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{{mylangbegin}}
{{mylangbegin}}
{{mylang|Visual Basic|Active (in VB for Applications)}}
{{mylang|VBA|Active}}
{{mylang|BASIC|Somewhat Rusty}}
{{mylang|BASIC|Somewhat Rusty}}
{{mylang|Fortran|Stuck in Fortran 77, WATFOR, WATFIV etc.}}
{{mylang|Fortran|Stuck in Fortran 77, WATFOR, WATFIV etc.}}
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=VBA Examples=
=VBA Examples=
Some nontrivial VBA Examples (until there is a separate VBA category).
Some nontrivial VBA Examples (to be moved).


In MS Office program (Word, Excel, Access...): open the Visual Basic window. Paste the code in a module. Execute it by typing a suitable command in the Immediate Window. Output will be directed to the Immediate Window unless stated otherwise...
In MS Office program (Word, Excel, Access...): open the Visual Basic window. Paste the code in a module. Execute it by typing a suitable command in the Immediate Window. Output will be directed to the Immediate Window unless stated otherwise...


==[[Letter frequency]]==
==[[Dijkstra algorithm]]==
<lang>
<lang vb>
'Dijkstra globals
Public Sub LetterFrequency(fname)
Const MaxGraph As Integer = 100 'max. number of nodes in graph
'count number of letters in text file (ASCII-coded)
Const Infinity = 1E+308
'note: we count all characters but print only the letter frequencies
Dim E(1 To MaxGraph, 1 To MaxGraph) As Double 'the edge costs (Infinity if no edge)

Dim A(1 To MaxGraph) As Double 'the distances calculated
Dim Freqs(255) As Long
Dim P(1 To MaxGraph) As Integer 'the previous/path array
Dim abyte As Byte
Dim Q(1 To MaxGraph) As Boolean 'the queue
Dim ascal as Byte 'ascii code for lowercase a
Dim ascau as Byte 'ascii code for uppercase a
Public Sub Dijkstra(n, start)

'simple implementation of Dijkstra's algorithm
'try to open the file
'n = number of nodes in graph
On Error GoTo CantOpen
'start = index of start node
Open fname For Input As #1
'init distances A
On Error GoTo 0
For j = 1 To n

A(j) = Infinity
'initialize
For i = 0 To 255
Next j
Freqs(i) = 0
A(start) = 0
'init P (path) to "no paths" and Q = set of all nodes
For j = 1 To n
Q(j) = True
P(j) = 0
Next j
Do While True 'loop will exit! (see below)
'find node u in Q with smallest distance to start
dist = Infinity
For i = 1 To n
If Q(i) Then
If A(i) < dist Then
dist = A(i)
u = i
End If
End If
Next i
If dist = Infinity Then Exit Do 'no more nodes available - done!
'remove u from Q
Q(u) = False
'loop over neighbors of u that are in Q
For j = 1 To n
If Q(j) And E(u, j) <> Infinity Then
'check if path to neighbor j via u is shorter than current estimated distance to j
alt = A(u) + E(u, j)
If alt < A(j) Then
'yes, replace with new distance and remember "previous" hop on the path
A(j) = alt
P(j) = u
End If
End If
Next j
Loop
End Sub
Public Function GetPath(source, target) As String
'reconstruct shortest path from source to target
'by working backwards from target using the P(revious) array
Dim path As String
If P(target) = 0 Then
GetPath = "No path"
Else
path = ""
u = target
Do While P(u) > 0
path = Format$(u) & " " & path
u = P(u)
Loop
GetPath = Format$(source) & " " & path
End If
End Function
Public Sub DijkstraTest()
'main function to solve Dijkstra's algorithm and return shortest path between
'a node and every other node in a digraph
' define problem:
' number of nodes
n = 5
' reset connection/cost per edge
For i = 1 To n
For j = 1 To n
E(i, j) = Infinity
Next j
P(i) = 0
Next i
Next i
' fill in the edge costs
E(1, 2) = 10
E(1, 3) = 50
E(1, 4) = 65
E(2, 3) = 30
E(2, 5) = 4
E(3, 4) = 20
E(3, 5) = 44
E(4, 2) = 70
E(4, 5) = 23
E(5, 1) = 6
'Solve it for every node


For v = 1 To n
'process file byte-per-byte
Dijkstra n, v
While Not EOF(1)
'Print solution
abyte = Asc(Input(1, #1))
Debug.Print "From", "To", "Cost", "Path"
Freqs(abyte) = Freqs(abyte) + 1
For j = 1 To n
Wend
If v <> j Then Debug.Print v, j, IIf(A(j) = Infinity, "---", A(j)), GetPath(v, j)
Close #1
Next j

Debug.Print
'add lower and upper case together and print result
Next v
Debug.Print "Frequencies:"
ascal = Asc("a")
ascau = Asc("A")
For i = 0 To 25
Debug.Print Chr$(ascal + i), Freqs(ascal + i) + Freqs(ascau + i)
Next i
Exit Sub

CantOpen:
Debug.Print "can't find or read the file "; fname
Close
End Sub
End Sub
</lang>
</lang>


Output (using the same graph as in the Floyd-Warshall algorithm below):
Output:
<pre>
<pre>
DijkstraTest
LetterFrequency "d:\largetext.txt"
From To Cost Path
Frequencies:
a 24102
1 2 10 1 2
b 4985
1 3 40 1 2 3
c 4551
1 4 60 1 2 3 4
d 19127
1 5 14 1 2 5
e 61276
f 2734
g 10661
h 8243
i 21589
j 4904
k 7186
l 12026
m 7454
n 31963
o 19021
p 4960
q 37
r 21166
s 13403
t 21090
u 6117
v 8612
w 5017
x 168
y 299
z 4159
</pre>


