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Answers to Selected Problems

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<h2 id="answers-to-selected-problems">Answers to Selected Problems</h2>

<p>The answers presented here use parentheses to indicate nesting. It’s alright if you use spacing to indicate nesting so your answers look like the results displayed by <span class="small-caps">APL2</span> as long as you can unambiguously tell that you have the correct answer.</p>

<p>Because of the variety of functions in <span class="small-caps">APL2</span>, there is frequently more than one good solution to a problem. You may often come up with a different solution to a problem than the one shown here. If so, be sure that your solution is equivalent or better than the one shown.</p>

<h3 id="chapter-1-working-with-apl2">Chapter 1: Working with APL2<a href="#chapter-1-working-with-apl2" class="section-link">§</a></h3>

<h4 id="section-1.1-doing-ordinary-arithmetic">Section 1.1 — Doing Ordinary Arithmetic<a href="chapter1.html#exercises-for-section-1.1">↩︎</a><a href="#section-1.1-doing-ordinary-arithmetic" class="section-link">§</a></h4>

<ol>

</ol></li>

</ol>

<h4 id="section-1.2-arithmetic-on-arrays">Section 1.2 — Arithmetic on Arrays<a href="chapter1.html#exercises-for-section-1.2">↩︎</a><a href="#section-1.2-arithmetic-on-arrays" class="section-link">§</a></h4>

<ol>

<p>You should be able to get this numerical answer even though the structure of the result has not been discussed.</p></li>

</ol></li>

</ol></li>

</ol>

<h4 id="section-1.3-remembering-data">Section 1.3 — Remembering Data<a href="chapter1.html#exercises-for-section-1.3">↩︎</a><a href="#section-1.3-remembering-data" class="section-link">§</a></h4>

<ol>

<li>no change</li>

<li>no change</li>

</ol></li>

</ol>

<h4 id="section-1.4-evaluation-of-expressions">Section 1.4 — Evaluation of Expressions<a href="chapter1.html#exercises-for-section-1.4">↩︎</a><a href="#section-1.4-evaluation-of-expressions" class="section-link">§</a></h4>

<ol>

<li><code>5</code> redundant</li>

<li><code>30</code> rightmost pair redundant</li>

<li><code>58</code> outer pair redundant</li>

</ol></li>

</ol></li>

</ol></li>

</ol></li>

<li value=12><code>×/.01 STAX PRICE QTY</code></li>

</ol>

<h4 id="section-1.6-errors">Section 1.6 — Errors<a href="chapter1.html#exercises-for-section-1.6">↩︎</a><a href="#section-1.6-errors" class="section-link">§</a></h4>

<ol>

<li>three stars</li>

<li>two stars</li>

<li>empty</li>

</ol></li>

</ol>

<h3 id="chapter-2-working-with-vectors">Chapter 2: Working with Vectors<a href="#chapter-2-working-with-vectors" class="section-link">§</a></h3>

<h4 id="section-2.1-functions-that-produce-vectors">Section 2.1 — Functions that Produce Vectors<a href="chapter2.html#exercises-for-section-2.1">↩︎</a><a href="#section-2.1-functions-that-produce-vectors" class="section-link">§</a></h4>

<ol>

</ol></li>

<li value=6><code>MONTHS←MONTHS,65</code></li>

</ol>

<h4 id="section-2.2-character-data">Section 2.2 — Character Data<a href="chapter2.html#exercises-for-section-2.2">↩︎</a><a href="#section-2.2-character-data" class="section-link">§</a></h4>

<ol>

<li value=4>All of these answers are one-item vectors:

</ol></li>

</ol>

<h4 id="section-2.3-empty-vectors">Section 2.3 — Empty Vectors<a href="chapter2.html#exercises-for-section-2.3">↩︎</a><a href="#section-2.3-empty-vectors" class="section-link">§</a></h4>

<ol>

</ol>

<h4 id="section-2.4-functions-that-manipulate-vectors">Section 2.4 — Functions that Manipulate Vectors<a href="chapter2.html#exercises-for-section-2.4">↩︎</a><a href="#section-2.4-functions-that-manipulate-vectors" class="section-link">§</a></h4>

<ol>

</ol></li>

</ol></li>

<li value=6><code>'TRIBUTARY'[4 5 6]</code> or <code>3↑3↓'TRIBUTARY'</code></li>

</ol>

<h4 id="section-2.5-scalar-functions">Section 2.5 — Scalar Functions<a href="chapter2.html#exercises-for-section-2.5">↩︎</a><a href="#section-2.5-scalar-functions" class="section-link">§</a></h4>

