Introduction to Computer Systems

1. Introduction to Computer Systems Lecturer: Steve Maybank Department of Computer Science and Information Systems sjmaybank@dcs.bbk.ac.uk Autumn 2013 Week 9a: Algorithm Design Birkbeck College

2. Review: Pseudo Code Structures • Assignment • if … then … else • while … do … end while • procedure … end procedure Birkbeck College

3. Review: Exercise procedure descending(A) j=0; flag=0; while flag==0 && j<Length[A]-1 do if A[j]<A[j+1] then flag=1; print(j); j=j+1; end while if flag==0 then print(-1); end procedure Birkbeck College

4. Bottom Up Strategy • Solve many small parts of the problem and gradually accumulate the information needed to solve the entire problem. • Examples: evaluation of Boolean expressions, searching an unordered list. Brookshear, Section 5.3

5. Example: Evaluation of a Boolean expression • Suppose that A, B, C are Boolean variables such that A=0, B=1, C=0. Evaluate the Boolean expression (A AND B AND C) OR (A AND NOT(B)) Birkbeck College

6. Example: Searching an Unsorted List input: list L and element a output: 1 if a is in L otherwise 0 procedure search (L, a) if Length(L)==0 then print 0 and goto end procedure; e=L[0]; while ((a<>e) && (e is not last entry of L)) do e=next entry of L; end while; if e==a then print 1 else print 0; end procedure Compare Brookshear Section 5.4

7. Top Down Strategy • Divide the problem into two or more simpler problems. • Solve the simpler problems and then combine the answers. • Examples: route finding, binary search of a sorted list. Brookshear Section 5.3

8. Binary Search of a Sorted List input: sorted list L, element a output: 1 if a is in L, otherwise 0 procedure searchSortedList(L, a) if Length(L)==0 then print 0 and goto end procedure; i1=0; i2=Length(L)-1; while i2>i1+1 do j=largest integer ≤ (i1+i2)/2; if L[j]==a then print 1 and goto end procedure; if a<L[j] then i2=j else i1=j; end while; if a==L[i1] or a==L[i2] then print 1 else print 0; end procedure Compare Brookshear, Section 5.5

9. Other Strategies • Find out if somebody else has solved the problem. • Solve a simpler but related problem. • Iteration: repetition of a standard calculation • Find a data structure for the problem suited to a computer. • Enumeration. Birkbeck College

10. Solve a Simpler but Related Problem Program to draw a polygon in any part of the display screen Program to draw a polygon at the centre of the display screen Program to draw a square in any part of the display screen Birkbeck College

11. Example: iteration input: none output: estimate of the square root of 2 procedure sqrt2 x=1; while (x2 > 2.001) or (x2 < 1.999 ) do x=(1/x)+(x/2); end while; print x; end procedure; Birkbeck College

12. Enumeration • List all the possible states of the problem and search for the solution. • Example 1: find all numbers which divide 10 by checking 1,2,…10. • Advantages: thorough, simple, good for small cases. • Disadvantages: very long run times, inefficient. Birkbeck College

13. Ferry Problem • A man wishes to ferry a wolf, a sheep and a bale of hay across as river. His boat will only hold one item at a time. The wolf cannot be left with the sheep and the sheep cannot be left with the hay. How can he ferry the three items? Birkbeck College

14. Data Structure • State: WSHb • Red: start side of river • Blue and underlined italic : other side of river • Example: WSHb • There are 16 states of which 10 are allowed Birkbeck College

15. Solution HSWb HS Wb HS Wb HSWb H S Wb H SWb HSW b H SW b H SWb HSWb Birkbeck College

16. Question 11 from 2003 Exam • Write an algorithm for calculation of tax for a yearly salary. The tax is zero when the salary is £3000 or less. It is 10% for the next salary band from £3001 to £8000. It is 20% for the part from £8001 to £20000, and it is 40% for any part of the salary over £20000. Birkbeck College

17. Question Design an algorithm that lists all possible rearrangements of the symbols in a string of five distinct characters. Birkbeck College