I have the following code in VBA:
For n = 1 To 15
Cells(n, 8) = Application.Combin(2 * n, n)
next n
I want the n in the cells(n,8) to have an incerement 2, so the code skips a line after each entry.
Is it possible to have an other increment variable in this same loop that jumps 2 at once?
Thanks in advance!
EDIT: after reading the comment: I think what is needed is a counter to count, 1,2,3,4,5,6...15, and another one to count 1,3,5,7...15
For that, here is what is need to be done:
basically, you want the first iterator to be a normal counter,
and the second iterator to be odd numbers only.
So here is a simply input output table
input output
----- -----
1 1
2 3
3 5
4 7
5 9
6 11
From the above, we can deduce the formula needed to convert the input into the desired output: output = (input x 2) -1
And so, we can re-write our for loop to be like so:
For n=1 to 15
Cells(n,8) = Application.Combin(2*n-1,n)
Next
============= End of Edit =========================
Simply, use the keyword STEP in the for loop
For n = 1 To 15 STEP 2 'STEP can also be negative
'but you have to reverse the starting, and endin
'value of the iterator
The values for n will be: 1, 3, 5, 7, 9, 11 , 13, 15
Alternatively, use a local variable inside the for loop for that purpose (in-case you want the loop to execute 15 times)
For n=1 to 15
i = n + 1
Cells(i,8) = Application.Combine(2*n,n)
Next
Related
The following SQL query is supposed to return the max consecutive numbers in a set.
WITH RECURSIVE Mystery(X,Y) AS (SELECT A AS X, A AS Y FROM R)
UNION (SELECT m1.X, m2.Y
FROM Mystery m1, Mystery m2
WHERE m2.X = m1.Y + 1)
SELECT MAX(Y-X) + 1 FROM Mystery;
This query on the set {7, 9, 10, 14, 15, 16, 18} returns 3, because {14 15 16} is the longest chain of consecutive numbers and there are three numbers in that chain. But when I try to work through this manually I don't see how it arrives at that result.
For example, given the number set above I could create two columns:
m1.x
m2.y
7
7
9
9
10
10
14
14
15
15
16
16
18
18
If we are working on rows and columns, not the actual data, as I understand it WHERE m2.X = m1.Y + 1 takes the value from the next row in Y and puts it in the current row of X, like so
m1.X
m2.Y
9
7
10
9
14
10
15
14
16
15
18
16
18
Null?
The main part on which I am uncertain is where in the SQL recursion actually happens. According to Denis Lukichev recursion is the R part - or in this case the RECURSIVE Mystery(X,Y) - and stops when the table is empty. But if the above is true, how would the table ever empty?
Since I don't know how to proceed with the above, let me try a different direction. If WHERE m2.X = m1.Y + 1 is actually a comparison, the result should be:
m1.X
m2.Y
14
14
15
15
16
16
But at this point, it seems that it should continue recursively on this until only two rows are left (nothing else to compare). If it stops here to get the correct count of 3 rows (2 + 1), what is actually stopping the recursion?
I understand that for the above example the MAX(Y-X) + 1 effectively returns the actual number of recursion steps and adds 1.
But if I have 7 consecutive numbers and the recursion flows down to 2 rows, should this not end up with an incorrect 3 as the result? I understand recursion in C++ and other languages, but this is confusing to me.
Full disclosure, yes it appears this is a common university question, but I am retired, discovered this while researching recursion for my use, and need to understand how it works to use similar recursion in my projects.
Based on this db<>fiddle shared previously, you may find it instructive to alter the CTE to include an iteration number as follows, and then to show the content of the CTE rather than the output of final SELECT. Here's an amended CTE and its content after the recursion is complete:
Amended CTE
WITH RECURSIVE Mystery(X,Y) AS ((SELECT A AS X, A AS Y, 1 as Z FROM R)
UNION (SELECT m1.X, m2.A, Z+1
FROM Mystery m1
JOIN R m2 ON m2.A = m1.Y + 1))
CTE Content
x
y
z
7
7
1
9
9
1
10
10
1
14
14
1
15
15
1
16
16
1
18
18
1
9
10
2
14
15
2
15
16
2
14
16
3
The Z field holds the iteration count. Where Z = 1 we've simply got the rows from the table R. The, values X and Y are both from the field A. In terms of what we are attempting to achieve these represent sequences consecutive numbers, which start at X and continue to (at least) Y.