<ol>

<li><code>3 2</code> (two-item vector)</li>

<li><code>12</code> (scalar)</li>

<li>(empty vector)</li>

<li><code>10 20</code> (two-item vector)</li>

<li><code>10</code> (one-item vector)</li>

<li>(empty vector)</li>

<li><code>10</code> (scalar)</li>

</ol></li>

</ol></li>

</ol></li>

<li>second <code>−</code></li>

<li>second <code>|</code></li>

<li><code>−</code> and second <code>×</code></li>

</ol></li>

</ol></li>

</ol>

<h3 id="chapter-3-working-with-programs">Chapter 3: Working with Programs<a href="#chapter-3-working-with-programs" class="section-link">§</a></h3>

<h4 id="section-3.1-operators-apply-to-functions">Section 3.1 — Operators Apply to Functions<a href="chapter3.html#exercises-for-section-3.1">↩︎</a><a href="#section-3.1-operators-apply-to-functions" class="section-link">§</a></h4>

<ol>

<li><code>4 6</code> (a scalar)</li>

<li><code>3 7</code> (simple)</li>

<li><code>8 9</code> (scalar)</li>

</ol></li>

</ol>

<h4 id="section-3.2-programs-remember-expressions">Section 3.2 — Programs Remember Expressions<a href="chapter3.html#exercises-for-section-3.2">↩︎</a><a href="#section-3.2-programs-remember-expressions" class="section-link">§</a></h4>

<ol>

<li value=2><pre> ∇ Z←PERDED DENTAL COST;PER;DED

[1] ⍝ compute dental cost

[2] (PER DED)←PERDED ⍝ separate left arg

[3] Z←⌊PER×COST−DED ⍝ part for insurance

[4] Z←(COST−Z)Z

∇</pre></li>

<li value=4><pre> ∇ Z← MC CHARGE DIMEN;UC

[1] ⍝ compute shipping cost

[2] ⍝ MC is minimum charge and unit charge

[3] ⍝ DIMEN is three dimensions in inches

[4] (MC UC)←MC ⍝ separate minimum and unit charges

[5] Z←MC⌈UC××/DIMEN÷12

[6] ∇</pre></li>

<li value=6><pre> ∇ Z← PERCENT V

[1] ⍝ compute percentage distribution

[2] ⍝ V — vector of sets of answers to questions

[3] ⍝ Z — vector of question percentages

[4] Z←⌊100×V÷+/¨V

[5] ∇</pre></li>

<li value=8><pre> ∇ Z←L PLUS R

[1] Z←L+R ⍝ addition

[2] ∇

∇ Z←WHAT R

[1] Z←R ⍝ do nothing

[2] ∇

∇ Z←IS R

[1] Z←R ⍝ do nothing

[2] ∇</pre></li>

<li value=10><p>Assume three variables <code>AMT</code>, <code>YEARS</code>, and <code>RATE</code>.</p>

<pre> AMT÷1+YEARS×RATE×.01</pre></li>

<li value=12><p><code>XX</code> is a defined sequence with an explicit result, not a variable.</p></li>

</ol>

<h3 id="chapter-4-working-in-the-apl2-environment">Chapter 4: Working in the APL2 Environment<a href="#chapter-4-working-in-the-apl2-environment" class="section-link">§</a></h3>

<h4 id="section-4.1-libraries">Section 4.1 — Libraries<a href="chapter4.html#exercises-for-section-4.2">↩︎</a><a href="#section-4.1-libraries" class="section-link">§</a></h4>

<ol>

2-f<br>

3-p<br>

4-d<br>

5-n<br>

6-l<br>

7-h<br>

8-a<br>

9-m<br>

10-r<br>

11-g<br>

12-q<br>

13-j<br>

14-c<br>

15-e</div></li>

</ol>

<h3 id="chapter-5-working-with-arrays">Chapter 5: Working with Arrays<a href="#chapter-5-working-with-arrays" class="section-link">§</a></h3>

<h4 id="section-5.1-properties-of-arrays">Section 5.1 — Properties of Arrays<a href="chapter5.html#exercises-for-section-5.1">↩︎</a><a href="#section-5.1-properties-of-arrays" class="section-link">§</a></h4>

