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Recursion - UAH CPE 212 Fundamentals of Software...

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UAH CPE 212 Fundamentals of Software Engineering Agenda Class 15 Recursion Recursion Key Concepts
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UAH CPE 212 Today Last Time Priority Queues This Time Recursion
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UAH CPE 212 Recursion Procedure calls itself Recursion: Divide and Conquer Steps: Define Base Case Arrange calls to work to a solution Inductively assume all cases make progress Identify termination Do Not Forget the stack Has short memory x 0 = 1 x 1 = x x n = (x 2 ) n/2 even x n = x n-1 x odd float Power(float x, int n) { if (n == 0) return 1; if (n == 1) return x; if (n & 1) return Power(x, n-1) * x; else return power (x*x, n/2); }
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UAH CPE 212 Recursion 2 int main( ) { int i; cout << "Please type a non-negative number: "; cin >> i; cout << "The digits of that number are:" << endl; write_vertical(i); cout << "Please type a negative number: "; cin >> i; cout << "The digits of that number are:" << endl; super_write_vertical(i); cout << "Let's get vertical!" << endl; return EXIT_SUCCESS; } void write_vertical(unsigned int number) // Postcondition: The digits of number have been written, stacked vertically. // Library facilities used: iostream.h { if (number < 10) cout << number << endl; // Write the one digit else { write_vertical(number/10); // Write all but the last digit cout << number % 10 << endl; // Write the last digit } }
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UAH CPE 212 Recursion 3 ostream& operator << (ostream& out, const unsigned int value) { if (value < 10 ) out << digitCharacter(value); else { out << (value / 10); out << digitCharacter(value % 10); } return out; } print 456 print 45, then print 6 print 4, then print 5
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UAH CPE 212 Recursion Examples Fractals Mazes
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