Humorous Asides

“A journey begins with single step”

 Large problems hard to solve  Thinking about & solving small problems easier  Splitting problems into smaller ones often helps  Before you start coding, plan each assignment  Break up large functions with many if s and loops  Move repeated action into small functions Solving Problems

Smaller is Better

CENSORED

Smaller is Better  (At least for programming) CENSORED

 Should be boring, easy, understandable drone  Given its parameters, perform the expected action  Only perform action defined for its parameters  Should not cure cancer  Do not worry about the larger problem  Solving entire problem is not this function’s issue  Split into tasks since solving whole problem hard Goal of a Function

 re-cur-sion  re-cur-sion: Method of solving problem by combining solutions to identical, smaller problems Recursion

 re-cur-sion  re-cur-sion: Method of solving problem by combining solutions to identical, smaller problems Recursion

 Recursive stepbase case(s)  Recursive step simplifies problem to base case(s)  Recast using slightly easier version in recursive step 4! = 4 * 3! See Recursion Work

 Recursive stepbase case(s)  Recursive step simplifies problem to base case(s)  Recast using slightly easier version in recursive step 4! = 4 * 3! = 4 * (3 * 2!) See Recursion Work

 Recursive stepbase case(s)  Recursive step simplifies problem to base case(s)  Recast using slightly easier version in recursive step 4! = 4 * 3! = 4 * (3 * 2!) = 4 * (3 * (2 * 1!)) See Recursion Work

 Recursive stepbase case(s)  Recursive step simplifies problem to base case(s)  Recast using slightly easier version in recursive step 4! = 4 * 3! = 4 * (3 * 2!) = 4 * (3 * (2 * 1!))  Base case(s) handle and solve obvious cases = 4 * (3 * (2 * 1)) See Recursion Work

 Recursive stepbase case(s)  Recursive step simplifies problem to base case(s)  Recast using slightly easier version in recursive step 4! = 4 * 3! = 4 * (3 * 2!) = 4 * (3 * (2 * 1!))  Base case(s) handle and solve obvious cases = 4 * (3 * (2 * 1))  After base case, combine solutions in recursive steps = 4 * (3 * 2) See Recursion Work

 Recursive stepbase case(s)  Recursive step simplifies problem to base case(s)  Recast using slightly easier version in recursive step 4! = 4 * 3! = 4 * (3 * 2!) = 4 * (3 * (2 * 1!))  Base case(s) handle and solve obvious cases = 4 * (3 * (2 * 1))  After base case, combine solutions in recursive steps = 4 * (3 * 2) = 4 * 6 See Recursion Work

 Recursive stepbase case(s)  Recursive step simplifies problem to base case(s)  Recast using slightly easier version in recursive step 4! = 4 * 3! = 4 * (3 * 2!) = 4 * (3 * (2 * 1!))  Base case(s) handle and solve obvious cases = 4 * (3 * (2 * 1))  After base case, combine solutions in recursive steps = 4 * (3 * 2) = 4 * 6 = 24 See Recursion Work

Very easy to create solution that does not work  Infinite recursion occurs if base case never reached  Frame-by-frame stack grows from function calls  Program crashes without warning or explanation For Recursion To Work

Very easy to create solution that does not work Recursive step must advance toward a base case  If there are multiple, which base case is unimportant one  Get one step closer to base case at each recursive call  Must check if algorithm works for all possible inputs For Recursion To Work

recursive  A function is recursive if it calls itself: int factorial(int i) { if (i <= 1) { return 1; } else { return i * factorial(i - 1); } } Recursion in C++

recursive  A function is recursive if it calls itself: int factorial(int i) { if (i <= 1) { return 1; } else { int nextI = i – 1; int result = factorial(nextI); return i * result; } } Recursion in C++ Base case: Solution is simple

recursive  A function is recursive if it calls itself: int factorial(int i) { if (i <= 1) { return 1; } else { int nextI = i – 1; int result = factorial(nextI); return i * result; } } Recursion in C++ Recursive Step: 1 step Take 1 step to solution

recursive  A function is recursive if it calls itself: int factorial(int i) { if (i <= 1) { return 1; } else { int nextI = i – 1; int result = factorial(nextI); return i * result; } } Recursion in C++ Recursive Step: 1 step Take 1 step to solution Make 1 or more recursive calls

recursive  A function is recursive if it calls itself: int factorial(int i) { if (i <= 1) { return 1; } else { int nextI = i – 1; int result = factorial(nextI); return i * result; } } Recursion in C++ Recursive Step: 1 step Take 1 step to solution Make 1 or more recursive calls Simple process computes result

 Start with check for base case(s)  These cases must return blatantly obvious answer  1+ recursive calls found within recursive step(s)  Write these assuming recursive call works 1  Take 1 step toward base case (not 2, 3, or 10482) Recursive Function Basics

 Start with check for base case(s)  These cases must return blatantly obvious answer  1+ recursive calls found within recursive step(s)  Write these assuming recursive call works 1  Take 1 step toward base case (not 2, 3, or 10482) Recursive Function Basics

 No different than usual tracing we were doing  When function called, we add frame for the call  Local variables & parameters shown in frame  (Processors also include line being executed) Tracing Recursion

 No different than usual tracing we were doing  When function called, we add frame for the call  Local variables & parameters shown in frame  (Processors also include line being executed) NOT Tracing Recursion

int findMin(int[] a, int len, int j) { if (j == len - 1) { return a[j]; } else { int minFollowing = findMin(a, len, j+1); if (a[j] < minFollowing) { return a[j]; } return minFollowing; } } int[] example1 = { 0 }; findMin(example1, 1,0); Trace This, Buddy!

int findMin(int[] a, int len, int j) { if (j == len - 1) { return a[j]; } else { int minFollowing = findMin(a,len,j+1); if (a[j] < minFollowing) { return a[j]; } return minFollowing; } } int[] example2 = { 2, 3, 0, 1 }; findMin(example2, 4, 0); Trace This, Buddy!

Your Turn  Get into your groups and complete activity

For Next Lecture  Programming Project #3  Programming Project #3 due Friday