<ol>

<li>simple, shape 3, depth 1</li>

<li>simple, shape 2, depth 1</li>

<li>simple, shape empty, depth 0</li>

<li>simple, shape 4, depth 1</li>

<li>nested, shape 2, depth 2</li>

<li>nested, shape 2, depth 3</li>

<li>nested, shape 2, depth 4</li>

</ol></li>

<li value=4>yes—a scalar that contains an empty array.</li>

</ol>

<h4 id="section-5.2-building-and-displaying-arrays">Section 5.2 — Building and Displaying Arrays<a href="chapter5.html#exercises-for-section-5.2">↩︎</a><a href="#section-5.2-building-and-displaying-arrays" class="section-link">§</a></h4>

<ol>

</ol></li>

<p>Right argument can be any non-empty array containing only empty arrays.</p></li>

</ol>

<h4 id="section-5.3-measuring-arrays">Section 5.3 — Measuring Arrays<a href="chapter5.html#exercises-for-section-5.3">↩︎</a><a href="#section-5.3-measuring-arrays" class="section-link">§</a></h4>

<ol>

This is a scalar containing an empty vector.</li>

This is a scalar containing an empty vector.</li>

</ol></li>

<li value=4>Depth is 1. The rest of the result depends on the argument.</li>

</ol>

<h4 id="section-5.4-unshaping-and-nested-shaping-of-arrays">Section 5.4 — Unshaping and Nested Shaping of Arrays<a href="chapter5.html#exercises-for-section-5.4">↩︎</a><a href="#section-5.4-unshaping-and-nested-shaping-of-arrays" class="section-link">§</a></h4>

<ol>

<li>shape 2, depth 2</li>

<li>shape 3, depth 2</li>

<li>shape empty, depth 3</li>

<li>shape empty, depth 4</li>

<li>shape empty, depth 3</li>

<li>shape 2 3, depth 1</li>

<li>shape 3 4, depth 1</li>

<li>shape 8, depth 1</li>

<li>shape 2 3 4, depth 1</li>

</ol></li>

</ol>

<h4 id="section-5.5-manipulating-an-array-along-an-axis">Section 5.5 — Manipulating an Array along an Axis<a href="chapter5.html#exercises-for-section-5.5">↩︎</a><a href="#section-5.5-manipulating-an-array-along-an-axis" class="section-link">§</a></h4>

<ol>

<li>shape <code>N M</code>, rank 2, depth 1</li>

<li>shape <code>M N</code>, rank 2, depth 1</li>

<li><code>AXIS ERROR</code></li>

<li>shape<code>L I M J N K</code>, rank 6, depth 1</li>

<li>shape<code>M I L J N K</code>, rank 6, depth 1</li>

</ol></li>

<li><code>AXIS ERROR</code></li>

</ol></li>

</ol></li>

<li><p>shape 3 3, value:</p>

<pre>11 12 13

24 25 26

37 38 39</pre></li>

<li><p>shape 3 3, value:</p>

<pre>11 22 33

14 25 36

17 28 39</pre></li>

<li><p><code>RANK ERROR</code></p></li>

<li><p>shape 2 4 3, value:</p>

<pre> 110 220 330

410 520 630

710 820 930

1010 1120 1230

1310 1420 1530

1610 1720 1830

1910 2020 2130

2210 2320 2430</pre></li>

<li><p>shape 2 4 3, value:</p>

<pre> 101 202 303

404 505 606

707 808 909

1010 1111 1212

1301 1402 1503

1604 1705 1806

1907 2008 2109

2210 2311 2412</pre></li>

<li><p>shape 2 4 3, value:</p>

<pre> 101 202 303

404 505 606

707 808 909

1010 1111 1212

1301 1402 1503

1604 1705 1806

1907 2008 2109

2210 2311 2412</pre></li>

</ol></li>

<li value=14><pre> ∇ Z←APPEND R;MAT;S;AXIS

[1] ⍝ append scalar on each side of axis

[2] (MAT S AXIS)←R ⍝ unpack argument

[3] Z←S,[AXIS]MAT,[AXIS]S ⍝ append scalar

[4] ∇</pre></li>

</ol>

<h4 id="section-5.6-other-functions-on-higher-rank-arrays">Section 5.6 — Other Functions on Higher-Rank Arrays<a href="chapter5.html#exercises-for-section-5.6">↩︎</a><a href="#section-5.6-other-functions-on-higher-rank-arrays" class="section-link">§</a></h4>

<ol>

<li>shape 4, depth 3</li>

<li>shape 4, depth 1</li>

<li>shape empty, depth 2</li>

<li>shape 2 3, depth 1</li>

<li>shape empty, depth 0</li>

<li>shape empty, depth 2</li>

<li><code>INDEX ERROR</code></li>

<li>shape empty, depth 0</li>

</ol></li>

</ol></li>

</ol>

<h4 id="section-5.7-other-primitive-operators">Section 5.7 — Other Primitive Operators<a href="chapter5.html#exercises-for-section-5.7">↩︎</a><a href="#section-5.7-other-primitive-operators" class="section-link">§</a></h4>

