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I would like to split a rectangle in cells. In each cell it should be create a random coordinate (y, z).
The wide and height of the rectangle are known (initialW / initalH).
The size of the cells are calculated (dy / dz).
The numbers, in how many cells the rectangle to be part, are known. (numberCellsY / numberCellsZ)
Here my Code in Fortran to split the rectangle in Cells:
yRVEMin = 0.0
yRVEMax = initialW
dy = ( yRVEMax - yRVEMin ) / numberCellsY
zRVEMin = 0.0
zRVEMax = initialH
dz = ( zRVEMax - zRVEMin ) / numberCellsZ
do i = 1, numberCellsY
yMin(i) = (i-1)*dy
yMax(i) = i*dy
end do
do j = 1, numberCellsZ
zMin(j) = (j-1)*dz
zMax(j) = j*dz
end do
Now I would like to produce a random coordinate in each cell. The problem for me is, to store the coodinates in an array. It does not necessarily all be stored in one array, but as least as possible.
To fill the cells with coordinates it should start at the bottom left cell, go through the rows (y-direction), and after the last cell (numberCellsY) jump a column higher (z-dicrection) and start again by the first cell of the new row at left side. That should be made so long until a prescribed number (nfibers) is reached.
Here a deplorable try to do it:
call random_seed
l = 0
do k = 1 , nfibers
if (l < numberCellsY) then
l = l + 1
else
l = 1
end if
call random_number(y)
fiberCoordY(k) = yMin(l) + y * (yMax(l) - yMin(l))
end do
n = 0
do m = 1 , nfibers
if (n < numberCellsZ) then
n = n + 1
else
n = 1
end if
call random_number(z)
fiberCoordZ(m) = zMin(n) + z * (zMax(n) - zMin(n))
end do
The output is not what I want! fiberCoordZ should be stay on (zMin(1) / zMax(1) as long as numberCellsY-steps are reached.
The output for following settings:
nfibers = 9
numberCellsY = 3
numberCellsZ = 3
initialW = 9.0
initialH = 9.0
My random output for fiberCoordY is:
1.768946 3.362770 8.667685 1.898700 5.796713 8.770239 2.463412 3.546694 7.074708
and for fiberCoordZ is:
2.234807 5.213032 6.762228 2.948657 5.937295 8.649946 0.6795220 4.340364 8.352566
In this case the first 3 numbers of fiberCoordz should have a value between 0.0 and 3.0. Than number 4 - 6 a value between 3.0 and 6.0. And number 7 - 9 a value bewtween 6.0 - 9.0.
How can I solve this? If somebody has a solution with a better approach, please post it!
Thanks
Looking at
n = 0
do m = 1 , nfibers
if (n < numberCellsZ) then
n = n + 1
else
n = 1
end if
call random_number(z)
fiberCoordZ(m) = zMin(n) + z * (zMax(n) - zMin(n))
end do
we see that the z coordinate offset (the bottom cell boundary of interest) is being incremented inappropriately: for each consecutive nfibers/numberCellsZ coordinates n should be constant.
n should be incremented only every numberCellsY iterations, so perhaps a condition like
if (MOD(m, numberCellsY).eq.1) n=n+1
would be better.
Thanks francescalus! It works fine.
I added a little more for the case that nfibers > numberCellsY*numberCellsZ
n=0
do m = 1 , nfibers
if (MOD(m, numberCellsY).eq.1 .and. (n < numberCellsY)) then
n=n+1
end if
if (MOD(m, numberCellsY*numberCellsZ).eq.1 ) then
n = 1
end if
call random_number(z)
fiberCoordZ(m) = zMin(n) + z * (zMax(n) - zMin(n))
end do
I have a input stream where the input element consist of Date, Depth and Area.
I want to plot the Area against the Depth and want therefor to take out a window of Depth e.g. between 1.0-100.0m.
The problem is that I want to down sample the input stream since there can be many inputs with close Depth values.
I want to partition the input into x bins, e.g. 2 bins means all depth values between 1-50 is averaged in the first bin and 51-100 in the second bin.
