I Need to output an 2D Array that has a label header for the colums and the rows.
the columns is easy i just ouput a string above the table but i cannot figure out how to add the word ROW in vertical letters at the begining of the table.
it has to look like this.
C o l u m n s
| 1 2 3 4 5 6
----------------------------------
1 | 2 3 4 5 6 7
R 2 | 3 4 5 6 7 8
O 3 | 4 5 6 7 8 9
W 4 | 5 6 7 8 9 10
S 5 | 6 7 8 9 10 11
6 | 7 8 9 10 11 12
i cannot figure out how to get the rows label
Output should be like this
10 10 10 10 10 10 10 10 10 10
9 9 9 9 9 9 9 9 9
8 8 8 8 8 8 8 8
7 7 7 7 7 7 7
.
.
.
1
tyr it dear
l = [1,2,3,4,5,6,7,8,9,10]
d = []
for i in l:
d.extend([i]*i)
print d[::-1]
My understanding as far as data frame in R is that it has to be rectangular. It is not possible to have a data frame with unequal column lengths. Can I use the lists in R to achieve this? What are he pros and cons for such an approach?
You can use lists to store whatever you want, even dataframes or other lists! You can indeed assign different length vectors, or even completely different objects. It gives you the same functionality as dataframes in that you can index using the dollar sign:
> fooList <- list(a=1:12, b=1:11, c=1:10)
> fooList$a
[1] 1 2 3 4 5 6 7 8 9 10 11 12
> fooDF <- data.frame(a=1:10, b=1:10, c=1:10)
> fooDF$a
[1] 1 2 3 4 5 6 7 8 9 10
But numeric indexing is different:
> fooList[[1]]
[1] 1 2 3 4 5 6 7 8 9 10 11 12
> fooDF[,1]
[1] 1 2 3 4 5 6 7 8 9 10
as well as the structure and printing method:
> fooList
$a
[1] 1 2 3 4 5 6 7 8 9 10 11 12
$b
[1] 1 2 3 4 5 6 7 8 9 10 11
$c
[1] 1 2 3 4 5 6 7 8 9 10
> fooDF
a b c
1 1 1 1
2 2 2 2
3 3 3 3
4 4 4 4
5 5 5 5
6 6 6 6
7 7 7 7
8 8 8 8
9 9 9 9
10 10 10 10
Simply said a dataframe is a matrix and a list more of a container.
A list is meant to keep all sorts of stuff together, and a dataframe is the usual data format (a subject/case for each row and a variable for each column). It is used in a lot of analyses, allows to index the scores of a subject, can be more easilly transformed and other things.
However if you have unequal length columns then I doubt each row resembles a subject/case in your data. In that case I guess you don't need much of the functionality of dataframes.
If each row does resemble a subject/case, then you should use NA for any missing values and use a data frame.
I'm trying to search a big project for all examples of where I've declared an array with [48] as the size or any multiples of 48.
Can I use a regular expression function to find matches of 48 * n?
Thanks.
Here you go (In PHP's PCRE syntax):
^(0*|(1(01*?0)*?1|0)+?0{4})$
Usage:
preg_match('/^(0*|(1(01*?0)*?1|0)+?0{4})$/', decbin($number));
Now, why it works:
Well we know that 48 is really just 3 * 16. And 16 is just 2*2*2*2. So, any number divisible by 2^4 will have the 4 most bits in its binary representation 0. So by ending the regexp with 0{4}$ is equivalent to saying that the number is divisible by 2^4 (or 16). So then, the bits to the left need to be divisible by 3. So using the regexp from this answer, we can tell if they are divisible by 3. So if the whole regexp matches, the number is divisible by both 3 and 16, and hence 48...
QED...
(Note, the leading 0| case handles the failed match when $number is 0). I've tested this on all numbers from 0 to 48^5, and it correctly matches each time...
A generalization of your question is asking whether x is a string representing a multiple of n in base b. This is the same thing as asking whether the remainder of x divided by n is 0. You can easily create a DFA to compute this.
Create a DFA with n states, numbered from 0 to n - 1. State 0 is both the initial state and the sole accepting state. Each state will have b outgoing transitions, one for each symbol in the alphabet (since base-b gives you b digits to work with).
Each state represents the remainder of the portion of x we've seen so far, divided by n. This is why we have n of them (dividing a number by n yields a remainder in the range 0 to n - 1), and also why state 0 is the accepting state.
Since the digits of x are processed from left to right, if we have a number y from the first few digits of x and read the digit d, we get the new value of y from yb + d. But more importantly, the remainder r changes to (rb + d) mod n. So we now know how to connect the transition arcs and complete the DFA.
You can do this for any n and b. Here, for example, is one that accepts multiples of 18 in base-10 (states on the rows, inputs on the columns):
| 0 1 2 3 4 5 6 7 8 9
---+-------------------------------
→0 | 0 1 2 3 4 5 6 7 8 9 ←accept
1 | 10 11 12 13 14 15 16 17 0 1
2 | 2 3 4 5 6 7 8 9 10 11
3 | 12 13 14 15 16 17 0 1 2 3
4 | 4 5 6 7 8 9 10 11 12 13
5 | 14 15 16 17 0 1 2 3 4 5
6 | 6 7 8 9 10 11 12 13 14 15
7 | 16 17 0 1 2 3 4 5 6 7
8 | 8 9 10 11 12 13 14 15 16 17
9 | 0 1 2 3 4 5 6 7 8 9
10 | 10 11 12 13 14 15 16 17 0 1
11 | 2 3 4 5 6 7 8 9 10 11
12 | 12 13 14 15 16 17 0 1 2 3
13 | 4 5 6 7 8 9 10 11 12 13
14 | 14 15 16 17 0 1 2 3 4 5
15 | 6 7 8 9 10 11 12 13 14 15
16 | 16 17 0 1 2 3 4 5 6 7
17 | 8 9 10 11 12 13 14 15 16 17
These get really tedious as n and b get larger, but you can obviously write a program to generate them for you no problem.
