Programming in Java: Recursion
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The document discusses recursion as an alternative method to looping in programming, emphasizing its structure of a base case and recursive calls. It uses examples such as the Fibonacci sequence to illustrate how recursion functions and the need for a stopping condition. Furthermore, it highlights the importance of understanding recursion as it appears in future modules of study.
Programming in Java: Recursion
- 2. •By demand, from highest to lowest: •Recursion •Break •Recursion •Objects and Classes •Break •Arrays and Array Lists
- 4. What do we need to make a loop run? for (int i = 0; i<=10; i++) { System.out.println(i); }
- 5. for (int i = 0; i<=10; i++) { System.out.println(i); } What do we need to make a loop run? the ‘movement’
- 6. for (int i = 0; i<=10; i++) { System.out.println(i); } What do we need to make a loop run? the ‘change’
- 7. for (int i = 0; i<=10; i++) { System.out.println(i); } What do we need to make a loop run? ‘when to stop’
- 8. for (int i = 0; i<=10; i++) { System.out.println(i); } What do we need to make a loop run? the content
- 9. How do we loop without a loop?
- 10. How do we loop without a loop? the ‘movement’
- 11. the ‘change’ How do we loop without a loop?
- 12. ‘when to stop’ How do we loop without a loop?
- 13. the content How do we loop without a loop?
- 14. How do we loop without a loop? base case recursive case
- 15. Reverse, reverse. What happens here?
- 21. If we tell the compiler to execute non- conditional code then at some point it must be executed.
- 28. Reverse, reverse. methodA ! methodA ! 3 2
- 31. Reverse, reverse. methodA 1 ! methodA 0 ! methodA ! -1 methodA End of the method, so return
- 33. Reverse, reverse. methodA ! methodA ! methodA ! methodA ! 0 1 2 3
- 34. Reverse, reverse. methodA ! methodA ! methodA ! methodA ! 0 1 2 3
- 35. Reverse, reverse. methodA ! methodA ! methodA ! methodA ! 0 1 2 3
- 36. Reverse engineering is fine, but how do I build something from scratch?
- 37. 0 1 2 3 4 5 6 7 8 9 10 0 1 1 2 3 5 8 13 21 34 55
- 38. 0 1 2 3 4 5 0 1 1 2 3 5 Fibonacci Sequence Every number is the sum of the two previous, when possible.nth fib
- 40. base case Ask, when do we not need to do any computation? When can we simply return a number rather than doing any addition? Determining the 0 1 2 3 4 5 0 1 1 2 3 5
- 41. Ask, when do we not need to do any computation? When can we simply return a number rather than doing any addition? Determining the 0 1 2 3 4 5 0 1 1 2 3 5 base case
- 44. 0 0
- 45. 0 1 2 3 4 5 base case Ask, when do we not need to do any computation? When can we simply return a number rather than doing any addition? Determining the 0 1 1 2 3 5
- 46. 1 1
- 47. 0 1 1 2 3 5 Determining the recursive case 0 1 2 3 4 5 What is the general case? Can this case be carried on indefinitely?
- 48. 0 1 1 2 3 5 0 1 2 3 4 5 Determining the + = recursive case What is the general case? Can this case be carried on indefinitely?
- 49. 0 1 1 2 3 5 0 1 2 3 4 5 Determining the + = recursive case + = What is the general case? Can this case be carried on indefinitely?
- 51. static int fib(int n) { if (n == 0) { return 0; } if (n == 1) { return 1; } else { return fib(n-1) + fib(n-2); } } 2 1 0
- 52. Determining the recursive case 0 1 1 2 3 5 0 1 2 3 4 5 + = + = fib ( ) fib ( ) fib ( )
- 53. 0 1 2 3 4 5 fib ( ) fib ( ) fib ( ) Determining the recursive case 0 1 1 2 3 5+ = + =
- 54. 0 1 2 3 4 5 fib ( ) fib ( ) fib ( ) Determining the recursive case 0 1 1 2 3 5+ = + =
- 55. 0 1 5 fib ( n ) fib (n-2) fib (n-1) Determining the recursive case 0 1 1 2 3 5+ = + = This operation is consistent, so we can generalise.
