Lecture07 - Recursion Many problems can be formulated...

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CS2134 Recursion Many problems can be formulated recursively: fact(n) = 1*2* ... *n fact(n) = 1 if n = 0 n*fact(n-1) if n > 0 recursive definitions translate easily into recursive C++ functions: int fact(int n)    {// pre : n >= 0       if (n==0) return 1;       return n*fact(n-1);    }
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CS2134 Recursion Examples Recursive Binary Search Recursive printing : if n <= 9 print n else print n/10 then print n%10 (last digit) (More generally ... change of base) Recursive Max Contiguous Subsequence Simpler than O(n) algorithm O(n log n) Lots of recursive sorting algorithms (later)
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CS2134 Principles of Recursion Divide and Conquer Base Case Always make progress toward base case Move computation that is needed in every instance into driver To reason about correctness, use mathematical induction: assume recursive calls solve small instances and use this to prove that program handles large instance correctly.
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CS2134 When NOT to use recursion Sometimes the same problem instance occurs in many recursive calls, e.g. Fibonnaci
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