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{SECT 0 {EXCHG {PARA 200 "" 0 "" {TEXT 202 31 "Math 365D Lab Three - F
all 2005" }{TEXT 203 0 "" }{TEXT 203 1 "\n" }}{PARA 201 "" 0 "" {TEXT 
204 19 "BOOLEAN EXPRESSIONS" }{TEXT 203 0 "" }{TEXT 203 51 "\nA Boolea
n expression is one whose value is either " }{TEXT 205 5 "true " }
{TEXT 203 3 "or " }{TEXT 205 5 "false" }{TEXT 203 19 " (but not both) \+
or " }{TEXT 205 4 "FAIL" }{TEXT 203 96 " if its truth or falsity is un
known. One example we have seen so far is the return value of the " }
{TEXT 206 8 "isprime " }{TEXT 203 8 "command." }{TEXT 203 0 "" }{TEXT 
203 1 "\n" }{TEXT 203 151 "\nIn Math s21, we learned how to construct \+
Boolean expressions using disjunction (\"inclusive or\"), conjunction \+
(\"and\"), and negation (\"not\"). The words " }{TEXT 206 2 "or" }
{TEXT 203 2 ", " }{TEXT 206 3 "and" }{TEXT 203 6 ", and " }{TEXT 206 
3 "not" }{TEXT 203 95 " are used in Maple in exactly the same way. In \+
addition, Maple has an \"exclusive or\" operator, " }{TEXT 206 3 "xor"
 }{TEXT 203 27 ", which returns a value of " }{TEXT 205 4 "true" }
{TEXT 203 58 " if and only if exactly one of its two arguments is fals
e." }{TEXT 203 0 "" }{TEXT 203 1 "\n" }{TEXT 203 79 "\nThe following s
imple examples illustrate the use of these logical expressions." }
{TEXT 203 0 "" }}}{EXCHG {PARA 202 "> " 0 "" {MPLTEXT 1 207 17 "(2=3) \+
or (2+2=4);" }{MPLTEXT 1 207 0 "" }}{PARA 203 "" 1 "" {XPPMATH 20 "6#I
%trueGI*protectedGF$" }{TEXT 208 0 "" }}}{EXCHG {PARA 202 "> " 0 "" 
{MPLTEXT 1 207 18 "(2=3) and (2+2=4);" }{MPLTEXT 1 207 0 "" }}{PARA 
203 "" 1 "" {XPPMATH 20 "6#I&falseGI*protectedGF$" }{TEXT 208 0 "" }}}
{EXCHG {PARA 202 "> " 0 "" {MPLTEXT 1 207 21 "not (2+2=4) or (2=2);" }
{MPLTEXT 1 207 0 "" }}{PARA 203 "" 1 "" {XPPMATH 20 "6#I%trueGI*protec
tedGF$" }{TEXT 208 0 "" }}}{EXCHG {PARA 202 "> " 0 "" {MPLTEXT 1 207 
62 "not ( (2+2=4) or (2=2) ); # compare to the previous expression" }
{MPLTEXT 1 207 0 "" }}{PARA 203 "" 1 "" {XPPMATH 20 "6#I&falseGI*prote
ctedGF$" }{TEXT 208 0 "" }}}{EXCHG {PARA 202 "> " 0 "" {MPLTEXT 1 207 
16 "(1=1) xor (1<2);" }{MPLTEXT 1 207 0 "" }}{PARA 203 "" 1 "" 
{XPPMATH 20 "6#I&falseGI*protectedGF$" }{TEXT 208 0 "" }}}{EXCHG 
{PARA 202 "> " 0 "" {MPLTEXT 1 207 31 "not ( (1=2) or (2=3) or (3=4));
" }{MPLTEXT 1 207 0 "" }}{PARA 203 "" 1 "" {XPPMATH 20 "6#I%trueGI*pro
tectedGF$" }{TEXT 208 0 "" }}}{EXCHG {PARA 202 "> " 0 "" {MPLTEXT 1 
207 80 "x:= (1=2) or (1=1 and isprime(3)); # we can assign a Boolean v
alue to a variable" }{MPLTEXT 1 207 0 "" }}{PARA 203 "" 1 "" {XPPMATH 
