Admin
Assign 2 due Wed
Today’s topics
•Functional recursion
Reading
•Reader ch. 4-5-6 (today-W-F)
Lec ture #8
Solving problems recursively
A recursive function calls itself — wacky!
Idea: solve problem using coworkers (clones) who
work and act like you
•Delegate similar, smaller problem to clone
•Combine result from clone(s) to solve total problem
•Work toward trivial version that is directly solvable
For problems that exhibit "self-similarity"
•Structure repeats within at different levels of scale
•Solving larger problem means solving smaller problem(s) within
Feels mysterious at first
•"Leap of faith" required
•With practice, master the art of recursive decomposition
•Eventually grok the underlying patterns
Functional recursion
Function that returns answer/result
•Outer problem result uses result from smaller, same problem(s)
Base case
•Simplest version of problem
•Can be directly solved
Recursive case
•Make call(s) to self to get results for smaller, simpler version(s)
•Recursive calls must advance toward base case
•Results of recursive calls combined to solve larger version
Power example
C++ has no exponentiation op
Iterative formulation for Raise function
•baseexp = base * base * .... * base (exp times)
int Raise(int base, int exp)
{
int result = 1;
for (int i = 0; i < exp; i++)
result *= base;
return result;
}