From To Cost Path
==[[Horner's rule for polynomial evaluation]]==
2 1 10 2 5 1
2 3 30 2 3
2 4 50 2 3 4
2 5 4 2 5


From To Cost Path
Note: this function Horner gets its coefficients in a ParamArray which has no specified length. This array collect all arguments after the first one. This means you must specify x first, then the coefficients.
3 1 49 3 4 5 1
3 2 59 3 4 5 1 2
3 4 20 3 4
3 5 43 3 4 5


From To Cost Path
<lang>
4 1 29 4 5 1
Public Function Horner(x, ParamArray coeff())
4 2 39 4 5 1 2
Dim result As Double
4 3 69 4 5 1 2 3
Dim ncoeff As Integer
4 5 23 4 5


From To Cost Path
result = 0
5 1 6 5 1
ncoeff = UBound(coeff())
5 2 16 5 1 2

5 3 46 5 1 2 3
For i = ncoeff To 0 Step -1
5 4 66 5 1 2 3 4
result = (result * x) + coeff(i)
Next i
Horner = result
End Function
</lang>

Output:
<pre>
print Horner(3, -19, 7, -4, 6)
128
</pre>
</pre>


==[[Floyd-Warshall algorithm]]==
==[[Floyd-Warshall algorithm]]==
[[File:FloydGraph.png|thumb|250px|Graph used in this and Dijkstra's algorithm]]
The [http://en.wikipedia.org/wiki/Floyd-Warshall_algorithm Floyd algorithm or Floyd-Warshall algorithm] finds the shortest path between all pairs of nodes in a weighted, directed graph. It is an example of dynamic programming.
The [http://en.wikipedia.org/wiki/Floyd-Warshall_algorithm Floyd algorithm or Floyd-Warshall algorithm] finds the shortest path between all pairs of nodes in a weighted, directed graph. It is an example of dynamic programming.


Usage: fill in the number of nodes (n) and the non-zero edge distances or costs in sub Floyd or in sub FloydWithPaths.
Usage: fill in the number of nodes (n) and the edge distances or costs in sub Floyd or in sub FloydWithPaths.
Then run "Floyd" or "FloydWithPaths".
Then run "Floyd" or "FloydWithPaths".


Line 126: Line 173:
FloydWithPaths: this sub prints the lengths and the nodes along the paths
FloydWithPaths: this sub prints the lengths and the nodes along the paths


<lang>
<lang vb>
Option Compare Database

'Floyd globals
'Floyd globals
Const MaxGraph As Integer = 100 'max. number of vertices in graph
Const MaxGraph As Integer = 100 'max. number of vertices in graph
Const Infinity = 1E+308 'very large number
Const Infinity = 1E+308
Dim E(1 To MaxGraph, 1 To MaxGraph) As Double
Dim E(1 To MaxGraph, 1 To MaxGraph) As Double
Dim A(1 To MaxGraph, 1 To MaxGraph) As Double
Dim A(1 To MaxGraph, 1 To MaxGraph) As Double
Dim Nxt(1 To MaxGraph, 1 To MaxGraph) As Integer
Dim Nxt(1 To MaxGraph, 1 To MaxGraph) As Integer

Public Sub SolveFloyd(n)
Public Sub SolveFloyd(n)
'Floyd's algorithm: all-pairs shortest-paths cost
'Floyd's algorithm: all-pairs shortest-paths cost
Line 142: Line 191:
'inputs:
'inputs:
' n : number of vertices (maximum value is maxGraph)
' n : number of vertices (maximum value is maxGraph)
' E(i,j) : cost (length,...) of edge from i to j or <=0 if no edge between i and j
' E(i,j) : cost (length,...) of edge from i to j or "Infinity" if no edge between i and j
'output:
'output:
' A(i,j): minimal cost for path from i to j
' A(i,j): minimal cost for path from i to j
'constant:
'constant:
' Infinity : very large number (guaranteed to be larger than largest possible cost of any path)
' Infinity : very large number
For i = 1 To n
For i = 1 To n
For j = 1 To n
For j = 1 To n
If E(i, j) > 0 Then A(i, j) = E(i, j) Else A(i, j) = Infinity
If E(i, j) <> Infinity Then A(i, j) = E(i, j) Else A(i, j) = Infinity
Next j
Next j
A(i, i) = 0
A(i, i) = 0
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Next k
Next k
End Sub
End Sub

Public Sub SolveFloydWithPaths(n)
Public Sub SolveFloydWithPaths(n)
'cf. SolveFloyd, but here we
'cf. SolveFloyd, but here we
Line 168: Line 217:
For i = 1 To n
For i = 1 To n
For j = 1 To n
For j = 1 To n
If E(i, j) > 0 Then A(i, j) = E(i, j) Else A(i, j) = Infinity
If E(i, j) <> Infinity Then A(i, j) = E(i, j) Else A(i, j) = Infinity
Next j
Next j
A(i, i) = 0
A(i, i) = 0
Line 183: Line 232:
Next k
Next k
End Sub
End Sub

Public Function GetPath(i, j) As String
Public Function GetPath(i, j) As String
'recursively reconstruct shortest path from i to j using A and Nxt
'recursively reconstruct shortest path from i to j using A and Nxt
Line 197: Line 246:
End If
End If
End Function
End Function