20 "6#>I\"xG6\"I%trueGI*protectedGF'" }{TEXT 208 0 "" }}}{PARA 204 "" 
0 "" {TEXT 209 0 "" }{TEXT 209 7 "\nSTACKS" }{TEXT 210 0 "" }{TEXT 
210 3 "\nA " }{TEXT 211 5 "stack" }{TEXT 210 253 " is a very aptly-nam
ed data structure. Its name should call to mind a physical stack of ob
jects piled one on top of another. Just as with its physical counterpa
rt, a stack in Maple operates on a last-in, first-out (LIFO) principle
 - we can only insert (" }{TEXT 211 4 "push" }{TEXT 211 2 ") " }{TEXT 
210 12 "and remove (" }{TEXT 211 3 "pop" }{TEXT 211 2 ") " }{TEXT 210 
363 "objects from the very top of the stack (or the whole thing will c
ollapse). In order to remove an object near the bottom of the stack, w
e must first remove all the objects above it. However, we can check th
e value of an object anywhere in the stack. In the next lab, we will l
earn about other data structures that are useful in situations where s
tacks are awkward." }{TEXT 212 0 "" }{TEXT 212 1 "\n" }}{EXCHG {PARA 
202 "> " 0 "" {MPLTEXT 1 207 56 "s:=stack[new](): # creates a new, emp
ty stack called 's'" }{MPLTEXT 1 207 0 "" }}}{EXCHG {PARA 202 "> " 0 "
" {MPLTEXT 1 207 91 "stack[push](Euler, s):stack[push](Gauss, s):stack
[push](Riemann, s):stack[push](Cauchy, s):" }{MPLTEXT 1 207 0 "" }}}
{EXCHG {PARA 202 "> " 0 "" {MPLTEXT 1 207 77 "eval(s); # the 0th eleme
nt in the table is the number of objects in the stack" }{MPLTEXT 1 
207 0 "" }}{PARA 203 "" 1 "" {XPPMATH 20 "6#-I&TABLEGI*protectedGF%6#7
'/\"\"!\"\"%/\"\"\"I&EulerG6\"/\"\"#I&GaussGF./\"\"$I(RiemannGF./F*I'C
auchyGF." }{TEXT 208 0 "" }}}{EXCHG {PARA 202 "> " 0 "" {MPLTEXT 1 
207 61 "stack[depth](s); # returns the number of objects in the stack"
 }{MPLTEXT 1 207 0 "" }}{PARA 203 "" 1 "" {XPPMATH 20 "6#\"\"%" }
{TEXT 208 0 "" }}}{EXCHG {PARA 202 "> " 0 "" {MPLTEXT 1 207 71 "s[2]; \+
# returns the second object from the bottom but doesn't remove it" }
{MPLTEXT 1 207 0 "" }}{PARA 203 "" 1 "" {XPPMATH 20 "6#I&GaussG6\"" }
{TEXT 208 0 "" }}}{EXCHG {PARA 202 "> " 0 "" {MPLTEXT 1 207 54 "stack[
pop](s); # returns the top object AND removes it" }{MPLTEXT 1 207 0 ""
 }}{PARA 203 "" 1 "" {XPPMATH 20 "6#I'CauchyG6\"" }{TEXT 208 0 "" }}}
{EXCHG {PARA 202 "> " 0 "" {MPLTEXT 1 207 8 "eval(s);" }{MPLTEXT 1 
207 0 "" }}{PARA 203 "" 1 "" {XPPMATH 20 "6#-I&TABLEGI*protectedGF%6#7
&/\"\"!\"\"$/\"\"\"I&EulerG6\"/\"\"#I&GaussGF./F*I(RiemannGF." }{TEXT 
208 0 "" }}}{EXCHG {PARA 202 "> " 0 "" {MPLTEXT 1 207 51 "while not st
ack[empty](s) do stack[pop](s); end do;" }{MPLTEXT 1 207 0 "" }
{MPLTEXT 1 207 68 "\n# a loop to pop all the objects off the stack sta
