11-recursive_programming

11-recursive_programming - CSE 143 Lecture 11 Recursive...

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1 CSE 143 Lecture 11 Recursive Programming slides created by Marty Stepp http://www.cs.washington.edu/143/ 2 Decimal Numbers • A visual review of decimal numbers: – We get 348 by adding powers of 10 348 = 300 + 40 + 8 = 3 × 10 2 + 4 × 10 1 + 8 × 10 0 • That’s why the decimal system is base 10
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2 3 Binary Numbers • Binary is exactly the same, but base 2 Decimal Binary Sum 0 0 0 × 2 0 1 1 1 × 2 0 2 10 1 × 2 1 + 0 × 2 0 3 11 1 × 2 1 + 1 × 2 0 4 100 1 × 2 2 + 0 × 2 1 + 0 × 2 0 5 101 1 × 2 2 + 0 × 2 1 + 1 × 2 0 6 110 1 × 2 2 + 1 × 2 1 + 0 × 2 0 7 111 1 × 2 2 + 1 × 2 1 + 1 × 2 0 8 1000 1 × 2 3 + 0 × 2 2 + 0 × 2 1 + 0 × 2 0 4 Exercise • Write a recursive method printBinary that accepts an integer and prints that number's representation in binary (base 2) . – Example: printBinary(7) prints 111 – Example: printBinary(12) prints 1100 – Example: printBinary(42) prints 101010 – Write the method recursively and without using any loops. place 10 1 32 16 8 4 2 1 value 4 2 1 0 1 0 1 0
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3 5 Case analysis • Recursion is about solving a small piece of a large problem. – What is 69743 in binary? • Do we know anything about its representation in binary? – Case analysis: • What is/are easy numbers to print in binary? • Can we express a larger number in terms of a smaller number(s)? – Suppose we are examining some arbitrary integer N . • if N 's binary representation is 1001010101 1 •(N / 2) 's binary representation is 1001010101 •(N % 2) 's binary representation is 1 6 printBinary solution // Prints the given integer's binary representation. // Precondition: n >= 0
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This note was uploaded on 09/29/2010 for the course CSE 143 taught by Professor Sr during the Spring '08 term at University of Washington.

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11-recursive_programming - CSE 143 Lecture 11 Recursive...

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