I was thinking something like this:
var q = from e in input
where (e.Depth > 1) && (e.Depth <= 100)
// here I need some way of partition the sequence into bins
// and averaging the elements.
Split a collection into `n` parts with LINQ? wants to do something similar without rx.
Modified answer as per your comment. steps = number of buckets.
var min = 1, max = 100;
var steps = 10;
var f = (max - min + 1) / steps; // The extra 1 is really an epsilon. #hack
var q = from e in input
where e.Depth > 1 && e.depth <= 100
let x = e.Depth - min
group e by x < max ? (x - (x % f)) : ;
This is the function we're grouping by for the given e.Depth.
This probably won't work so great with floating point values (due to precision), unless you floor/ceil the selection, but then you might run out of integers, so you may need to scale a bit... something like group e by Math.Floor((x - (x % f)) * scaleFactor).
This should do what you want
static int GetBucket(double value, double min, double max, int bucketCount)
{
return (int)((value - min) / (max - min) * bucketCount + 0.5);
}
var grouped = input.GroupBy(e => GetBucket(e.Depth, 1, 100, 50));
Problem: We have x checkboxes and we want to check y of them evenly.
Example 1: select 50 checkboxes of 100 total.
[-]
[x]
[-]
[x]
...
Example 2: select 33 checkboxes of 100 total.
[-]
[-]
[x]
[-]
[-]
[x]
...
Example 3: select 66 checkboxes of 100 total:
[-]
[x]
[x]
[-]
[x]
[x]
...
But we're having trouble to come up with a formula to check them in code, especially once you go 11/111 or something similar. Anyone has an idea?
Let's first assume y is divisible by x. Then we denote p = y/x and the solution is simple. Go through the list, every p elements, mark 1 of them.
Now, let's say r = y%x is non zero. Still p = y/x where / is integer devision. So, you need to:
In the first p-r elements, mark 1 elements
In the last r elements, mark 2 elements
Note: This depends on how you define evenly distributed. You might want to spread the r sections withx+1 elements in between p-r sections with x elements, which indeed is again the same problem and could be solved recursively.
Alright so it wasn't actually correct. I think this would do though:
Regardless of divisibility:
if y > 2*x, then mark 1 element every p = y/x elements, x times.
if y < 2*x, then mark all, and do the previous step unmarking y-x out of y checkboxes (so like in the previous case, but x is replaced by y-x)
Note: This depends on how you define evenly distributed. You might want to change between p and p+1 elements for example to distribute them better.
Here's a straightforward solution using integer arithmetic:
void check(char boxes[], int total_count, int check_count)
{
int i;
for (i = 0; i < total_count; i++)
boxes[i] = '-';
for (i = 0; i < check_count; i++)
boxes[i * total_count / check_count] = 'x';
}
total_count is the total number of boxes, and check_count is the number of boxes to check.
First, it sets every box to unchecked. Then, it checks check_count boxes, scaling the counter to the number of boxes.
Caveat: this is left-biased rather than right-biased like in your examples. That is, it prints x--x-- rather than --x--x. You can turn it around by replacing
boxes[i * total_count / check_count] = 'x';
with:
boxes[total_count - (i * total_count / check_count) - 1] = 'x';
Correctness
Assuming 0 <= check_count <= total_count, and that boxes has space for at least total_count items, we can prove that:
No check marks will overlap. i * total_count / check_count increments by at least one on every iteration, because total_count >= check_count.
This will not overflow the buffer. The subscript i * total_count / check_count
Will be >= 0. i, total_count, and check_count will all be >= 0.
Will be < total_count. When n > 0 and d > 0:
(n * d - 1) / d < n
In other words, if we take n * d / d, and nudge the numerator down, the quotient will go down, too.
Therefore, (check_count - 1) * total_count / check_count will be less than total_count, with the assumptions made above. A division by zero won't happen because if check_count is 0, the loop in question will have zero iterations.
Say number of checkboxes is C and the number of Xes is N.