Where Z = 2, the second iteration, we find all the rows first iteration where there is a value in R which is one higher than our Y value, or one higher than the last member of our sequence of consecutive numbers. That becomes the new highest number, and we add one to the number of iterations. As only three numbers in our original data set have successors within the set, there are only three rows output in the second iteration.
Where Z = 3, the third iteration, we find all the rows of the second iteration (note we are not considering all the rows of the first iteration again), where there is, again, a value in R which is one higher than our Y value, or one higher than the last member of our sequence of consecutive numbers. That, again, becomes the new highest number, and we add one to the number of iterations.
The process will attempt a fourth iteration, but as there are no rows in R where the value is one more than the Y values from our third iteration, no extra data gets added to the CTE and recursion ends.
Going back to the original db<>fiddle, the process then searches our CTE content to output MAX(Y-X) + 1, which is the maximum difference between the first and last values in any consecutive sequence, plus one. This finds it's value from the record produced in the third iteration, using ((16-14) + 1) which has a value of 3.
For this specific piece of code, the output is always equivalent to the value in the Z field as every addition of a row through the recursion adds one to Z and adds one to Y.
I'd like to find the contiguous sequences of equal elements (e.g. of length 2) in a list
my #s = <1 1 0 2 0 2 1 2 2 2 4 4 3 3>;
say grep {$^a eq $^b}, #s;
# ==> ((1 1) (2 2) (4 4) (3 3))
This code looks ok but when one more 2 is added after the sequence of 2 2 2 or when one 2 is removed from it, it says Too few positionals passed; expected 2 arguments but got 1 How to fix it? Please note that I'm trying to find them without using for loop, i.e. I'm trying to find them using a functional code as much as possible.
Optional: In the bold printed section:
<1 1 0 2 0 2 1 2 2 2 4 4 3 3>
multiple sequences of 2 2 are seen. How to print them the number of times they are seen? Like:
((1 1) (2 2) (2 2) (4 4) (3 3))
There are an even number of elements in your input:
say elems <1 1 0 2 0 2 1 2 2 2 4 4 3 3>; # 14
Your grep block consumes two elements each time:
{$^a eq $^b}
So if you add or remove an element you'll get the error you're getting when the block is run on the single element left over at the end.
There are many ways to solve your problem.
But you also asked about the option of allowing for overlapping so, for example, you get two (2 2) sub-lists when the sequence 2 2 2 is encountered. And, in a similar vein, you presumably want to see two matches, not zero, with input like:
<1 2 2 3 3 4>
So I'll focus on solutions that deal with those issues too.
Despite the narrowing of solution space to deal with the extra issues, there are still many ways to express solutions functionally.
One way that just appends a bit more code to the end of yours:
my #s = <1 1 0 2 0 2 1 2 2 2 4 4 3 3>;
say grep {$^a eq $^b}, #s .rotor( 2 => -1 ) .flat
The .rotor method converts a list into a list of sub-lists, each of the same length. For example, say <1 2 3 4> .rotor: 2 displays ((1 2) (3 4)). If the length argument is a pair, then the key is the length and the value is an offset for starting the next pair. If the offset is negative you get sub-list overlap. Thus say <1 2 3 4> .rotor: 2 => -1 displays ((1 2) (2 3) (3 4)).
The .flat method "flattens" its invocant. For example, say ((1,2),(2,3),(3,4)) .flat displays (1 2 2 3 3 4).
A perhaps more readable way to write the above solution would be to omit the flat and use .[0] and .[1] to index into the sub-lists returned by rotor:
say #s .rotor( 2 => -1 ) .grep: { .[0] eq .[1] }
See also Elizabeth Mattijsen's comment for another variation that generalizes for any sub-list size.