Public Sub Floyd()
Public Sub Floyd()
'main function to apply Floyd's algorithm
'main function to apply Floyd's algorithm
'see description in wp:en:Floyd-Warshall algorithm
'see description in wp:en:Floyd-Warshall algorithm

' define problem:
' define problem:
' number of vertices?
' number of vertices?
Line 208: Line 257:
For i = 1 To n
For i = 1 To n
For j = 1 To n
For j = 1 To n
E(i, j) = 0
E(i, j) = Infinity
Next j
Next j
Next i
Next i
Line 219: Line 268:
E(3, 4) = 20
E(3, 4) = 20
E(3, 5) = 44
E(3, 5) = 44
E(4, 2) = 7
E(4, 2) = 70
E(4, 5) = 13
E(4, 5) = 23
E(5, 1) = 6

'Solve it
'Solve it
SolveFloyd n
SolveFloyd n

'Print solution
'Print solution
'note: for large graphs the output may be too large for the Immediate panel
'note: for large graphs the output may be too large for the Immediate panel
Line 235: Line 285:
Next i
Next i
End Sub
End Sub

Public Sub FloydWithPaths()
Public Sub FloydWithPaths()
'main function to solve Floyd's algorithm and return shortest path between
'main function to solve Floyd's algorithm and return shortest path between
'any two vertices
'any two vertices

' define problem:
' define problem:
' number of vertices?
' number of vertices?
Line 246: Line 296:
For i = 1 To n
For i = 1 To n
For j = 1 To n
For j = 1 To n
E(i, j) = 0
E(i, j) = Infinity
Nxt(i, j) = 0
Nxt(i, j) = 0
Next j
Next j
Line 258: Line 308:
E(3, 4) = 20
E(3, 4) = 20
E(3, 5) = 44
E(3, 5) = 44
E(4, 2) = 7
E(4, 2) = 70
E(4, 5) = 13
E(4, 5) = 23
E(5, 1) = 6

'Solve it
'Solve it
SolveFloydWithPaths n
SolveFloydWithPaths n

'Print solution
'Print solution
'note: for large graphs the output may be too large for the Immediate panel
'note: for large graphs the output may be too large for the Immediate panel
Line 274: Line 325:
Next i
Next i
End Sub
End Sub
</lang>
</lang>


Output:
Output:
<pre>
<pre>Floyd
Floyd
From To Cost
From To Cost
1 2 10
1 2 10
Line 284: Line 334:
1 4 60
1 4 60
1 5 14
1 5 14
2 1 No path!
2 1 10
2 3 30
2 3 30
2 4 50
2 4 50
2 5 4
2 5 4
3 1 No path!
3 1 49
3 2 27
3 2 59
3 4 20
3 4 20
3 5 31
3 5 43
4 1 No path!
4 1 29
4 2 7
4 2 39
4 3 37
4 3 69
4 5 11
4 5 23
5 1 No path!
5 1 6
5 2 No path!
5 2 16
5 3 No path!
5 3 46
5 4 No path!
5 4 66



FloydWithPaths
FloydWithPaths
Line 308: Line 357:
1 4 60 2 3
1 4 60 2 3
1 5 14 2
1 5 14 2
2 1 --- No path!
2 1 10 5
2 3 30
2 3 30
2 4 50 3
2 4 50 3
2 5 4
2 5 4
3 1 --- No path!
3 1 49 4 5
3 2 27 4
3 2 59 4 5 1
3 4 20
3 4 20
3 5 31 4 2
3 5 43 4
4 1 --- No path!
4 1 29 5
4 2 7
4 2 39 5 1
4 3 37 2
4 3 69 5 1 2
4 5 11 2
4 5 23
5 1 --- No path!
5 1 6
5 2 --- No path!
5 2 16 1
5 3 --- No path!
5 3 46 1 2
5 4 --- No path!
5 4 66 1 2 3
</pre>

==[[KWIC index]]==

<lang vb>
'KWIC index
'assumptions:
' - all titles and catalog numbers can be held in an array in main memory
' - disregard punctuation in titles
' - the KWIC index itself may be too large for main memory - do not store it in memory
' - the KWIC index consists of one line per title/keyword combination and consists of:
' - the catalog number
' - the title with the keyword centered in a line of given length (e.g. 80 or 120)
' (constant-width font assumed)
' note: long titles may be truncated at the beginning or the end of the line

'globals
Const MAXKEYS = 20 'max. number of keywords in a title
Const STOPWORDS = "a an and by for is it of on or the to with " 'that last space is needed!
Dim title() As String 'list of titles to be included in KWIC index
Dim catno() As Integer 'list of catalog numbers
Dim ntitle As Integer 'number of titles
Dim index() As Integer 'holds title number and position of keyword in title
Dim nkeys As Long 'total number of keywords found

Sub ReadTitles()
' read or - in this case - set the titles and catalog numbers
ntitle = 10
ReDim title(1 To ntitle)
ReDim catno(1 To ntitle)
title(1) = "Microsoft Visio 2003 User's Guide"
title(2) = "Microsoft Office Excel 2003 Inside Out"
title(3) = "Mastering Excel 2003 Programming with VBA"
title(4) = "Excel 2003 Formulas"
title(5) = "Excel for Scientists and Engineers"
title(6) = "Excel 2003 VBA Programmer's Reference"
title(7) = "Automated Data Analysis Using Excel"
title(8) = "Beginning Excel: What-if Data Analysis Tools"
title(9) = "How to do Everything with Microsoft Office Excel 2003"
title(10) = "Data Analysis Using SQL and Excel"
catno(1) = 10
catno(2) = 13
catno(3) = 3435
catno(4) = 987
catno(5) = 1010
catno(6) = 1244
catno(7) = 709
catno(8) = 9088
catno(9) = 33
catno(10) = 7733
End Sub