<ol>

<li><p>shape 3 4, depth 1, value:</p>

<pre>3 9 18 19

8 10 14 18

9 16 21 24</pre></li>

<li><p>shape 3 4, depth 1, value:</p>

<pre>3 ¯3 6 5

8 6 10 6

9 2 7 4</pre></li>

<li><p>shape 3 4, depth 1, value:</p>

<pre> 3 6 9 1

11 8 13 5

20 15 18 8</pre></li>

<li><p>shape 3 4, depth 1, value:</p>

<pre> 3 6 9 1

¯5 4 5 ¯3

4 11 10 0</pre></li>

</ol></li>

<li><p>shape 1, depth 2, value:</p>

<pre> 22 44 66 88

11 33 55 77

99 22 44 66

88 11 33 55</pre></li>

<li><p>shape 2, depth 2, value:</p>

<pre> 6 10 14 60 100 140

4 8 12 40 80 120

11 6 10 110 60 100

9 4 8 90 40 80</pre></li>

<li><p>shape 2, depth 2, value:</p>

<pre> 3 7 11 15 30 70 110 150

10 5 9 13 100 50 90 130

17 3 7 11 170 30 70 110</pre></li>

<li><p>shape empty, depth 2, value:</p>

<pre> 0 0 0

0 0 0

0 0 0</pre></li>

<li><p>shape empty, depth 2, value:</p>

<pre> 0 0 0

0 0 0

0 0 0</pre></li>

<li><p>shape 2, depth 2, value:</p>

<pre> 6 15 24 ¯6 ¯15 ¯24

33 42 51 ¯33 ¯42 ¯51

60 69 78 ¯60 ¯69 ¯78</pre></li>

<li><p>shape 2, depth 2, value:</p>

<pre> 30 33 36 ¯30 ¯33 ¯36

39 42 45 ¯39 ¯42 ¯45

48 51 54 ¯48 ¯51 ¯54</pre></li>

<li><p>shape 2, depth 2, value:</p>

<pre> 12 15 18 ¯12 ¯15 ¯18

39 42 45 ¯39 ¯42 ¯45

66 69 72 ¯66 ¯69 ¯72</pre></li>

<li><p>shape 2, depth 2, value:</p>

<pre> 3 5 ¯3 ¯5

9 11 ¯9 ¯11

15 17 ¯15 ¯17

21 23 ¯21 ¯23

27 29 ¯27 ¯29

33 35 ¯33 ¯35

39 41 ¯39 ¯41

45 47 ¯45 ¯47

51 53 ¯51 ¯53</pre></li>

<li><p>shape 2, depth 2, value:</p>

<pre> 11 13 15 ¯11 ¯13 ¯15

17 19 21 ¯17 ¯19 ¯21

23 25 27 ¯23 ¯25 ¯27

29 31 33 ¯29 ¯31 ¯33

35 37 39 ¯35 ¯37 ¯39

41 43 45 ¯41 ¯43 ¯45</pre></li>

<li><p>shape 2, depth 2, value:</p>

<pre> 5 7 9 ¯5 ¯7 ¯9

11 13 15 ¯11 ¯13 ¯15

23 25 27 ¯23 ¯25 ¯27

29 31 33 ¯29 ¯31 ¯33

41 43 45 ¯41 ¯43 ¯45

47 49 51 ¯47 ¯49 ¯51</pre></li>

</ol></li>

<li value=6><pre> ∇Z←CHECK M

[1] ⍝ 1 for row in ascending order

[2] Z←∧/M=⌈\M

[3] ∇</pre></li>

<li><p>shape 3 3, value:</p>

<pre> 2 4 8

5 25 125

10 100 1000</pre></li>

<li><p>shape 3 4, value:</p>

<pre>1 2 3 4

2 2 3 4

3 3 3 4</pre></li>

<li><p>shape 4 3, value:</p>

<pre>1 1 1

1 2 2

1 2 3

1 2 3</pre></li>

<li><p>shape 3 2, value:</p>

<pre> 5 6 4

7 7 7

8 8 8</pre></li>

<li><p>shape 2 3, value:</p>

<pre> 5 7 6 7 3 9

8 5 8 4 8 9 </pre></li>

<li><p>shape 3 2, value:</p>

<pre> A 10

BC 30 40

AB 10 20</pre></li>

<li><p>shape 3 2, value:</p>

<pre>AX

CZ</pre></li>

<li><p>shape 3 2, value:</p>

<pre> 1 AB 1 CDE

2 AB 2 CDE

3 AB 3 CDE </pre></li>

<li><p>shape 3 2, value:</p>

<pre> 1 AB 1 CDE

2 AB 2 CDE

3 AB 3 CDE</pre></li>

</ol></li>

<li><p>shape 3 3, value:</p>

<pre>1 2 3

4 5 6

7 8 9</pre></li>

<li><p>shape 3 3, value:</p>

<pre> 1 0 0 0 2 0 0 0 3 0 0 0

0 4 0 0 0 5 0 0 0 6 0 0

0 0 7 0 0 0 8 0 0 0 9 0 </pre></li>

</ol></li>

</ol>