You example states that having C=111 and N=11 is your most troublesome case.
Try this: divide C/N. Call it D. Have index in the array as double number I. Have another variable as counter, M.
double D = (double)C / (double)N;
double I = 0.0;
int M = N;
while (M > 0) {
if (checkboxes[Round(I)].Checked) { // if we selected it, skip to next
I += 1.0;
continue;
}
checkboxes[Round(I)].Checked = true;
M --;
I += D;
if (Round(I) >= C) { // wrap around the end
I -= C;
}
}
Please note that Round(x) should return nearest integer value for x.
This one could work for you.
I think the key is to keep count of how many boxes you expect to have per check.
Say you want 33 checks in 100 boxes. 100 / 33 = 3.030303..., so you expect to have one check every 3.030303... boxes. That means every 3.030303... boxes, you need to add a check. 66 checks in 100 boxes would mean one check every 1.51515... boxes, 11 checks in 111 boxes would mean one check every 10.090909... boxes, and so on.
double count = 0;
for (int i = 0; i < boxes; i++) {
count += 1;
if (count >= boxes/checks) {
checkboxes[i] = true;
count -= count.truncate(); // so 1.6 becomes 0.6 - resetting the count but keeping the decimal part to keep track of "partial boxes" so far
}
}
You might rather use decimal as opposed to double for count, or there's a slight chance the last box will get skipped due to rounding errors.
Bresenham-like algorithm is suitable to distribute checkboxes evenly. Output of 'x' corresponds to Y-coordinate change. It is possible to choose initial err as random value in range [0..places) to avoid biasing.
def Distribute(places, stars):
err = places // 2
res = ''
for i in range(0, places):
err = err - stars
if err < 0 :
res = res + 'x'
err = err + places
else:
res = res + '-'
print(res)
Distribute(24,17)
Distribute(24,12)
Distribute(24,5)
output:
x-xxx-xx-xx-xxx-xx-xxx-x
-x-x-x-x-x-x-x-x-x-x-x-x
--x----x----x---x----x--
Quick html/javascript solution:
<html>
<body>
<div id='container'></div>
<script>
var cbCount = 111;
var cbCheckCount = 11;
var cbRatio = cbCount / cbCheckCount;
var buildCheckCount = 0;
var c = document.getElementById('container');
for (var i=1; i <= cbCount; i++) {
// make a checkbox
var cb = document.createElement('input');
cb.type = 'checkbox';
test = i / cbRatio - buildCheckCount;
if (test >= 1) {
// check the checkbox we just made
cb.checked = 'checked';
buildCheckCount++;
}
c.appendChild(cb);
c.appendChild(document.createElement('br'));
}
</script>
</body></html>
Adapt code from one question's answer or another answer from earlier this month. Set N = x = number of checkboxes and M = y = number to be checked and apply formula (N*i+N)/M - (N*i)/M for section sizes. (Also see Joey Adams' answer.)
In python, the adapted code is:
N=100; M=33; p=0;
for i in range(M):
k = (N+N*i)/M
for j in range(p,k-1): print "-",
print "x",
p=k
which produces
- - x - - x - - x - - x - - [...] x - - x - - - x where [...] represents 25 --x repetitions.
With M=66 the code gives
x - x x - x x - x x - x x - [...] x x - x x - x - x where [...] represents mostly xx- repetitions, with one x- in the middle.
Note, in C or java: Substitute for (i=0; i<M; ++i) in place of for i in range(M):. Substitute for (j=p; j<k-1; ++j) in place of for j in range(p,k-1):.
Correctness: Note that M = x boxes get checked because print "x", is executed M times.
What about using Fisher–Yates shuffle ?
Make array, shuffle and pick first n elements. You do not need to shuffle all of them, just first n of array. Shuffling can be find in most language libraries.
I'm working on a custom data pager for a custom google maps control. The control needs to work out what range of pages to display. For example, if the user is on page 6 then the control must display pages 1 through to 10. If the user is on page 37, then the control must display pages 30 throught to 40.