1|48|2304|110592|5308416
You are unlikely to have declared an array of size 48^5 or larger.
No, regular expressions can't calculate multiples (except in the unary number system: decimal 4 = unary 1111; decimal 8 = unary 11111111, so the regex ^(1111)+$ matches multiples of 4).
import re
# For real example,
# construction of a chain with integers multiples of 48
# and integers not multiple of 48.
from random import *
w = [ 48*randint( 1,10) for j in xrange(10) ]
w.extend( 48*randint(11,20) for j in xrange(10) )
w.extend( 48*randint(21,70) for j in xrange(10) )
a = [ el if el%48!=0 else el+1 for el in sample(xrange(1000),40) ]
w.extend(a)
shuffle(w)
texte = [ ''.join(sample(' abcdefghijklmonopqrstuvwxyz',randint(1,7))) for i in xrange(40) ]
X = ''.join(texte[i]+str(w[i]) for i in xrange(40))
# Searching the multiples of 48 in the chain X
def mult48(match):
g1 = match.group()
if int(g1)%48==0:
return ( g1, X[0:match.end()] )
else:
return ( g1, 'not multiple')
for match in re.finditer('\d+',X):
print '%s %s\n' % mult48(match)
Any multiple is difficult, but here's a (python-style) regexp that matches the first 200 multiples of 48.
0$|1(?:0(?:08$|56$)|1(?:04$|52$)|2(?:00$|48$|96$)|3(?:44$|92$)|4(?:4(?:$|0$)|88$\
)|5(?:36$|84$)|6(?:32$|80$)|7(?:28$|76$)|8(?:24$|72$)|9(?:2(?:$|0$)|68$))|2(?:0(\
?:16$|64$)|1(?:12$|60$)|2(?:08$|56$)|3(?:04$|52$)|4(?:0(?:$|0$)|48$|96$)|5(?:44$\
|92$)|6(?:40$|88$)|7(?:36$|84$)|8(?:32$|8(?:$|0$))|9(?:28$|76$))|3(?:0(?:24$|72$\
)|1(?:20$|68$)|2(?:16$|64$)|3(?:12$|6(?:$|0$))|4(?:08$|56$)|5(?:04$|52$)|6(?:00$\
|48$|96$)|7(?:44$|92$)|8(?:4(?:$|0$)|88$)|9(?:36$|84$))|4(?:0(?:32$|80$)|1(?:28$\
|76$)|2(?:24$|72$)|3(?:2(?:$|0$)|68$)|4(?:16$|64$)|5(?:12$|60$)|6(?:08$|56$)|7(?\
:04$|52$)|8(?:$|0(?:$|0$)|48$|96$)|9(?:44$|92$))|5(?:0(?:40$|88$)|1(?:36$|84$)|2\
(?:32$|8(?:$|0$))|3(?:28$|76$)|4(?:24$|72$)|5(?:20$|68$)|6(?:16$|64$)|7(?:12$|6(\
?:$|0$))|8(?:08$|56$)|9(?:04$|52$))|6(?:0(?:00$|48$|96$)|1(?:44$|92$)|2(?:4(?:$|\
0$)|88$)|3(?:36$|84$)|4(?:32$|80$)|5(?:28$|76$)|6(?:24$|72$)|7(?:2(?:$|0$)|68$)|\
8(?:16$|64$)|9(?:12$|60$))|7(?:0(?:08$|56$)|1(?:04$|52$)|2(?:0(?:$|0$)|48$|96$)|\
3(?:44$|92$)|4(?:40$|88$)|5(?:36$|84$)|6(?:32$|8(?:$|0$))|7(?:28$|76$)|8(?:24$|7\
2$)|9(?:20$|68$))|8(?:0(?:16$|64$)|1(?:12$|6(?:$|0$))|2(?:08$|56$)|3(?:04$|52$)|\
4(?:00$|48$|96$)|5(?:44$|92$)|6(?:4(?:$|0$)|88$)|7(?:36$|84$)|8(?:32$|80$)|9(?:2\
8$|76$))|9(?:0(?:24$|72$)|1(?:2(?:$|0$)|68$)|2(?:16$|64$)|3(?:12$|60$)|4(?:08$|5\
6$)|5(?:04$|52$)|6(?:$|0$))
I am currently working on an assignment for a datastructures and algorithms class.
I have to delete the node out of the heap given;
6 after replacing the node ; 20
/ \ / \
11 9 11 9
/ \ / \ / \ / \
17 18 15 10 17 18 15 10
/
20
The question I have is would I downheap to the right, the left or does it matter?
Since you have a min-heap there, your downheap operation should swap the new parent with the smaller of its children. Otherwise your swap could result in a violation of the heap condition.
You, need to swap the parent node with that child node which is having the smaller value and this process need to continued untill the base condition for heap is satisfied