierent cases. Third One or more of these cases should provide a solution that does not require recursion. These are the base cases, or stopping cases. Fourth One or more cases must include a recursive invocation of the method using a smaller argument. 10 / 19
- 17. Images/cinvestav- Design guidelines for successful recursion First The method must be given an input value. Second The method denition must contain logic that involves this input value and leads to dierent cases. Third One or more of these cases should provide a solution that does not require recursion. These are the base cases, or stopping cases. Fourth One or more cases must include a recursive invocation of the method using a smaller argument. 10 / 19
- 18. Images/cinvestav- Design guidelines for successful recursion First The method must be given an input value. Second The method denition must contain logic that involves this input value and leads to dierent cases. Third One or more of these cases should provide a solution that does not require recursion. These are the base cases, or stopping cases. Fourth One or more cases must include a recursive invocation of the method using a smaller argument. 10 / 19
- 19. Images/cinvestav- Design guidelines for successful recursion First The method must be given an input value. Second The method denition must contain logic that involves this input value and leads to dierent cases. Third One or more of these cases should provide a solution that does not require recursion. These are the base cases, or stopping cases. Fourth One or more cases must include a recursive invocation of the method using a smaller argument. 10 / 19
- 20. Images/cinvestav- So, be careful Innite recursion A recursive method that does not check for a base case, or that misses the base case, will execute forever. This situation is known as innite recursion. Which is known as This situation is known as innite recursion. 11 / 19
- 21. Images/cinvestav- So, be careful Innite recursion A recursive method that does not check for a base case, or that misses the base case, will execute forever. This situation is known as innite recursion. Which is known as This situation is known as innite recursion. 11 / 19
- 22. Images/cinvestav- Outline 1 Introduction 2 Recursive Method Questions to Answer When Designing a Recursion 3 Design guidelines for successful recursion Examples of Code with Innite Recursion Example 12 / 19
- 23. Images/cinvestav- Example of code with innite recursion Code /∗∗ Counts down from a given positive integer . @param integer an integer 0 ∗/ p u b l i c s t a t i c v o i d countDown ( i n t i n t e g e r ) { System . out . p r i n t l n ( i n t e g e r ) ; countDown ( i n t e g e r − 1 ) ; } // end countDown 13 / 19
- 24. Images/cinvestav- Recursive Methods That Return a Value The nice stu about recursion You can return values For example We can compute the sum 1 + 2 + 3 + ... + n 14 / 19
- 25. Images/cinvestav- Recursive Methods That Return a Value The nice stu about recursion You can return values For example We can compute the sum 1 + 2 + 3 + ... + n 14 / 19
- 26. Images/cinvestav- How the code will look Partial Code /∗∗ @param n an integer 0 @return the sum 1 + 2 + . . . + n ∗/ p u b l i c s t a t i c i n t sumOf ( i n t n ) { i n t sum ; // What do we put here? r e t u r n sum ; } // end sumOf 15 / 19
- 27. Images/cinvestav- Debugging a recursive method Something Notable 1 Does the method have at least one input value? 2 Does the method contain a statement that tests an input value and leads to dierent cases? 3 Did you consider all possible cases? Does at least one of these cases cause at least one recursive call? 4 Do these recursive calls involve smaller arguments, smaller tasks, or tasks that get closer to the solution? 5 If these recursive calls produce or return correct results, will the method produce or return a correct result? 6 Is at least one of the cases a base case that has no recursive call? 7 Are there enough base cases? 8 Does each base case produce a result that is correct for that case? 9 If the method returns a value, does each of the cases return a value? 16 / 19
- 28. Images/cinvestav- Debugging a recursive method Something Notable 1 Does the method have at least one input value? 2 Does the method contain a statement that tests an input value and leads to dierent cases? 3 Did you consider all possible cases? Does at least one of these cases cause at least one recursive call? 4 Do these recursive calls involve smaller arguments, smaller tasks, or tasks that get closer to the solution? 5 If these recursive calls produce or return correct results, will the method produce or return a correct result? 6 Is at least one of the cases a base case that has no recursive call? 7 Are there enough base cases? 8 Does each base case produce a result that is correct for that case? 9 If the method returns a value, does each of the cases return a value? 16 / 19
- 29. Images/cinvestav- Debugging a recursive method Something Notable 1 Does the method have at least one input value? 2 Does the method contain a statement that tests an input value and leads to dierent cases? 3 Did you consider all possible cases? Does at least one of these cases cause at least one recursive call? 4 Do these recursive calls involve smaller arguments, smaller tasks, or tasks that get closer to the solution? 5 If these recursive calls produce or return correct results, will the method produce or return a correct result? 6 Is at least one of the cases a base case that has no recursive call? 7 Are there enough base cases? 8 Does each base case produce a result that is correct for that case? 9 If the method returns a value, does each of the cases return a value? 16 / 19