The variables I have available are:
X - Total results (points on the map)
Y - The current page size. i.e. the amount of points per page.
Z - The current page being displayed
Q - The number of page numbers to display (a const of 10)
I have come up with:
Starting Index = Z - (Z % Q)
Ending Index = Z - (Z % Q) + Q
This, however, doesn't work for when the current page is less than 10. It also doesn't figure out whether there is a max page reached, i.e. we always display a full range of 10. However, if we display the range 30-40 the final page could actually be 38.
If anyone can come up with a more elegant algorithm it would be appreciated.
It might be easier if you think in terms of chapters.
Say each set of pages is a chapter, chapter are numbered starting from 0, 1, 2,...
Then the rth chapter has pages in the range
Qr + 1 <= page <= Q(r+1)
Now consider floor(page/Q). This is r if page is not a multiple of Q, otherwise it is r+1.
Given an r, you can find out the pages of the chapter as Lower = Qr + 1 and higher = min(max, Q(r+1)).
So you can do this.
if (Z < 1 || Z > max_page) { error;}
if (Z % Q == 0) {
r = Z/Q - 1; // integer division, gives floor.
}
else {
r = Z/Q; // floor.
}
Begin = Q*r + 1;
End = Min (Q*(r+1), max_page);
To get rid of the if, you can now replace it with
if (Z < 1 || Z > max_page) { error;}
r = (Z-1)/Q;
Begin = Q*r + 1;
End = Min (Q*(r+1), max_page);
This works because:
Qr + 1 <= Z <= Q(r+1) if and only if
Qr <= Z-1 <= Qr + (Q-1).
Thus floor((Z-1)/Q) = r.
Here we go:
def lower(Z):
return (Z - 1) // Q * Q + 1
def upper(Z):
return min(int(ceil(X / Y)), ((Z - 1) // Q + 1) * Q)
// is integer division.
This question already has answers here:
How to convert a column number (e.g. 127) into an Excel column (e.g. AA)
(60 answers)
Closed 9 years ago.
How would you determine the column name (e.g. "AQ" or "BH") of the nth column in Excel?
Edit: A language-agnostic algorithm to determine this is the main goal here.
I once wrote this function to perform that exact task:
public static string Column(int column)
{
column--;
if (column >= 0 && column < 26)
return ((char)('A' + column)).ToString();
else if (column > 25)
return Column(column / 26) + Column(column % 26 + 1);
else
throw new Exception("Invalid Column #" + (column + 1).ToString());
}
Here is the cleanest correct solution I could come up with (in Java, but feel free to use your favorite language):
String getNthColumnName(int n) {
String name = "";
while (n > 0) {
n--;
name = (char)('A' + n%26) + name;
n /= 26;
}
return name;
}
But please do let me know of if you find a mistake in this code, thank you.
A language agnostic algorithm would be as follows:
function getNthColumnName(int n) {
let curPower = 1
while curPower < n {
set curPower = curPower * 26
}
let result = ""
while n > 0 {
let temp = n / curPower
let result = result + char(temp)
set n = n - (curPower * temp)
set curPower = curPower / 26
}
return result
This algorithm also takes into account if Excel gets upgraded again to handle more than 16k columns. If you really wanted to go overboard, you could pass in an additional value and replace the instances of 26 with another number to accomodate alternate alphabets
Thanks, Joseph Sturtevant! Your code works perfectly - I needed it in vbscript, so figured I'd share my version:
Function ColumnLetter(ByVal intColumnNumber)
Dim sResult
intColumnNumber = intColumnNumber - 1
If (intColumnNumber >= 0 And intColumnNumber < 26) Then
sResult = Chr(65 + intColumnNumber)
ElseIf (intColumnNumber >= 26) Then
sResult = ColumnLetter(CLng(intColumnNumber \ 26)) _
& ColumnLetter(CLng(intColumnNumber Mod 26 + 1))
Else
err.Raise 8, "Column()", "Invalid Column #" & CStr(intColumnNumber + 1)
End If
ColumnLetter = sResult
End Function
Joseph's code is good but, if you don't want or need to use a VBA function, try this.
