ENCM 335 Fall 2018 Tutorial for Week 13

Transcription

1 ENCM 335 Fall 2018 Tutorial for Week 13 Steve Norman, PhD, PEng Electrical & Computer Engineering Schulich School of Engineering University of Calgary 06 December, 2018

2 ENCM 335 Tutorial 06 Dec 2018 slide 2/12 Today s tutorial Exercises on recursion. A Python text file input exercise. Note: Online copies of ENCM 335 Fall 2018 tutorials can be found by following links starting at

3 ENCM 335 Tutorial 06 Dec 2018 slide 3/12 Exercise A: Recursive factorial function In mathematics, n!, called n factorial is defined as follows, for non-negative values of n: { 1 if n = 0 or n = 1 n! = n (n 1) 1 if n > 1 For example, 4! = = 24. What is a recursive solution to the problem of computing n!... a solution based on the solution to a simpler problem of the same kind? For the program on the next slide, let s make diagrams for the last time at (1), and the first and second times at (2).

4 ENCM 335 Tutorial 06 Dec 2018 slide 4/12 #include <stdio.h> double factorial(unsigned int n) { double r = 1.0; // (1) if (n > 1) r = n * factorial(n - 1); } // (2) return r; int main(void) { double ans = factorial(3); printf("3! is %g.\n", ans); return 0; } What is the base case for the recursive function factorial?

5 ENCM 335 Tutorial 06 Dec 2018 slide 5/12 Remarks: A non-recursive version of factorial with a simple loop would be more efficient! Simple examples of recursion tend to solve problems that are better solved with loops in C or Python.

6 ENCM 335 Tutorial 06 Dec 2018 slide 6/12 Exercise B: Recursive solution to an array problem Here s another simple problem that can be easily and efficient solved with a loop: Find the smallest value of array elements a[lo], a[lo+1],..., a[hi-1], where lo < hi. A simple loop-based solution is shown on the next slide.

7 ENCM 335 Tutorial 06 Dec 2018 slide 7/12 int min_val(const int *a, int lo, int hi) { int result = a[lo]; for (int i = lo + 1; i < hi; i++) if (a[i] < result) result = a[i]; return result; } int main(void) { int x[ ] = {20, -10, -15, 5}, y; y = min_val(x, 0, 4); return 0; }

8 ENCM 335 Tutorial 06 Dec 2018 slide 8/12 Let s design a recursive version of min_val. It won t be more more efficient than the loop-base version, but it s good practice for learning to think recursively. What is a good base case for finding the smallest value in a collection of one or more items? For the problem of finding the smallest value in a collection of N items, what is a simpler problem of the same kind? Let s write a function definition.

9 ENCM 335 Tutorial 06 Dec 2018 slide 9/12 Exercise C: Divide-and-conquer design As far as I know, there are no examples of divide-and-conquer algorithms that are both really useful and really easy to code. (Mergesort comes closest, I think, but coding a correct and efficient merge is not totally easy to do.) So examples of divide-and-conquer algorithms in ENCM 339 tend toward being not too hard to code, but also even easier to implement non-recursively with a loop... int all_same(const int* a, int lo, int hi); // REQUIRES: lo < hi, // elements a[lo]... a[hi-1] exist. // PROMISES: Return value is 1 if a[lo]... a[hi-1] // all have the same value, 0 otherwise. Implement all_same with divide-and-conquer recursion.

10 ENCM 335 Tutorial 06 Dec 2018 slide 10/12 Exercise D: More divide-and-conquer Note that the range of indexes is specified differently from how it was done in Exercise A... int count(const int* a, int lo, int hi, int key); // REQUIRES: lo <= hi, // elements a[lo]... a[hi] exist. // PROMISES: Return value indicates how many of // a[lo]... a[hi] are equal to key.

11 ENCM 335 Tutorial 06 Dec 2018 slide 11/12 How to describe a range of items in a collection Review: Exercises C and D: a[lo] is part of the range. Exercise C: a[hi] is not part of the range. Exercise D: a[hi] is part of the range. The scheme used in Exercise C is more convenient not only for divide-and-conquer recursion, but also for many other algorithms. The Exercise C scheme matches the way ranges and slices are set up in Python, and the way things called iterators work in the standard C++ library.

12 ENCM 335 Tutorial 06 Dec 2018 slide 12/12 Exercise E: Text file input with Python Suppose that foo.txt is a huge text file, supposedly full of representations of int values separated by whitespace (spaces, tabs, and/or newlines). Write a Python program that either... reports the smallest and largest values in foo.txt, if the file contents are what they are supposed to be; reports the line number where it is discovered that the file contents are not what they are supposed to be.