<h3 id="chapter-6-working-with-data">Chapter 6: Working with Data<a href="#chapter-6-working-with-data" class="section-link">§</a></h3>

<h4 id="section-6.1-ways-of-comparing">Section 6.1 — Ways of Comparing<a href="chapter6.html#exercises-for-section-6.1">↩︎</a><a href="#section-6.1-ways-of-comparing" class="section-link">§</a></h4>

<ol>

<li value=4><code>+/RETAIL<10</code></li>

<li value=6>keeps only the first <code>1</code></li>

<li>shape 5,depth 1,value: <code>1 1 1 1 1</code></li>

<li>shape 5, depth 1, value: <code>1 1 0 1 1</code></li>

<li><code>LENGTH ERROR</code> (scalar function)</li>

<li>shape empty, depth 0, value: <code>1</code></li>

<li>shape empty, depth 0, value: <code>0</code></li>

<li>shape empty, depth 0, value: <code>1</code></li>

<li>shape empty, depth 0, value: <code>0</code></li>

<li>shape empty, depth 0, value: <code>1</code></li>

<li>shape empty, depth 0, value: <code>0</code></li>

<li>shape empty, depth 0, value: <code>1</code></li>

<li>shape empty, depth 0, value: <code>0</code></li>

<li>shape 2,depth 2, value: <code>1 1 0 1 1 1 1 1</code></li>

<li>shape empty, depth 0, value: <code>0</code></li>

<li>shape 2, depth 1, value: <code>0 1</code></li>

<li>shape 2,depth 2, value: <code>1 0 1 0 0 1 0</code></li>

</ol></li>

</ol>

<h4 id="section-6.2-selecting-subsets-of-arrays">Section 6.2 — Selecting Subsets of Arrays<a href="chapter6.html#exercises-for-section-6.2">↩︎</a><a href="#section-6.2-selecting-subsets-of-arrays" class="section-link">§</a></h4>

<ol>

<li value=2><code>TM[1]</code> is always a scalar. <code>↑TM</code> is, in general, an arbitrary array and, in particular, it is a <code>2 2</code> matrix.</li>

<li value=4><code>INVENTORY∼INVENTORY∼RLIST</code></li>

<li>depth 1, value: <code>EF</code></li>

<li>depth 1, value: empty</li>

<li>depth 1, value: <code>BYBY</code></li>

<li>depth 1, value: <code>BYEBYE</code></li>

<li>depth 2, value: <code> BYEBYE</code></li>

<li>depth 2, value: <code> CAB DAD</code></li>

<li>depth 2, value: <code> CB DAD</code></li>

<li>depth 2, value: <code> CAB DAD</code></li>

<li>depth 2, value: <code> C DD</code></li>

</ol></li>

<li><pre>AB C D

AB C D

AB C D</pre></li>

<li><pre>1 2 3 4

0 0 0 0

1 2 3 4

0 0 0 0

1 2 3 4</pre></li>

<li><code>LENGTH ERROR</code>; length of right argument is not the sum of the left argument.</li>

<li><code>0 0</code>; scalar containing two zeros</li>

</ol></li>

</ol>

<h4 id="section-6.3-searching-and-sorting">Section 6.3 — Searching and Sorting<a href="chapter6.html#exercises-for-section-6.3">↩︎</a><a href="#section-6.3-searching-and-sorting" class="section-link">§</a></h4>

<ol>

<li value=6><pre> ∇ Z← I RECEIPT STOCK;T

[1] ⍝ Z: a matrix listing of names and prices

[2] ⍝ matching I

[3] ⍝ STOCK: vector of vectors, each item consists of

[4] ⍝ (inventory no.)(item name) (item price)