Function IsStopword(aword) As Boolean
'search for aword in stopword list
'add an extra space to avoid ambiguity
IsStopword = InStr(STOPWORDS, LCase(aword) & " ") > 0
End Function

Sub ProcessTitles()
'find positions of keywords in titles, store in index array
'Note: we cannot use Split here because that function doesn't return
'the positions of the words it finds
nkeys = 0
For i = 1 To ntitle
atitle = title(i) & " " 'add extra space as sentinel
p1 = 1
Do While p1 <= Len(atitle)
'find next word:
'a) find next non-space
While Mid$(atitle, p1, 1) = " ": p1 = p1 + 1: Wend
'b) extend word
p2 = p1
While Mid$(atitle, p2, 1) <> " ": p2 = p2 + 1: Wend
aword = Mid$(atitle, p1, p2 - p1)
'for now we assume there is no punctuation, i.e. no words
'in parentheses, brackets or quotation marks
If Not IsStopword(aword) Then
'remember position of this keyword
'we probably should check for overflow (too many keywords) here!
nkeys = nkeys + 1
index(nkeys, 1) = i
index(nkeys, 2) = p1
End If
'continue searching
p1 = p2 + 1
Loop
Next i
End Sub

Function Shift(aString, pos)
'return shifted string (part beginning at position "pos" followed by part before it)
Shift = Mid$(aString, pos) & " " & Left$(aString, pos - 1)
End Function

Sub SortTitles()
' sort the index() array to represent shifted titles in alphabetical order
' more efficient sorting algorithms can be applied here...
switched = True
Do While switched
'scan array for two shifted strings in the wrong order and swap
'(swap the index entries, not the strings)
'use case-insensitive compare
switched = False
For i = 1 To nkeys - 1
string1 = LCase(Shift(title(index(i, 1)), index(i, 2)))
string2 = LCase(Shift(title(index(i + 1, 1)), index(i + 1, 2)))
If string2 < string1 Then 'swap
For j = 1 To 2
temp = index(i, j)
index(i, j) = index(i + 1, j)
index(i + 1, j) = temp
Next
switched = True
End If
Next i
Loop
End Sub

Sub PrintKWIC(linelength)
'print the KWIC index
spaces = Space(linelength / 2)
Debug.Print "Cat. number", "|"; Space((linelength - 10) / 2); "KWIC string"
Debug.Print String(linelength + 15, "-")
For i = 1 To nkeys
atitle = title(index(i, 1))
pos = index(i, 2)
'create shifted string so that keyword is centered in the line
part2 = Mid$(atitle, pos)
part1 = Right$(spaces & Left$(atitle, pos - 1), linelength / 2)
kwicstring = Right$(part1, linelength / 2) & Left$(part2, linelength / 2)
Debug.Print catno(index(i, 1)), "|"; kwicstring
Next
End Sub

Sub KWIC()
'main program for KWIC index
ReadTitles
'set array
ReDim index(ntitle * MAXKEYS, 2)
'index(.,1) is title nr.
'index(.,2) is keyword position in title
ProcessTitles
SortTitles
PrintKWIC 80 'argument is the length of the KWIC lines (excluding catalog numbers)
End Sub
</lang>

Output (note that some titles are truncated at the start or the end. An improvement could be to wrap these titles around if there is room on the other end):
<pre>
kwic
Cat. number | KWIC string
-----------------------------------------------------------------------------------------------
987 | Excel 2003 Formulas
33 | Everything with Microsoft Office Excel 2003
13 | Microsoft Office Excel 2003 Inside Out
3435 | Mastering Excel 2003 Programming with VBA
10 | Microsoft Visio 2003 User's Guide
1244 | Excel 2003 VBA Programmer's Reference
9088 | Beginning Excel: What-if Data Analysis Tools
709 | Automated Data Analysis Using Excel
7733 | Data Analysis Using SQL and Excel
709 | Automated Data Analysis Using Excel
9088 | Beginning Excel: What-if Data Analysis T
9088 | Beginning Excel: What-if Data Analysis Tools
709 | Automated Data Analysis Using Excel
7733 | Data Analysis Using SQL and Excel
33 | How to do Everything with Microsoft Office Exce
1010 | Excel for Scientists and Engineers
33 | How to do Everything with Microsoft Office Excel 2
987 | Excel 2003 Formulas
33 | to do Everything with Microsoft Office Excel 2003
13 | Microsoft Office Excel 2003 Inside Out
3435 | Mastering Excel 2003 Programming with VBA
1244 | Excel 2003 VBA Programmer's Reference
709 | Automated Data Analysis Using Excel
7733 | Data Analysis Using SQL and Excel
1010 | Excel for Scientists and Engineers
9088 | Beginning Excel: What-if Data Analysis Tools
987 | Excel 2003 Formulas
10 | Microsoft Visio 2003 User's Guide
33 | How to do Everything with Microsoft Offi
13 | Microsoft Office Excel 2003 Inside Out
3435 | Mastering Excel 2003 Programming with VB
33 | How to do Everything with Microsoft Office Excel 2003
13 | Microsoft Office Excel 2003 Inside Out
10 | Microsoft Visio 2003 User's Guide
33 | How to do Everything with Microsoft Office Excel 2003
13 | Microsoft Office Excel 2003 Inside Out
13 | Microsoft Office Excel 2003 Inside Out
1244 | Excel 2003 VBA Programmer's Reference
3435 | Mastering Excel 2003 Programming with VBA
1244 | Excel 2003 VBA Programmer's Reference
1010 | Excel for Scientists and Engineers
7733 | Data Analysis Using SQL and Excel
9088 | Beginning Excel: What-if Data Analysis Tools
10 | Microsoft Visio 2003 User's Guide
709 | Automated Data Analysis Using Excel
7733 | Data Analysis Using SQL and Excel
3435 | Mastering Excel 2003 Programming with VBA
1244 | Excel 2003 VBA Programmer's Reference
10 | Microsoft Visio 2003 User's Guide
9088 | Beginning Excel: What-if Data Analysis Tools
</pre>
</pre>