- 56. 0 1 5 fib ( n ) fib (n-2) fib (n-1) Determining the recursive case 0 1 1 2 3 5+ = + =
- 57. static int fib(int n) { if (n == 0) { return 0; } if (n == 1) { return 1; } else { return fib(n-1) + fib(n-2); } }
- 58. static int fib(int n) { if (n == 0) { return 0; } if (n == 1) { return 1; } else { return fib(n-1) + fib(n-2); } } 5
- 59. Recursion creates a tree
- 60. 1 = actual value 1 0 1 1 0 01 1
- 61. 1 = actual value 1 0 1 1 0 01 + 1
- 62. 1 = actual value 1 0 1 1 0 01 + + 1
- 63. 1 = actual value 1 0 1 1 0 01 + + + ! ! 1
- 64. static int fib(int n) { if (n == 0) { return 0; } if (n == 1) { return 1; } else { return fib(n-1) + fib(n-2); } } !
- 65. 1 = actual value 1 0 1 1 0 01 + + + ! ! 1
- 66. 1 = actual value 1 0 1 1 0 01 + + + ! !! 1 +
- 67. 1 = actual value 1 0 1 1 0 01 1 + + + ! !! 1 +
- 68. 0 1 2 3 4 5 0 1 1 2 3 5 Fibonacci Sequence Every number is the sum of the two previous, when possible.
- 69. 1 = actual value 1 0 1 1 0 01 1 + + + ! !! 1 +
- 70. 1 = actual value 1 0 1 1 0 01 1 + + + ! !! 1 +
- 71. 1 = actual value 1 0 1 1 0 01 1 + + + 2 ! !! 1 +
- 72. 0 1 2 3 4 5 0 1 1 2 3 5 Fibonacci Sequence Every number is the sum of the two previous, when possible.
- 73. 1 = actual value 1 0 1 1 0 01 1 + + + 2 ! !! 1 +
- 74. 1 = actual value 1 0 1 1 0 01 1 + + + 2 ! !! + 1 +
- 75. 1 = actual value 1 0 1 1 0 01 1 + + + 2 ! ! 1 + 1 +
- 76. 1 = actual value 1 0 1 1 0 01 1 + + + 2 ! ! 1 + 1 +
- 77. 1 = actual value 1 0 1 1 0 01 1 + + + 2 ! ! 1 3 + 1 +
- 78. + 1 = actual value 1 0 1 1 0 01 1 + + + 2 ! ! 1 3 + + 1
- 79. 1 = actual value 1 0 1 1 0 01 1 + + + 2 ! ! 1 3 + ++ 1 +
- 80. 1 = actual value 1 0 1 1 0 01 1 + + + 2 ! 1 3 + ++ 1 1 +
- 81. + 1 = actual value 1 0 1 1 0 01 1 + + + 2 ! 1 3 + ++ 1 1
- 82. + 1 = actual value 1 0 1 1 0 01 1 + + + 2 1 3 + ++ 1 1 2
- 83. 1 = actual value 1 0 1 1 0 01 1 + + + 2 1 3 + ++ 1 1 2+
- 84. 1 = actual value 1 0 1 1 0 01 1 + + + 2 1 3 + ++ 1 1 2 5 +
- 85. static int fib(int n) { if (n == 0) { return 0; } if (n == 1) { return 1; } else { return fib(n-1) + fib(n-2); } } Think, when do I not have to do any computation? This will also be when my code stops. base case SUMMARY base case
- 86. static int fib(int n) { if (n == 0) { return 0; } if (n == 1) { return 1; } else { return fib(n-1) + fib(n-2); } } When I do have to compute something, what is the pattern? If I can prove it for one case, it should work for them all. recursive case SUMMARY base case base case
- 88. SUMMARY • Recursion is just another way of looping, with information changing each time. • Recursion consists of a recursive call and a base case. • If there is code after a recursive call it must be executed and will be executed in reverse order. • Recursion is a natural solution if you can visualise the call in any instance i.e. Fibonacci numbers.
- 89. WILL I SEE RECURSION AGAIN? • Yes, sorry. • But it will give you more of a chance to understand it. • Modules which touch on recursion (at least): DST (Semester 2, 1st year) and Algorithm Modules.