[5] ⍝ Assume that values of I are always found in stock

[6] T←↑¨STOCK

[7] Z←⊃1↓¨ STOCK[T⍳I]

[8] ∇</pre></li>

</ol></li>

</ol></li>

</ol></li>

</ol></li>

</ol></li>

</ol>

<h4 id="section-6.4-computation">Section 6.4 — Computation<a href="chapter6.html#exercises-for-section-6.4">↩︎</a><a href="#section-6.4-computation" class="section-link">§</a></h4>

<ol>

<p>(When you enter the sixth country, you have crossed five borders.)</p></li>

</ol></li>

<li value=6><code>'0123456789ABCDEF'[1+(8⍴16)⊤N]</code></li>

</ol></li>

<li><pre> 1 0 0 0

¯1 1 0 0

0 ¯1 1 0

0 0 ¯1 1</pre></li>

<li><pre>1 ¯1 0 0

0 1 ¯1 0

0 0 1 ¯1

0 0 0 1</pre></li>

</ol></li>

</ol></li>

</ol>

<h4 id="section-6.5-generating-random-numbers">Section 6.5 — Generating Random Numbers<a href="chapter6.html#exercises-for-section-6.5">↩︎</a><a href="#section-6.5-generating-random-numbers" class="section-link">§</a></h4>

<ol>

</ol></li>

</ol>

<h3 id="chapter-7-working-with-program-control">Chapter 7: Working with Program Control<a href="#chapter-7-working-with-program-control" class="section-link">§</a></h3>

<h4 id="section-7.1-control-of-execution-branching">Section 7.1 — Control of Execution: Branching<a href="chapter7.html#exercises-for-section-7.1">↩︎</a><a href="#section-7.1-control-of-execution-branching" class="section-link">§</a></h4>

<ol>

<li><code>→(I=1 2 3)/L1 L2 L3</code> (Falls through if <code>I</code> is incorrect.)</li>

<li><code>→(L1 L2 L3)[I]</code> (Fails if <code>I</code> is incorrect.)</li>

</ol></li>

<li><code>A</code> simple</li>

<li><code>N</code> integer</li>

<li>first three characters of <code>ANS</code> are <code>'END'</code></li>

<li><code>WORD</code> contains a vowel</li>

<li>Three-way branch for negative, zero, or positive (assuming three names are labels)</li>

<li><code>ANS</code> is empty</li>

</ol></li>

</ol>

<h4 id="section-7.2-debugging-your-program">Section 7.2 — Debugging Your Program<a href="chapter7.html#exercises-for-section-7.2">↩︎</a><a href="#section-7.2-debugging-your-program" class="section-link">§</a></h4>

<ol>

<li value=2>experimentation only</li>

</ol>

<h4 id="section-7.3-prompting-for-input">Section 7.3 — Prompting for Input<a href="chapter7.html#exercises-for-section-7.3">↩︎</a><a href="#section-7.3-prompting-for-input" class="section-link">§</a></h4>

<ol>

<li>none— shorter row would be padded</li>

</ol></li>

</ol>

<h4 id="section-7.4-output-with-quad-and-quote-quad">Section 7.4 — Output with Quad and Quote-Quad<a href="chapter7.html#exercises-for-section-7.4">↩︎</a><a href="#section-7.4-output-with-quad-and-quote-quad" class="section-link">§</a></h4>

<ol>

</ol>

<h4 id="section-7.5-controlling-output">Section 7.5 — Controlling Output<a href="chapter7.html#exercises-for-section-7.5">↩︎</a><a href="#section-7.5-controlling-output" class="section-link">§</a></h4>

<ol>

<li value=2><pre> ∇ Z←NUMBER A;R

[1] R←↑⍴A

[2] Z←⊃[2]'[',¨(⊂[2]⍕(R,1)⍴⍳R),¨']',¨⊂[2]A

[3] ∇</pre></li>

<li value=4><p>(<strong>Note:</strong> “<code>∼</code>” indicates where blanks appear in the result, to assist you in seeing the spacing.)</p>