Assuming that the value of n is in cell A2
Use this function:
=MID(ADDRESS(1,A2),2,LEN(ADDRESS(1,A2))-3)
IF(COLUMN()>=26,CHAR(ROUND(COLUMN()/26,1)+64)&CHAR(MOD(COLUMN(),26)+64),CHAR(COLUMN()+64))
This works 2 letter columns (up until column ZZ). You'd have to nest another if statement for 3 letter columns.
The formula above fails on columns AY, AZ and each of the following nY and nZ columns. The corrected formula is:
=IF(COLUMN()>26,CHAR(ROUNDDOWN((COLUMN()-1)/26,0)+64)&CHAR(MOD((COLUMN()-1),26)+65),CHAR(COLUMN()+64)
Ruby one-liner:
def column_name_for(some_int)
some_int.to_s(26).split('').map {|c| (c.to_i(26) + 64).chr }.join # 703 => "AAA"
end
It converts the integer to base26 then splits it and does some math to convert each character from ascii. Finally joins 'em all back together. No division, modulus, or recursion.
Fun.
FROM wcm:
If you don't want to use VBA, you can use this
replace colnr with the number you want
=MID(ADDRESS(1,colnr),2,LEN(ADDRESS(1,colnr))-3)
Please be aware of the fact that this formula is volatile because of the usage of the ADDRESS function. Volatile functions are functions that are recalculated by excel after EVERY change.
Normally excel recalculates formula's only when their dependent references changes.
It could be a performance killer, to use this formula.
And here is a conversion from the VBScript version to SQL Server 2000+.
CREATE FUNCTION [dbo].[GetExcelColRef]
(
#col_seq_no int
)
RETURNS varchar(5)
AS
BEGIN
declare #Result varchar(5)
set #Result = ''
set #col_seq_no = #col_seq_no - 1
If (#col_seq_no >= 0 And #col_seq_no < 26)
BEGIN
set #Result = char(65 + #col_seq_no)
END
ELSE
BEGIN
set #Result = [dbo].[GetExcelColRef] (#col_seq_no / 26) + '' + [dbo].[GetExcelColRef] ((#col_seq_no % 26) + 1)
END
Return #Result
END
GO
This works fine in MS Excel 2003-2010. Should work for previous versions supporting the Cells(...).Address function:
For the 28th column - taking columnNumber=28; Cells(1, columnNumber).Address returns "$AB$1".
Doing a split on the $ sign returns the array: ["","AB","1"]
So Split(Cells(1, columnNumber).Address, "$")(1) gives you the column name "AB".
UPDATE:
Taken from How to convert Excel column numbers into alphabetical characters
' The following VBA function is just one way to convert column number
' values into their equivalent alphabetical characters:
Function ConvertToLetter(iCol As Integer) As String
Dim iAlpha As Integer
Dim iRemainder As Integer
iAlpha = Int(iCol / 27)
iRemainder = iCol - (iAlpha * 26)
If iAlpha > 0 Then
ConvertToLetter = Chr(iAlpha + 64)
End If
If iRemainder > 0 Then
ConvertToLetter = ConvertToLetter & Chr(iRemainder + 64)
End If
End Function
APPLIES TO: Microsoft Office Excel 2007 SE / 2002 SE / 2000 SE / 97 SE
I suppose you need VBA code:
Public Function GetColumnAddress(nCol As Integer) As String
Dim r As Range
Set r = Range("A1").Columns(nCol)
GetColumnAddress = r.Address
End Function
This does what you want in VBA
Function GetNthExcelColName(n As Integer) As String
Dim s As String
s = Cells(1, n).Address
GetNthExcelColName = Mid(s, 2, InStr(2, s, "$") - 2)
End Function
This seems to work in vb.net
Public Function Column(ByVal pColumn As Integer) As String
pColumn -= 1
If pColumn >= 0 AndAlso pColumn < 26 Then
Return ChrW(Asc("A"c) + pColumn).ToString
ElseIf (pColumn > 25) Then
Return Column(CInt(math.Floor(pColumn / 26))) + Column((pColumn Mod 26) + 1)
Else
stop
Throw New ArgumentException("Invalid column #" + (pColumn + 1).ToString)
End If
End Function
I took Joseph's and tested it to BH, then fed it 980-1000 and it looked good.