If you needed a more general coding pattern you might write something like:
say #s .pairs .map: { .value xx 2 if .key < #s - 1 and [eq] #s[.key,.key+1] }
The .pairs method on a list returns a list of pairs, each pair corresponding to each of the elements in its invocant list. The .key of each pair is the index of the element in the invocant list; the .value is the value of the element.
.value xx 2 could have been written .value, .value. (See xx.)
#s - 1 is the number of elements in #s minus 1.
The [eq] in [eq] list is a reduction.
If you need text pattern matching to decide what constitutes contiguous equal elements you might convert the input list into a string, match against that using one of the match adverbs that generate a list of matches, then map from the resulting list of matches to your desired result. To match with overlaps (eg 2 2 2 results in ((2 2) (2 2)) use :ov:
say #s .Str .match( / (.) ' ' $0 /, :ov ) .map: { .[0].Str xx 2 }
TIMTOWDI!
Here's an iterative approach using gather/take.
say gather for <1 1 0 2 0 2 1 2 2 2 4 4 3 3> {
state $last = '';
take ($last, $_) if $last == $_;
$last = $_;
};
# ((1 1) (2 2) (2 2) (4 4) (3 3))
I would like to change the outcome of a SQL statement formula to 1, 2, 3, 4 or 5 (these are working days).
Example 1: when I have day 1, minus 2 days the outcome should be 4.
Example 2: when I have day 4, plus 2 days the outcome should be 1.
Example 3: when I have day 5, minus 20 days, the outcome should be 5
At the moment I'm using a table as shown below (I have the input and days-back and the output is what i want to see):
Input, days-back, output:
1 0 1
Input, days-back, output:
1 1 5
Input, days-back, output:
1 2 4
Input, days-back, output:
2 4 3
P.s. I do not have a date, only day numbers.
I hope you understand what I'm looking for :)
If you want to have "days-back" greater than 5 you need to use the following formula:
((Input + ((5*days-back)-1) - days-back) % 5) + 1
How this works - If you look at the prior formula you can see I'm adding 5 to input to make sure we are always positive before I subtract one and the days back. I then mod by 5 and add the one back in so that we go from 1 to 5 instead of 0 to 4
Since I don't know how large days-back is going to be I need something larger but I also need to have it not effect the mod 5 calculation so I just multiply it by 5. I then subtract one (so I can add it later and offset 0 to 4 to 1 to 5) and we are done.
prior answer below
I note I missed the 5 case -- here is the formula that works for that:
((Input + 4 - days-back) % 5) + 1
original answer
You need to use use modulus math. The formula you want is
(Input + 5 - days-back) % 5
Where % means modulus. In SQL Server you can use % in Oracle it is MOD, etc -- it depends on the platform.
For those that care here is my DB2 test code:
WITH TEST_TABLE(input, days_back) AS
(
VALUES
(1,0),
(1,1),
(1,2),
(2,4)
)
SELECT TEST_TABLE.*
MOD(INPUT+4-DAYS_BACK,5)+1
FROM TEST_TABLE
I have been trying to find a way to move data labels either above or below points.
Starting at point 1, for every two consecutive points, I'd like to move the data labels above the point, and for the next 2, I'd like to move them below. I'm not sure how to change my for loop or if statement to accommodate this condition. So in the end, the data labels for points 1 and 2 would be positioned above, the data labels for points 3 and 4 would be positioned below, 5 and 6 above...etc
If anyone can help, I'd greatly appreciate it.
Dim FlowIndex As Long
With ActiveChart.SeriesCollection(1)
For FlowIndex = 1 To .Points.Count
With .Points(FlowIndex)
If .HasDataLabel Then
With .DataLabel
.Position = xlLabelPositionAbove
.Orientation = xlHorizontal
End With
End If
End With
Next
End With
This is a mathematical question of how to perform your loop. Think of the values 1,2,3,4,5,6,7,8. What mathematical rule would put 1,2,5,6 in the same group, and 3,4,7,8 in another group?