<li><p>shape 40:</p>

<pre> '−5,551.55 '⍕W

93.73 −27.8 −192.83 6,754

∼∼∼∼ ∼∼∼∼ ∼∼∼∼ ∼∼ ∼∼∼∼</pre></li>

<li><p>shape 48:</p>

<pre> '$5,551.50CR '⍕W

93.73 $27.80CR $192.83CR 6,754.00

∼∼∼∼ ∼∼∼∼∼∼ ∼∼∼ ∼∼ ∼∼∼</pre></li>

<li><p>shape 52:</p>

<pre> '$_5,553.10CR '⍕W

$ 93.73 $ 27.80CR $ 192.83CR $ 6,754.00

∼∼∼ ∼ ∼∼∼∼∼∼ ∼ ∼∼∼ ∼ ∼ ∼ ∼∼∼</pre></li>

<li><p>shape 48:</p>

<pre> '$ −5,551.55 '⍕W

$ 93.73 $ −27.8 $ −192.83 $ 6,754

∼∼∼∼∼ ∼ ∼∼∼∼ ∼∼ ∼∼∼ ∼ ∼∼ ∼∼∼∼</pre></li>

<li><p>shape 48:</p>

<pre> '$_−5,551.55 '⍕W

93.73 $ −27.8 $ −192.83 6,754

∼∼∼∼∼∼ ∼∼∼∼ ∼ ∼∼∼∼ ∼ ∼∼∼∼ ∼∼∼∼</pre></li>

<li><p>shape 56:</p>

<pre> '$_5,554.10_CR '⍕W

$ 93.73 $ 27.80 CR $ 192.83 CR $ 6,754.00

∼∼∼∼ ∼∼∼∼ ∼∼∼∼ ∼ ∼ ∼∼∼ ∼ ∼ ∼ ∼∼∼∼</pre></li>

<li><p>error:</p>

<pre> '5,555.55 '⍕W

DOMAIN ERROR (no provision for negative sign)</pre></li>

</ol></li>

</ol>

<h4 id="section-7.6-control-of-execution-iteration">Section 7.6 — Control of Execution: Iteration<a href="chapter7.html#exercises-for-section-7.6">↩︎</a><a href="#section-7.6-control-of-execution-iteration" class="section-link">§</a></h4>

<ol>

<li value=2><pre> ∇ Z←INTERVAL N;I

[1] ⍝ loop simulating monadic iota

[2] Z←⍳0

[3] I←1

[4] L1:→(I>N)/0

[5] Z←Z,I

[6] I←I+1

[7] →L1

[8] ∇</pre></li>

</ol>

<h4 id="section-7.7-control-of-execution-recursion">Section 7.7 — Control of Execution: Recursion<a href="chapter7.html#exercises-for-section-7.7">↩︎</a><a href="#section-7.7-control-of-execution-recursion" class="section-link">§</a></h4>

<ol>

<li><pre> ∇ Z←ADDREC R

[1] ⍝ recursive routine to add up numbers

[2] Z←R

[3] →(2>⍴R)/0

[4] Z←ADDREC(R[1]+R[2]),2↓R

[5] ∇</pre></li>

<li><pre> ∇ Z←ADDLOOP R;I

[1] ⍝ looping routine to add up numbers

[2] I←Z←0

[3] L1:I←I+1

[4] →(I>⍴R)/0

[5] Z←Z+R[I]

[6] →L1

[7] ∇</pre>

(It is generally more efficient to use indexing rather than to use <code>↑R</code> and <code>↓R</code>.)</li>

</ol></li>

<li value=4><pre> ∇ Z←INTERVALR N;I

[1] ⍝ recursive routine simulating monadic iota

[2] Z←⍳0

[3] →(N≤0)/0

[4] Z←(INTERVAL N−1),N

[5] ∇</pre></li>

<li value=6><code>⍴MDEPTH ⍴MDEPTH A</code></li>

<li value=8><pre> ∇ Z←(F MDEPTH1 N)R

[1] ⍝ apply F to each array of depth N

[2] →(N<≡R)/L1 ⍝ branch not requested depth

[3] Z←F R ⍝ F of simple

[4] →0 ⍝ exit

[5] L1:Z←(F MDEPTH1 N)¨R ⍝ recur

[6] ∇</pre></li>

<li value=10><pre> ∇ Z←L(F DDEPTHB)R

[1] ⍝ apply F to each simple array in R

[2] →(1<≡R)/I1 ⍝ branch not simple

[3] Z←L F R ⍝ F of simple

[4] →0 ⍝ exit

[5] L1:Z←(⊂L)(F DDEPTHB)¨R ⍝ recur

[6] ∇</pre></li>

</ol>

<h3 id="chapter-8-working-with-applications">Chapter 8: Working with Applications<a href="#chapter-8-working-with-applications" class="section-link">§</a></h3>

<h4 id="section-8.1-a-magazine-collection">Section 8.1 — A Magazine Collection<a href="chapter8.html#exercises-for-section-8.1">↩︎</a><a href="#section-8.1-a-magazine-collection" class="section-link">§</a></h4>