Latest revision as of 14:33, 23 November 2011

My Favorite Languages
Language Proficiency
VBA Active
BASIC Somewhat Rusty
Fortran Stuck in Fortran 77, WATFOR, WATFIV etc.
Pascal Rusty
PHP Learning
MATLAB Learning
JavaScript Semi-Active
SQL Semi-Active
APL is way back

VBA Examples

Some nontrivial VBA Examples (to be moved).

In MS Office program (Word, Excel, Access...): open the Visual Basic window. Paste the code in a module. Execute it by typing a suitable command in the Immediate Window. Output will be directed to the Immediate Window unless stated otherwise...

Dijkstra algorithm

<lang vb> 'Dijkstra globals Const MaxGraph As Integer = 100 'max. number of nodes in graph Const Infinity = 1E+308 Dim E(1 To MaxGraph, 1 To MaxGraph) As Double 'the edge costs (Infinity if no edge) Dim A(1 To MaxGraph) As Double 'the distances calculated Dim P(1 To MaxGraph) As Integer 'the previous/path array Dim Q(1 To MaxGraph) As Boolean 'the queue

Public Sub Dijkstra(n, start) 

 'simple implementation of Dijkstra's algorithm
 'n = number of nodes in graph
 'start = index of start node
 'init distances A
   For j = 1 To n
     A(j) = Infinity
   Next j
   A(start) = 0
 'init P (path) to "no paths" and Q = set of all nodes
 For j = 1 To n
   Q(j) = True
   P(j) = 0
 Next j
 
 Do While True 'loop will exit! (see below)
 'find node u in Q with smallest distance to start
   dist = Infinity
   For i = 1 To n
     If Q(i) Then
       If A(i) < dist Then
         dist = A(i)
         u = i
       End If
     End If
   Next i
   If dist = Infinity Then Exit Do 'no more nodes available - done!
   'remove u from Q
   Q(u) = False
   'loop over neighbors of u that are in Q
   For j = 1 To n
     If Q(j) And E(u, j) <> Infinity Then
       'check if path to neighbor j via u is shorter than current estimated distance to j
       alt = A(u) + E(u, j)
       If alt < A(j) Then
         'yes, replace with new distance and remember "previous" hop on the path
         A(j) = alt
         P(j) = u
       End If
     End If
   Next j
 Loop

End Sub

Public Function GetPath(source, target) As String 

'reconstruct shortest path from source to target
'by working backwards from target using the P(revious) array
Dim path As String
If P(target) = 0 Then
  GetPath = "No path"
Else
  path = ""
  u = target
  Do While P(u) > 0
    path = Format$(u) & " " & path
    u = P(u)
  Loop
  GetPath = Format$(source) & " " & path
End If

End Function


Public Sub DijkstraTest() 'main function to solve Dijkstra's algorithm and return shortest path between 'a node and every other node in a digraph

' define problem: ' number of nodes n = 5 ' reset connection/cost per edge For i = 1 To n 

 For j = 1 To n
   E(i, j) = Infinity
 Next j
 P(i) = 0

Next i ' fill in the edge costs E(1, 2) = 10 E(1, 3) = 50 E(1, 4) = 65 E(2, 3) = 30 E(2, 5) = 4 E(3, 4) = 20 E(3, 5) = 44 E(4, 2) = 70 E(4, 5) = 23 E(5, 1) = 6

'Solve it for every node

For v = 1 To n 

 Dijkstra n, v
 'Print solution
 Debug.Print "From", "To", "Cost", "Path"
 For j = 1 To n
   If v <> j Then Debug.Print v, j, IIf(A(j) = Infinity, "---", A(j)), GetPath(v, j)
 Next j
 Debug.Print

Next v End Sub </lang>

Output (using the same graph as in the Floyd-Warshall algorithm below): 

DijkstraTest
From          To            Cost          Path
 1             2             10           1 2 
 1             3             40           1 2 3 
 1             4             60           1 2 3 4 
 1             5             14           1 2 5 

From          To            Cost          Path
 2             1             10           2 5 1 
 2             3             30           2 3 
 2             4             50           2 3 4 
 2             5             4            2 5 

From          To            Cost          Path
 3             1             49           3 4 5 1 
 3             2             59           3 4 5 1 2 
 3             4             20           3 4 
 3             5             43           3 4 5 

From          To            Cost          Path
 4             1             29           4 5 1 
 4             2             39           4 5 1 2 
 4             3             69           4 5 1 2 3 
 4             5             23           4 5 

From          To            Cost          Path
 5             1             6            5 1 
 5             2             16           5 1 2 
 5             3             46           5 1 2 3 
 5             4             66           5 1 2 3 4

Floyd-Warshall algorithm

Graph used in this and Dijkstra's algorithm

The Floyd algorithm or Floyd-Warshall algorithm finds the shortest path between all pairs of nodes in a weighted, directed graph. It is an example of dynamic programming.

