We often encounter situations where we would like to create lists of data
that involve namers. For example, we may wish to create large lists of
numbers to test a function like <#62649#><#12790#>extract1<#12790#><#62649#> in
section~#seclistinlist#12791> on large lists instead of hand-coded small
ones. Sometimes we would like to visualize randomly picked data. We can
create such functions using recursion on natural numbers and a
random number generator.
<#12795#>Exercise 11.3.1<#12795#>
Scheme provides the operation <#62650#><#12798#>random<#12798#><#62650#>. It consumes a natural number,
<#62651#><#12799#>n<#12799#><#62651#>, and produces a random integer between <#62652#><#12800#>0<#12800#><#62652#> and <#62653#><#12801#>n<#12801#>\ <#12802#>-<#12802#>\ <#12803#>1<#12803#><#62653#>:
<#70999#>;; <#62654#><#12808#>random<#12808#> <#12809#>:<#12809#> <#12810#>N<#12810#> <#12811#><#12811#><#12812#>-;SPMgt;<#12812#><#12813#><#12813#> <#12814#>N<#12814#><#62654#><#70999#>
<#71000#>;; to compute a natural number between <#62655#><#12815#>0<#12815#><#62655#> and <#62656#><#12816#>n-1<#12816#><#62656#><#71000#>
<#12817#>(define<#12817#> <#12818#>(random<#12818#> <#12819#>n<#12819#> <#12820#>m)<#12820#> <#12821#>...)<#12821#>
Two successive uses of <#62657#><#12825#>(random<#12825#>\ <#12826#>n)<#12826#><#62657#> may produce two distinct results.
Now consider the following definition:
<#71001#>;; <#62658#><#12831#>random-n-m<#12831#> <#12832#>:<#12832#> <#12833#>integer<#12833#> <#12834#>integer<#12834#> <#12835#><#12835#><#12836#>-;SPMgt;<#12836#><#12837#><#12837#> <#12838#>integer<#12838#><#62658#><#71001#>
<#12839#>;; ...<#12839#>
<#12840#>;; Assume: n ;SPMlt; m<#12840#>
<#12841#>(d<#12841#><#12842#>efine<#12842#> <#12843#>(random-n-m<#12843#> <#12844#>n<#12844#> <#12845#>m)<#12845#>
<#12846#>(+<#12846#> <#12847#>(random<#12847#> <#12848#>(-<#12848#> <#12849#>m<#12849#> <#12850#>n))<#12850#> <#12851#>n))<#12851#>
Formulate a succinct and precise purpose statement for <#62659#><#12855#>random-n-m<#12855#><#62659#>.
Use a number line with an interval to explain the result of <#62660#><#12856#>(random<#12856#><#12857#> <#12857#><#12858#>n)<#12858#><#62660#>. Use a symbolic evaluation to support your
explanation.~ 
Solution<#62661#><#62661#>
<#12864#>Exercise 11.3.2<#12864#>
Develop the function <#62662#><#12866#>tie-dyed<#12866#><#62662#>. It consumes a natural number and
produces a list of integers. Each of these integers should be between
<#62663#><#12867#>-20<#12867#><#62663#> and <#62664#><#12868#>120<#12868#><#62664#>. Use <#62665#><#12869#>tie-dyed<#12869#><#62665#> to test
<#62666#><#12870#>draw-circles<#12870#><#62666#> from
exercise~#exdrawlistshapes#12871>.~ Solution<#62667#><#62667#>
<#12877#>Exercise 11.3.3<#12877#>
Develop the function <#62668#><#12879#>create-temps<#12879#><#62668#>. It consumes a natural number <#62669#><#12880#>n<#12880#><#62669#>
and two integers, called <#62670#><#12881#>low<#12881#><#62670#> and <#62671#><#12882#>high<#12882#><#62671#>. It produces a list
of <#62672#><#12883#>n<#12883#><#62672#> integers that are between <#62673#><#12884#>low<#12884#><#62673#> and <#62674#><#12885#>high<#12885#><#62674#>.
Use <#62675#><#12886#>create-temps<#12886#><#62675#> to test <#62676#><#12887#>check-range<#12887#><#62676#> from
exercise~#excheckrange1#12888>.
Finally, discuss the following questions. Can we simply feed the result of
<#62677#><#12889#>create-temps<#12889#><#62677#> into <#62678#><#12890#>check-range<#12890#><#62678#> or do we need to know the
list that <#62679#><#12891#>create-temps<#12891#><#62679#> produced? Are there values for <#62680#><#12892#>low<#12892#><#62680#>
and <#62681#><#12893#>high<#12893#><#62681#> such that we don't need to know the result of
<#62682#><#12894#>create-temps<#12894#><#62682#> and yet we can predict the result of the test? Which
function tests which? What does this tell us about testing with
automatically generated test data?~ Solution<#62683#><#62683#>
<#12900#>Exercise 11.3.4<#12900#>
Develop the function <#62684#><#12902#>create-prices<#12902#><#62684#>, which consumes a natural
number and produces a list with a corresponding of prices between $.10 and
$10.00 with increments of a dime. Use <#62685#><#12903#>create-prices<#12903#><#62685#> to test
<#62686#><#12904#>dollar-store?<#12904#><#62686#> from exercise~#exdollarstore#12905>.
<#12906#>Hint:<#12906#> How many dimes are there between $.10 and $10.00?~ Solution<#62687#><#62687#>
<#12912#>Exercise 11.3.5<#12912#>
Develop a program that visualizes a student riot. In preparation of a
student riot, a small group of students meets to make paint-filled
balloons. The typical riot uses <#62688#><#12914#>RED<#12914#><#62688#> only. Then, on the evening of
the riot, the students enter a university's progressive theater with the
balloons and throw them all over the seats.
The program's only input should be a natural number, which represents the
number of balloons thrown. The visualization should use a canvas that
contains a black grid and the positions of the balls:
rawhtml21
Assume a random distribution of the balls over the theater's
seats. Each box in the grid represents a seat. Configure the program so
the change of one variable definition changes the number of columns in the
grid and a change to another changes the number of rows.
<#12915#>Hint:<#12915#> Develop auxiliary functions that draw some given number of lines in the
vertical and the horizontal direction.~ Solution<#62689#><#62689#>