rting from the top" }{MPLTEXT 1 207 0 "" }}{PARA 203 "" 1 "" {XPPMATH 
20 "6#I(RiemannG6\"" }{TEXT 208 0 "" }}{PARA 203 "" 1 "" {XPPMATH 20 "
6#I&GaussG6\"" }{TEXT 208 0 "" }}{PARA 203 "" 1 "" {XPPMATH 20 "6#I&Eu
lerG6\"" }{TEXT 208 0 "" }}}{PARA 204 "" 0 "" {TEXT 209 0 "" }{TEXT 
209 10 "\nEXERCISES" }{TEXT 212 0 "" }{TEXT 212 75 "\n1. Write a proce
dure that takes two integers as its arguments and returns " }{TEXT 
213 4 "true" }{TEXT 214 38 " if both are even or both are odd and " }
{TEXT 213 5 "false" }{TEXT 214 12 " otherwise. " }{TEXT 210 29 "Hint: \+
the Boolean expression " }{TEXT 211 11 "type(n,odd)" }{TEXT 210 9 " re
turns " }{TEXT 215 4 "true" }{TEXT 210 4 " if " }{TEXT 215 1 "n" }
{TEXT 210 12 " is odd and " }{TEXT 215 5 "false" }{TEXT 210 11 " other
wise." }{TEXT 212 0 "" }{TEXT 212 108 "\n2. Modify the previous proced
ure to take three integers as its arguments and perform a similar comp
utation." }{TEXT 212 0 "" }{TEXT 212 87 "\n3. Write a procedure that t
akes as its arguments a graph and two vertices and returns " }{TEXT 
213 4 "true" }{TEXT 214 4 " if " }{TEXT 212 70 "the vertex degrees are
 of the same parity (both even or both odd) and " }{TEXT 213 5 "false"
 }{TEXT 214 11 " otherwise." }{TEXT 212 0 "" }{TEXT 212 84 "\n4. Write
 a procedure that takes as its arguments a graph and two edges and ret
urns " }{TEXT 213 4 "true" }{TEXT 214 4 " if " }{TEXT 212 43 "the edge
s do not share a common vertex and " }{TEXT 213 5 "false" }{TEXT 214 
46 " otherwise. Hint: recall the networks command " }{TEXT 216 5 "ends
 " }{TEXT 214 27 "from Lab Two. For example, " }{TEXT 216 13 "ends(e5,
G)[2]" }{TEXT 214 54 " will return the second vertex of the fifth edge
 of G." }{TEXT 212 0 "" }{TEXT 212 135 "\n5. Write a procedure that ta
kes as its arguments a graph and a vertex and places the neighbors of \+
that vertex one by one onto a stack." }{TEXT 212 0 "" }{TEXT 212 52 "
\n6. Write a procedure that takes a positive integer " }{TEXT 213 1 "n
" }{TEXT 214 1 " " }{TEXT 212 50 "as its argument and places onto a st
ack the first " }{TEXT 213 1 "n" }{TEXT 214 67 " prime numbers, with t
he smallest prime at the bottom of the stack." }{TEXT 212 0 "" }{TEXT 
212 125 "\n7. Modify the previous procedure so that the primes are pla
ced onto a stack in the opposite order. Hint: use a second stack." }
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{TEXT 212 0 "" }}{PARA 204 "" 0 "" {TEXT 212 0 "" }}{PARA 204 "" 0 "" 
{TEXT 212 0 "" }}{PARA 204 "" 0 "" {TEXT -1 0 "" }}}{MARK "0 0 0" 0 }
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