Usage: fill in the number of nodes (n) and the edge distances or costs in sub Floyd or in sub FloydWithPaths. Then run "Floyd" or "FloydWithPaths".

Floyd: this sub prints the lengths or costs of the shortest paths but not the paths themselves

FloydWithPaths: this sub prints the lengths and the nodes along the paths

<lang vb> Option Compare Database

'Floyd globals Const MaxGraph As Integer = 100 'max. number of vertices in graph Const Infinity = 1E+308 Dim E(1 To MaxGraph, 1 To MaxGraph) As Double Dim A(1 To MaxGraph, 1 To MaxGraph) As Double Dim Nxt(1 To MaxGraph, 1 To MaxGraph) As Integer

Public Sub SolveFloyd(n) 

 'Floyd's algorithm: all-pairs shortest-paths cost
 'returns the cost (distance) of the least-cost (shortest) path
 'between all pairs in a labeled directed graph
 'note: this sub returns only the costs, not the paths!
 '
 'inputs:
 ' n : number of vertices (maximum value is maxGraph)
 ' E(i,j) : cost (length,...) of edge from i to j or "Infinity" if no edge between i and j
 'output:
 ' A(i,j): minimal cost for path from i to j
 'constant:
 ' Infinity : very large number

 For i = 1 To n
   For j = 1 To n
     If E(i, j) <> Infinity Then A(i, j) = E(i, j) Else A(i, j) = Infinity
   Next j
   A(i, i) = 0
 Next i
 For k = 1 To n
   For i = 1 To n
     For j = 1 To n
       If A(i, k) + A(k, j) < A(i, j) Then A(i, j) = A(i, k) + A(k, j)
     Next j
   Next i
 Next k

End Sub

Public Sub SolveFloydWithPaths(n) 

 'cf. SolveFloyd, but here we
 'use matrix "Nxt" to store information about paths
 For i = 1 To n
   For j = 1 To n
     If E(i, j) <> Infinity Then A(i, j) = E(i, j) Else A(i, j) = Infinity
   Next j
   A(i, i) = 0
 Next i
 For k = 1 To n
   For i = 1 To n
     For j = 1 To n
       If A(i, k) + A(k, j) < A(i, j) Then
         A(i, j) = A(i, k) + A(k, j)
         Nxt(i, j) = k
       End If
     Next j
   Next i
 Next k

End Sub

Public Function GetPath(i, j) As String 

'recursively reconstruct shortest path from i to j using A and Nxt
If A(i, j) = Infinity Then
  GetPath = "No path!"
Else
  tmp = Nxt(i, j)
  If tmp = 0 Then
    GetPath = " " 'there is an edge from i to j
  Else
    GetPath = GetPath(i, tmp) & Format$(tmp) & GetPath(tmp, j)
  End If
End If

End Function

Public Sub Floyd() 'main function to apply Floyd's algorithm 'see description in wp:en:Floyd-Warshall algorithm

' define problem: ' number of vertices? n = 5 ' reset connection/cost per edge matrix For i = 1 To n 

 For j = 1 To n
   E(i, j) = Infinity
 Next j

Next i ' fill in the edge costs E(1, 2) = 10 E(1, 3) = 50 E(1, 4) = 65 E(2, 3) = 30 E(2, 5) = 4 E(3, 4) = 20 E(3, 5) = 44 E(4, 2) = 70 E(4, 5) = 23 E(5, 1) = 6

'Solve it SolveFloyd n

'Print solution 'note: for large graphs the output may be too large for the Immediate panel 'in that case you could send the output to a text file Debug.Print "From", "To", "Cost" For i = 1 To n 

 For j = 1 To n
   If i <> j Then Debug.Print i, j, IIf(A(i, j) = Infinity, "No path!", A(i, j))
 Next j

Next i End Sub

Public Sub FloydWithPaths() 'main function to solve Floyd's algorithm and return shortest path between 'any two vertices

' define problem: ' number of vertices? n = 5 ' reset connection/cost per edge matrix For i = 1 To n 

 For j = 1 To n
   E(i, j) = Infinity
   Nxt(i, j) = 0
 Next j

Next i ' fill in the edge costs E(1, 2) = 10 E(1, 3) = 50 E(1, 4) = 65 E(2, 3) = 30 E(2, 5) = 4 E(3, 4) = 20 E(3, 5) = 44 E(4, 2) = 70 E(4, 5) = 23 E(5, 1) = 6

'Solve it SolveFloydWithPaths n

'Print solution 'note: for large graphs the output may be too large for the Immediate panel 'in that case you could send the output to a text file Debug.Print "From", "To", "Cost", "Via" For i = 1 To n 

 For j = 1 To n
   If i <> j Then Debug.Print i, j, IIf(A(i, j) = Infinity, "---", A(i, j)), GetPath(i, j)
 Next j

Next i End Sub 

</lang>

Output: 

Floyd
From          To            Cost
 1             2             10 
 1             3             40 
 1             4             60 
 1             5             14 
 2             1             10 
 2             3             30 
 2             4             50 
 2             5             4 
 3             1             49 
 3             2             59 
 3             4             20 
 3             5             43 
 4             1             29 
 4             2             39 
 4             3             69 
 4             5             23 
 5             1             6 
 5             2             16 
 5             3             46 
 5             4             66 

FloydWithPaths
From          To            Cost          Via
 1             2             10            
 1             3             40            2 
 1             4             60            2 3 
 1             5             14            2 
 2             1             10            5 
 2             3             30            
 2             4             50            3 
 2             5             4             
 3             1             49            4 5 
 3             2             59            4 5 1 
 3             4             20            
 3             5             43            4 
 4             1             29            5 
 4             2             39            5 1 
 4             3             69            5 1 2 
 4             5             23            
 5             1             6             
 5             2             16            1 
 5             3             46            1 2 
 5             4             66            1 2 3