In VBA, assuming lCol is the column number:
function ColNum2Letter(lCol as long) as string
ColNum2Letter = Split(Cells(1, lCol).Address, "$")(0)
end function
All these code samples that these good people have posted look fine.
There is one thing to be aware of. Starting with Office 2007, Excel actually has up to 16,384 columns. That translates to XFD (the old max of 256 colums was IV). You will have to modify these methods somewhat to make them work for three characters.
Shouldn't be that hard...
Here's Gary Waters solution
Function ConvertNumberToColumnLetter2(ByVal colNum As Long) As String
Dim i As Long, x As Long
For i = 6 To 0 Step -1
x = (1 - 26 ^ (i + 1)) / (-25) - 1 ‘ Geometric Series formula
If colNum > x Then
ConvertNumberToColumnLetter2 = ConvertNumberToColumnLetter2 & Chr(((colNum - x - 1)\ 26 ^ i) Mod 26 + 65)
End If
Next i
End Function
via http://www.dailydoseofexcel.com/archives/2004/05/21/column-numbers-to-letters/
Considering the comment of wcm (top value = xfd), you can calculate it like this;
function IntToExcel(n: Integer); string;
begin
Result := '';
for i := 2 down to 0 do
begin
if ((n div 26^i)) > 0) or (i = 0) then
Result := Result + Char(Ord('A')+(n div (26^i)) - IIF(i>0;1;0));
n := n mod (26^i);
end;
end;
There are 26 characters in the alphabet and we have a number system just like hex or binary, just with an unusual character set (A..Z), representing positionally the powers of 26: (26^2)(26^1)(26^0).
FYI T-SQL to give the Excel column name given an ordinal (zero-based), as a single statement.
Anything below 0 or above 16,383 (max columns in Excel2010) returns NULL.
; WITH TestData AS ( -- Major change points
SELECT -1 AS FieldOrdinal
UNION ALL
SELECT 0
UNION ALL
SELECT 25
UNION ALL
SELECT 26
UNION ALL
SELECT 701
UNION ALL
SELECT 702
UNION ALL
SELECT 703
UNION ALL
SELECT 16383
UNION ALL
SELECT 16384
)
SELECT
FieldOrdinal
, CASE
WHEN FieldOrdinal < 0 THEN NULL
WHEN FieldOrdinal < 26 THEN ''
WHEN FieldOrdinal < 702 THEN CHAR (65 + FieldOrdinal / 26 - 1)
WHEN FieldOrdinal < 16384 THEN CHAR (65 + FieldOrdinal / 676 - 1)
+ CHAR (65 + (FieldOrdinal / 26) - (FieldOrdinal / 676) * 26 - 1)
ELSE NULL
END
+ CHAR (65 + FieldOrdinal % 26)
FROM TestData
ORDER BY FieldOrdinal
I currently use this, but I have a feeling that it can be optimized.
private String GetNthExcelColName(int n)
{
String firstLetter = "";
//if number is under 26, it has a single letter name
// otherwise, it is 'A' for 27-52, 'B' for 53-78, etc
if(n > 26)
{
//the Converts to double and back to int are just so Floor() can be used
Double value = Convert.ToDouble((n-1) / 26);
int firstLetterVal = Convert.ToInt32(Math.Floor(value))-1;
firstLetter = Convert.ToChar(firstLetterValue + 65).ToString();
}
//second letter repeats
int secondLetterValue = (n-1) % 26;
String secondLetter = Convert.ToChar(secondLetterValue+65).ToString();
return firstLetter + secondLetter;
}
=CHAR(64+COLUMN())