Possible answer: when divided by 4, 1 & 2 round down to 0. 3 & 4 round up to 1. 7&8 round up to 3. So, one group rounds up to an even number, and one group rounds down to an odd number. There are many ways to reflect this principle, but here is one:
IF FlowIndex MOD 4 = 1 OR FlowIndex MOD 4 = 2 then 'There is a remainder of 1 or 2 when divided by 4 - put label above
'Do stuff
Else 'There is a remainder of 3 or 0 when divided by 4 - put label below
'Do other stuff
End If
To clarify on my answer to the last question you had, MOD is a method of dividing which returns the remainder after doing whole number division. So 5 MOD 3 is 2, 9 MOD 3 is 0, etc.
Alternatively:
bLabelAbove = True
For i = 0 to 20 step 2
For j = 1 to 2
If bLabelAbove Then
Series.DataLabels(i + j).Position = xlLabelPositionAbove
Else
Series.DataLabels(i + j).Position = xlLabelPositionBelow
End If
Next
bLabelAbove = Not bLabelAbove
Next
Divide
1, 2, 3, 4, 5, 6, 7, 8
by 2, and round up, to get:
1, 1, 2, 2, 3, 3, 4, 4
Then you can test whether1, 1, 2, 2, 3, 3, 4, 4 is odd or even. If odd, then label above. If even, then label below.
Given a NxN matrix and a (row,column) position, what is a method to select a different position in a random (or pseudo-random) order, trying to avoid collisions as much as possible?
For example: consider a 5x5 matrix and start from (1,2)
0 0 0 0 0
0 0 X 0 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
I'm looking for a method like
(x,y) hash (x,y);
to jump to a different position in the matrix, avoiding collisions as much as possible
(do not care how to return two different values, it doesn't matter, just think of an array).
Of course, I can simply use
row = rand()%N;
column = rand()%N;
but it's not that good to avoid collisions.
I thought I could apply twice a simple hash method for both row and column and use the results as new coordinates, but I'm not sure this is a good solution.
Any ideas?
Can you determine the order of the walk before you start iterating? If your matrices are large, this approach isn't space-efficient, but it is straightforward and collision-free. I would do something like:
Generate an array of all of the coordinates. Remove the starting position from the list.
Shuffle the list (there's sample code for a Fisher-Yates shuffle here)
Use the shuffled list for your walk order.
Edit 2 & 3: A modular approach: Given s array elements, choose a prime p of form 2+3*n, p>s. For i=1 to p, use cells (iii)%p when that value is in range 1...s-1. (For row-length r, cell #c subscripts are c%r, c/r.)
Effectively, this method uses H(i) = (iii) mod p as a hash function. The reference shows that as i ranges from 1 to p, H(i) takes on each of the values from 0 to p-1, exactly one time each.
For example, with s=25 and p=29 or 47, this uses cells in following order:
p=29: 1 8 6 9 13 24 19 4 14 17 22 18 11 7 12 3 15 10 5 16 20 23 2 21 0
p=47: 1 8 17 14 24 13 15 18 7 4 10 2 6 21 3 22 9 12 11 23 5 19 16 20 0
according to bc code like
s=25;p=29;for(i=1;i<=p;++i){t=(i^3)%p; if(t<s){print " ",t}}
The text above shows the suggestion I made in Edit 2 of my answer. The text below shows my first answer.
Edit 0: (This is the suggestion to which Seamus's comment applied): A simple method to go through a vector in a "random appearing" way is to repeatedly add d (d>1) to an index. This will access all elements if d and s are coprime (where s=vector length). Note, my example below is in terms of a vector; you could do the same thing independently on the other axis of your matrix, with a different delta for it, except a problem mentioned below would occur. Note, "coprime" means that gcd(d,s)=1. If s is variable, you'd need gcd() code.