<ol>

<li value=2><pre> ∇ Z←SORTUPBY R;N

[1] ⍝ R is the field to sort on, matrix

[2] (N Z)←R

[3] Z←Z[⍋Z[;N];]

[4] ∇</pre></li>

<li value=4><pre> ∇ADD R;IN

[1] ⍝ R is the new issue number

[2] L1:'enter values for issue number ' R

[3] ' ' 'Vol' 'No' 'Year' 'Mon' 'Price' 'Value' 'Own'

[4] IN←⍎⍞ ⍝ read input

[5] →((,7)≡⍴IN)/OK ⍝ must be 7 items

[6] ‘error - enter 7 items'

[7] →L1

[8] OK:MAG←MAG,[1]R,IN ⍝ add new row

[9] ∇</pre></li>

</ol>

<h4 id="section-8.2-simulation-of-a-vector-computer">Section 8.2 — Simulation of a Vector Computer<a href="chapter8.html#exercises-for-section-8.2">↩︎</a><a href="#section-8.2-simulation-of-a-vector-computer" class="section-link">§</a></h4>

<ol>

<li value=2><pre> ∇ LOADS R;V;A;S

[1] (V A)←R

[2] ⍝ load scalar register V from address in A

[3] SR[V]←MM[A]

[4] ∇

∇ STORES R;V;A

[1] (V A)←R

[2] ⍝ store scalar register V in address A

[3] MM[A]←SR[V]

[4] ∇</pre></li>

<li value=4><pre> ∇ VPROBLEM4

[1] 26 SETMEMORY 10 9 87 6 5 4 3

[2] 3 SETMEMORY 26

[3] 4 SETMEMORY 7

[4] 1 SETMEMORY O

[5] LOADS 2 1

[6] LOOP:LOADVCT 4

[7] →(0=VCT)/0

[8] LOADV 4 3 1

[9] PLUSREDUCE 4 2

[10] →LOOP

[11] ∇</pre></li>

</ol>

<h4 id="section-8.3-a-puzzle-solving-program">Section 8.3 — A Puzzle-Solving Program<a href="chapter8.html#exercises-for-section-8.3">↩︎</a><a href="#section-8.3-a-puzzle-solving-program" class="section-link">§</a></h4>

<ol>

<li value=2><pre> ∇ Z←STRT(MOVE SEARCH1CHK)G;B;M;NEWP;CNT

[1] ⍝ find path from start to goal

[2] ⍝ STRT ←→ starting position

[3] ⍝ I ←→ count of loops

[4] ⍝ G ←→ goal position

[5] ⍝ MOVE ←→ program to compute next positions

[6] M←,⊂,⊂STRT ⍝ initial path is STRT

[7] Z←⍳0 ⍝ return empty on failure

[8] I←0 ⍝ initial count

[9] LOOP:→(0=⍴M)/0 ⍝ quit no more paths

[10] ⍝(G≡B←↑↑M)/DONE ⍝ done if goal

[11] NEWP←MOVE B ⍝ compute new positions

[12] NEWP←(∼NEWP∊↑,/M)/NEWP ⍝ keep new positions

[13] M←(1↓M),(⊂¨NEWP),¨M[1] ⍝ add to paths

[14] I←I+1 ⍝ increment loop count

[15] →(0≠20∣I)/LOOP ⍝ continue if not 20 loops

[16] ⍞←I 'LOOPS - CONTINUE? (Y/N)'

[17] →('Y'∊⍞)/LOOP ⍝ back for next path

[18] →0 ⍝ exit early

[19] DONE:Z←⌽↑M ⍝ return with path

[20]∇</pre></li>

<li value=4><pre> ∇ Z←MOVE8 M;IB;MI;IN

[1] ⍝ move generator for 8 puzzle

[2] IB←(,M∊' ')/,MI←(⍳3)∘.,⍳3

[3] IN←(IN∊MI)/IN←,(0 1)(0 ¯1)(1 0)(¯1 0)∘.+IB

[4] Z←IN RMOVE8¨⊂M

[5] Z←Z (Z≡¨⊂3 3⍴'1238 4765')

[6] ∇

∇Z←RMOVE8 M

[1] ⍝ recursive replacer, subfunction of MOVE8

[2] (IB⊃Z)←(⊂I)⊃Z←M

[3] ((⊂I)⊃Z)←' '

[4] ∇</pre></li>

<li value=6><pre> ∇Z←EST1 P

[1] ⍝ number out of position est for 8 puzzle

[2] Z←+/,P≠3 3⍴'1238 4765'

[3] ∇</pre></li>

</ol>

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