KWIC index

<lang vb> 'KWIC index 'assumptions: ' - all titles and catalog numbers can be held in an array in main memory ' - disregard punctuation in titles ' - the KWIC index itself may be too large for main memory - do not store it in memory ' - the KWIC index consists of one line per title/keyword combination and consists of: ' - the catalog number ' - the title with the keyword centered in a line of given length (e.g. 80 or 120) ' (constant-width font assumed) ' note: long titles may be truncated at the beginning or the end of the line

'globals Const MAXKEYS = 20 'max. number of keywords in a title Const STOPWORDS = "a an and by for is it of on or the to with " 'that last space is needed! Dim title() As String 'list of titles to be included in KWIC index Dim catno() As Integer 'list of catalog numbers Dim ntitle As Integer 'number of titles Dim index() As Integer 'holds title number and position of keyword in title Dim nkeys As Long 'total number of keywords found

Sub ReadTitles() ' read or - in this case - set the titles and catalog numbers ntitle = 10 ReDim title(1 To ntitle) ReDim catno(1 To ntitle) 

 title(1) = "Microsoft Visio 2003 User's Guide"
 title(2) = "Microsoft Office Excel 2003 Inside Out"
 title(3) = "Mastering Excel 2003 Programming with VBA"
 title(4) = "Excel 2003 Formulas"
 title(5) = "Excel for Scientists and Engineers"
 title(6) = "Excel 2003 VBA Programmer's Reference"
 title(7) = "Automated Data Analysis Using Excel"
 title(8) = "Beginning Excel: What-if Data Analysis Tools"
 title(9) = "How to do Everything with Microsoft Office Excel 2003"
 title(10) = "Data Analysis Using SQL and Excel"
 catno(1) = 10
 catno(2) = 13
 catno(3) = 3435
 catno(4) = 987
 catno(5) = 1010
 catno(6) = 1244
 catno(7) = 709
 catno(8) = 9088
 catno(9) = 33
 catno(10) = 7733

End Sub

Function IsStopword(aword) As Boolean 'search for aword in stopword list 'add an extra space to avoid ambiguity IsStopword = InStr(STOPWORDS, LCase(aword) & " ") > 0 End Function

Sub ProcessTitles() 'find positions of keywords in titles, store in index array 'Note: we cannot use Split here because that function doesn't return 'the positions of the words it finds nkeys = 0 For i = 1 To ntitle 

 atitle = title(i) & " " 'add extra space as sentinel
 p1 = 1
 Do While p1 <= Len(atitle)
   'find next word:
   'a) find next non-space
   While Mid$(atitle, p1, 1) = " ": p1 = p1 + 1: Wend
   'b) extend word
   p2 = p1
   While Mid$(atitle, p2, 1) <> " ": p2 = p2 + 1: Wend
   aword = Mid$(atitle, p1, p2 - p1)
   'for now we assume there is no punctuation, i.e. no words
   'in parentheses, brackets or quotation marks
   If Not IsStopword(aword) Then
     'remember position of this keyword
     'we probably should check for overflow (too many keywords) here!
     nkeys = nkeys + 1
     index(nkeys, 1) = i
     index(nkeys, 2) = p1
   End If
   'continue searching
   p1 = p2 + 1
 Loop

Next i End Sub

Function Shift(aString, pos) 'return shifted string (part beginning at position "pos" followed by part before it) 

 Shift = Mid$(aString, pos) & " " & Left$(aString, pos - 1)

End Function

Sub SortTitles() 

 ' sort the index() array to represent shifted titles in alphabetical order
 ' more efficient sorting algorithms can be applied here...
 switched = True
 Do While switched
   'scan array for two shifted strings in the wrong order and swap
   '(swap the index entries, not the strings)
   'use case-insensitive compare
   switched = False
   For i = 1 To nkeys - 1
     string1 = LCase(Shift(title(index(i, 1)), index(i, 2)))
     string2 = LCase(Shift(title(index(i + 1, 1)), index(i + 1, 2)))
     If string2 < string1 Then 'swap
       For j = 1 To 2
         temp = index(i, j)
         index(i, j) = index(i + 1, j)
         index(i + 1, j) = temp
       Next
       switched = True
     End If
   Next i
 Loop

End Sub

Sub PrintKWIC(linelength) 'print the KWIC index 

 spaces = Space(linelength / 2)
 Debug.Print "Cat. number", "|"; Space((linelength - 10) / 2); "KWIC string"
 Debug.Print String(linelength + 15, "-")
 For i = 1 To nkeys
   atitle = title(index(i, 1))
   pos = index(i, 2)
   'create shifted string so that keyword is centered in the line
   part2 = Mid$(atitle, pos)
   part1 = Right$(spaces & Left$(atitle, pos - 1), linelength / 2)
   kwicstring = Right$(part1, linelength / 2) & Left$(part2, linelength / 2)
   Debug.Print catno(index(i, 1)), "|"; kwicstring
 Next

End Sub

Sub KWIC() 

 'main program for KWIC index
 ReadTitles
 'set array
 ReDim index(ntitle * MAXKEYS, 2)
 'index(.,1) is title nr.
 'index(.,2) is keyword position in title
 ProcessTitles
 SortTitles
 PrintKWIC 80 'argument is the length of the KWIC lines (excluding catalog numbers)