Example: Say s is 10. gcd(s,x) is 1 for x in {1,3,7,9} and is not 1 for x in {2,4,5,6,8,10}. Suppose we choose d=7, and start with i=0. i will take on values 0, 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, which modulo 10 is 0, 7, 4, 1, 8, 5, 2, 9, 6, 3, 0.
Edit 1 & 3: Unfortunately this will have a problem in the two-axis case; for example, if you use d=7 for x axis, and e=3 for y-axis, while the first 21 hits will be distinct, it will then continue repeating the same 21 hits. To address this, treat the whole matrix as a vector, use d with gcd(d,s)=1, and convert cell numbers to subscripts as above.
If you just want to iterate through the matrix, what is wrong with row++; if (row == N) {row = 0; column++}?
If you iterate through the row and the column independently, and each cycles back to the beginning after N steps, then the (row, column) pair will interate through only N of the N^2 cells of the matrix.
If you want to iterate through all of the cells of the matrix in pseudo-random order, you could look at questions here on random permutations.
This is a companion answer to address a question about my previous answer: How to find an appropriate prime p >= s (where s = the number of matrix elements) to use in the hash function H(i) = (i*i*i) mod p.
We need to find a prime of form 3n+2, where n is any odd integer such that 3*n+2 >= s. Note that n odd gives 3n+2 = 3(2k+1)+2 = 6k+5 where k need not be odd. In the example code below, p = 5+6*(s/6); initializes p to be a number of form 6k+5, and p += 6; maintains p in this form.
The code below shows that half-a-dozen lines of code are enough for the calculation. Timings are shown after the code, which is reasonably fast: 12 us at s=half a million, 200 us at s=half a billion, where us denotes microseconds.
// timing how long to find primes of form 2+3*n by division
// jiw 20 Sep 2011
#include <stdlib.h>
#include <stdio.h>
#include <sys/time.h>
double ttime(double base) {
struct timeval tod;
gettimeofday(&tod, NULL);
return tod.tv_sec + tod.tv_usec/1e6 - base;
}
int main(int argc, char *argv[]) {
int d, s, p, par=0;
double t0=ttime(0);
++par; s=5000; if (argc > par) s = atoi(argv[par]);
p = 5+6*(s/6);
while (1) {
for (d=3; d*d<p; d+=2)
if (p%d==0) break;
if (d*d >= p) break;
p += 6;
}
printf ("p = %d after %.6f seconds\n", p, ttime(t0));
return 0;
}
Timing results on 2.5GHz Athlon 5200+:
qili ~/px > for i in 0 00 000 0000 00000 000000; do ./divide-timing 500$i; done
p = 5003 after 0.000008 seconds
p = 50021 after 0.000010 seconds
p = 500009 after 0.000012 seconds
p = 5000081 after 0.000031 seconds
p = 50000021 after 0.000072 seconds
p = 500000003 after 0.000200 seconds
qili ~/px > factor 5003 50021 500009 5000081 50000021 500000003
5003: 5003
50021: 50021
500009: 500009
5000081: 5000081
50000021: 50000021
500000003: 500000003
Update 1 Of course, timing is not determinate (ie, can vary substantially depending on the value of s, other processes on machine, etc); for example:
qili ~/px > time for i in 000 004 010 058 070 094 100 118 184; do ./divide-timing 500000$i; done
p = 500000003 after 0.000201 seconds
p = 500000009 after 0.000201 seconds
p = 500000057 after 0.000235 seconds
p = 500000069 after 0.000394 seconds
p = 500000093 after 0.000200 seconds
p = 500000099 after 0.000201 seconds
p = 500000117 after 0.000201 seconds
p = 500000183 after 0.000211 seconds
p = 500000201 after 0.000223 seconds
real 0m0.011s
user 0m0.002s
sys 0m0.004s
Consider using a double hash function to get a better distribution inside the matrix,
but given that you cannot avoid colisions, what I suggest is to use an array of sentinels
and mark the positions you visit, this way you are sure you get to visit a cell once.