- 30. Images/cinvestav- Debugging a recursive method Something Notable 1 Does the method have at least one input value? 2 Does the method contain a statement that tests an input value and leads to dierent cases? 3 Did you consider all possible cases? Does at least one of these cases cause at least one recursive call? 4 Do these recursive calls involve smaller arguments, smaller tasks, or tasks that get closer to the solution? 5 If these recursive calls produce or return correct results, will the method produce or return a correct result? 6 Is at least one of the cases a base case that has no recursive call? 7 Are there enough base cases? 8 Does each base case produce a result that is correct for that case? 9 If the method returns a value, does each of the cases return a value? 16 / 19
- 31. Images/cinvestav- Debugging a recursive method Something Notable 1 Does the method have at least one input value? 2 Does the method contain a statement that tests an input value and leads to dierent cases? 3 Did you consider all possible cases? Does at least one of these cases cause at least one recursive call? 4 Do these recursive calls involve smaller arguments, smaller tasks, or tasks that get closer to the solution? 5 If these recursive calls produce or return correct results, will the method produce or return a correct result? 6 Is at least one of the cases a base case that has no recursive call? 7 Are there enough base cases? 8 Does each base case produce a result that is correct for that case? 9 If the method returns a value, does each of the cases return a value? 16 / 19
- 32. Images/cinvestav- Debugging a recursive method Something Notable 1 Does the method have at least one input value? 2 Does the method contain a statement that tests an input value and leads to dierent cases? 3 Did you consider all possible cases? Does at least one of these cases cause at least one recursive call? 4 Do these recursive calls involve smaller arguments, smaller tasks, or tasks that get closer to the solution? 5 If these recursive calls produce or return correct results, will the method produce or return a correct result? 6 Is at least one of the cases a base case that has no recursive call? 7 Are there enough base cases? 8 Does each base case produce a result that is correct for that case? 9 If the method returns a value, does each of the cases return a value? 16 / 19
- 33. Images/cinvestav- Debugging a recursive method Something Notable 1 Does the method have at least one input value? 2 Does the method contain a statement that tests an input value and leads to dierent cases? 3 Did you consider all possible cases? Does at least one of these cases cause at least one recursive call? 4 Do these recursive calls involve smaller arguments, smaller tasks, or tasks that get closer to the solution? 5 If these recursive calls produce or return correct results, will the method produce or return a correct result? 6 Is at least one of the cases a base case that has no recursive call? 7 Are there enough base cases? 8 Does each base case produce a result that is correct for that case? 9 If the method returns a value, does each of the cases return a value? 16 / 19
- 34. Images/cinvestav- Debugging a recursive method Something Notable 1 Does the method have at least one input value? 2 Does the method contain a statement that tests an input value and leads to dierent cases? 3 Did you consider all possible cases? Does at least one of these cases cause at least one recursive call? 4 Do these recursive calls involve smaller arguments, smaller tasks, or tasks that get closer to the solution? 5 If these recursive calls produce or return correct results, will the method produce or return a correct result? 6 Is at least one of the cases a base case that has no recursive call? 7 Are there enough base cases? 8 Does each base case produce a result that is correct for that case? 9 If the method returns a value, does each of the cases return a value? 16 / 19
- 35. Images/cinvestav- Debugging a recursive method Something Notable 1 Does the method have at least one input value? 2 Does the method contain a statement that tests an input value and leads to dierent cases? 3 Did you consider all possible cases? Does at least one of these cases cause at least one recursive call? 4 Do these recursive calls involve smaller arguments, smaller tasks, or tasks that get closer to the solution? 5 If these recursive calls produce or return correct results, will the method produce or return a correct result? 6 Is at least one of the cases a base case that has no recursive call? 7 Are there enough base cases? 8 Does each base case produce a result that is correct for that case? 9 If the method returns a value, does each of the cases return a value? 16 / 19
- 36. Images/cinvestav- Outline 1 Introduction 2 Recursive Method Questions to Answer When Designing a Recursion 3 Design guidelines for successful recursion Examples of Code with Innite Recursion Example 17 / 19
- 37. Images/cinvestav- Now, what if we solve a recursive function What we want to solve n choose k (combinations) We have n k = n − 1 k + n − 1 k − 1 , with 1 k n (1) Base Case n 1 = n (k = 1) , n n = 1(k = n) (2) 18 / 19
- 38. Images/cinvestav- Now, what if we solve a recursive function What we want to solve n choose k (combinations) We have n k = n − 1 k + n − 1 k − 1 , with 1 k n (1) Base Case n 1 = n (k = 1) , n n = 1(k = n) (2) 18 / 19
- 39. Images/cinvestav- Now, what if we solve a recursive function What we want to solve n choose k (combinations) We have n k = n − 1 k + n − 1 k − 1 , with 1 k n (1) Base Case n 1 = n (k = 1) , n n = 1(k = n) (2) 18 / 19
- 40. Images/cinvestav- Base Code so you can start Base Code c l a s s C o m b i n a ti o n s { p u b l i c s t a t i c i n t Co m b i n a t io n s ( i n t n , i n t k ) { } p u b l i c s t a t i c v o i d main ( S t r i n g [ ] a r g s ) { } } 19 / 19