End Sub </lang>

Output (note that some titles are truncated at the start or the end. An improvement could be to wrap these titles around if there is room on the other end): 

kwic
Cat. number   |                                   KWIC string
-----------------------------------------------------------------------------------------------
 987          |                                  Excel 2003 Formulas
 33           | Everything with Microsoft Office Excel 2003
 13           |                 Microsoft Office Excel 2003 Inside Out
 3435         |                        Mastering Excel 2003 Programming with VBA
 10           |                        Microsoft Visio 2003 User's Guide
 1244         |                                  Excel 2003 VBA Programmer's Reference
 9088         |          Beginning Excel: What-if Data Analysis Tools
 709          |                         Automated Data Analysis Using Excel
 7733         |                                   Data Analysis Using SQL and Excel
 709          |                                        Automated Data Analysis Using Excel
 9088         |                                        Beginning Excel: What-if Data Analysis T
 9088         |               Beginning Excel: What-if Data Analysis Tools
 709          |                              Automated Data Analysis Using Excel
 7733         |                                        Data Analysis Using SQL and Excel
 33           |                                 How to do Everything with Microsoft Office Exce
 1010         |               Excel for Scientists and Engineers
 33           |                              How to do Everything with Microsoft Office Excel 2
 987          |                                        Excel 2003 Formulas
 33           | to do Everything with Microsoft Office Excel 2003
 13           |                       Microsoft Office Excel 2003 Inside Out
 3435         |                              Mastering Excel 2003 Programming with VBA
 1244         |                                        Excel 2003 VBA Programmer's Reference
 709          |          Automated Data Analysis Using Excel
 7733         |            Data Analysis Using SQL and Excel
 1010         |                                        Excel for Scientists and Engineers
 9088         |                              Beginning Excel: What-if Data Analysis Tools
 987          |                             Excel 2003 Formulas
 10           |            Microsoft Visio 2003 User's Guide
 33           |                                        How to do Everything with Microsoft Offi
 13           |            Microsoft Office Excel 2003 Inside Out
 3435         |                                        Mastering Excel 2003 Programming with VB
 33           |              How to do Everything with Microsoft Office Excel 2003
 13           |                                        Microsoft Office Excel 2003 Inside Out
 10           |                                        Microsoft Visio 2003 User's Guide
 33           |    How to do Everything with Microsoft Office Excel 2003
 13           |                              Microsoft Office Excel 2003 Inside Out
 13           |     Microsoft Office Excel 2003 Inside Out
 1244         |                         Excel 2003 VBA Programmer's Reference
 3435         |                   Mastering Excel 2003 Programming with VBA
 1244         |            Excel 2003 VBA Programmer's Reference
 1010         |                              Excel for Scientists and Engineers
 7733         |                    Data Analysis Using SQL and Excel
 9088         | Beginning Excel: What-if Data Analysis Tools
 10           |                   Microsoft Visio 2003 User's Guide
 709          |                Automated Data Analysis Using Excel
 7733         |                          Data Analysis Using SQL and Excel
 3435         |  Mastering Excel 2003 Programming with VBA
 1244         |                             Excel 2003 VBA Programmer's Reference
 10           |                              Microsoft Visio 2003 User's Guide
 9088         |                       Beginning Excel: What-if Data Analysis Tools

Hailstone sequence

<lang> Public Function Hailstone(aNumber As Long, Optional Printit As Boolean = False) As Long 'return length of Hailstone sequence for aNumber 'if optional argument Printit is true, print the sequence in the Immediate window Dim nSteps As Long Const NumbersPerLine = 10 'when printing, start a new line after this much numbers

nSteps = 1 If Printit Then Debug.Print aNumber, While aNumber <> 1 

 If aNumber Mod 2 = 0 Then aNumber = aNumber / 2 Else aNumber = 3 * aNumber + 1
 nSteps = nSteps + 1
 If Printit Then Debug.Print aNumber,
 If Printit And (nSteps Mod NumbersPerLine = 0) Then Debug.Print

Wend If Printit Then Debug.Print "(Length:"; nSteps; ")" Hailstone = nSteps End Function

Public Sub HailstoneTest() Dim theNumber As Long Dim theSequenceLength As Long Dim SeqLength As Long Dim i as Long

'find and print the Hailstone sequence for 27 (note: the whole sequence, not just the first four and last four items!) Debug.Print "Hailstone sequence for 27:" theNumber = Hailstone(27, True)

'find the longest Hailstone sequence for numbers less than 100000. theSequenceLength = 0 For i = 2 To 99999 

 SeqLength = Hailstone(i)
 If SeqLength > theSequenceLength Then
   theNumber = i
   theSequenceLength = SeqLength
 End If

Next i Debug.Print theNumber; "has the longest sequence ("; theSequenceLength; ")." End Sub </lang>

Output: 

HailstoneTest
Hailstone sequence for 27:
 27            82            41            124           62            31            94            47            142           71           
 214           107           322           161           484           242           121           364           182           91           
 274           137           412           206           103           310           155           466           233           700          
 350           175           526           263           790           395           1186          593           1780          890          
 445           1336          668           334           167           502           251           754           377           1132         
 566           283           850           425           1276          638           319           958           479           1438         
 719           2158          1079          3238          1619          4858          2429          7288          3644          1822         
 911           2734          1367          4102          2051          6154          3077          9232          4616          2308         
 1154          577           1732          866           433           1300          650           325           976           488          
 244           122           61            184           92            46            23            70            35            106          
 53            160           80            40            20            10            5             16            8             4            
 2             1            (Length: 112 )
 77031 has the longest sequence ( 351 ).
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