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If there is an array that contains random integers in ascending order, how can I tell if this array contains a arithmetic sequence (length>3) with the common differece x?
Example:
Input: Array=[1,2,4,5,8,10,17,19,20,23,30,36,40,50]
x=10
Output: True
Explanation of the Example: the array contains [10,20,30,40,50], which is a arithmetic sequence (length=5) with the common differece 10.
Thanks!
I apologize that I have not try any code to solve this since I have no clue yet.
After reading the answers, I tried it in python.
Here are my codes:
df = [1,10,11,20,21,30,40]
i=0
common_differene=10
df_len=len(df)
for position_1 in range(df_len):
for position_2 in range(df_len):
if df[position_1] + common_differene == df[position_2]:
position_1=position_2
i=i+1
print(i)
However, it returns 9 instead of 4.
Is there anyway to prevent the repetitive counting in one sequence [10,20,30,40] and also prevent accumulating i from other sequences [1,11,21]?
You can solve your problem by using 2 loops, one to run through every element and the other one to check if the element is currentElement+x, if you find one that does, you can continue form there.
With the added rule of the sequence being more than 2 elements long, I have recreated your problem in FREE BASIC:
DIM array(13) As Integer = {1, 2, 4, 5, 8, 10, 17, 19, 20, 23, 30, 36, 40, 50}
DIM x as Integer = 10
DIM arithmeticArrayMinLength as Integer = 3
DIM index as Integer = 0
FOR position As Integer = LBound(array) To UBound(array)
FOR position2 As Integer = LBound(array) To UBound(array)
IF (array(position) + x = array(position2)) THEN
position = position2
index = index + 1
END IF
NEXT
NEXT
IF (index <= arithmeticArrayMinLength) THEN
PRINT false
ELSE
PRINT true
END IF
Hope it helps
Edit:
After reviewing your edit, I have come up with a solution in Python that returns all arithmetic sequences, keeping the order of the list:
def arithmeticSequence(A,n):
SubSequence=[]
ArithmeticSequences=[]
#Create array of pairs from array A
for index,item in enumerate(A[:-1]):
for index2,item2 in enumerate(A[index+1:]):
SubSequence.append([item,item2])
#finding arithmetic sequences
for index,pair in enumerate(SubSequence):
if (pair[1] - pair[0] == n):
found = [pair[0],pair[1]]
for index2,pair2 in enumerate(SubSequence[index+1:]):
if (pair2[0]==found[-1] and pair2[1]-pair2[0]==n):
found.append(pair2[1])
if (len(found)>2): ArithmeticSequences.append(found)
return ArithmeticSequences
df = [1,10,11,20,21,30,40]
common_differene=10
arseq=arithmeticSequence(df,common_differene)
print(arseq)
Output: [[1, 11, 21], [10, 20, 30, 40], [20, 30, 40]]
This is how you can get all the arithmetic sequences out of df for you to do whatever you want with them.
Now, if you want to remove the sub-sequences of already existing arithmetic sequences, you can try running it through:
def distinct(A):
DistinctArithmeticSequences = A
for index,item in enumerate(A):
for index2,item2 in enumerate([x for x in A if x != item]):
if (set(item2) <= set(item)):
DistinctArithmeticSequences.remove(item2)
return DistinctArithmeticSequences
darseq=distinct(arseq)
print(darseq)
Output: [[1, 11, 21], [10, 20, 30, 40]]
Note: Not gonna lie, this was fun figuring out!
Try from 1: check the presence of 11, 21, 31... (you can stop immediately)
Try from 2: check the presence of 12, 22, 32... (you can stop immediately)
Try from 4: check the presence of 14, 24, 34... (you can stop immediately)
...
Try from 10: check the presence of 20, 30, 40... (bingo !)
You can use linear searches, but for a large array, a hash map will be better. If you can stop as soon as you have found a sequence of length > 3, this procedure takes linear time.
Scan the list increasingly and for every element v, check if the element v + 10 is present and draw a link between them. This search can be done in linear time as a modified merge operation.
E.g. from 1, search 11; you can stop at 17; from 2, search 12; you can stop at 17; ... ; from 8, search 18; you can stop at 19...
Now you have a graph, the connected components of which form arithmetic sequences. You can traverse the array in search of a long sequence (or a longest), also in linear time.
In the given example, the only links are 10->-20->-30->-40->-50.
I have one array like below:
Array = [21.2, 13.6, 86.2, 54.6, 76, 34, 78, 12, 90, 4];
Now I want to add Array values from the first index to the fourth index, and from the seventh index to the tenth.
I wrote this code but it did not work correctly.
s = 0
for I=1:10
if 1<=I<=4 | I>6
s = s + Array(I);
end
end
Please help me with this problem.
You can implement it without any kind of loop that may slow your code. To make those sums, you just need to use 'sum'. For further help, please read this. In your case, I'd do the following:
a = [21.2, 13.6, 86.2, 54.6, 76, 34, 78, 12, 90, 4];
b = sum(a(1:4))+sum(a(8:end));
Let's assume a multi-dimensional array
import numpy as np
foo = np.random.rand(102,43,35,51)
I know that those last dimensions represent a 2D space (35,51) of which I would like to index a range of rows of a column
Let's say I want to have rows 8 to 30 of column 0
From my understanding of indexing I should call
foo[0][0][8::30][0]
Knowing my data though (unlike the random data used here), this is not what I expected
I could try this that does work but looks ridiculous
foo[0][0][[8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30],0]
Now from what I can find in this documentation I can also use
something like:
foo[0][0][[8,30],0]
which only gives me the values of rows 8 and 30
while this:
foo[0][0][[8::30],0]
gives an error
File "<ipython-input-568-cc49fe1424d1>", line 1
foo[0][0][[8::30],0]
^
SyntaxError: invalid syntax
I don't understand why the :: argument cannot be passed here. What is then a way to indicate a range in your indexing syntax?
So I guess my overall question is what would be the proper pythonic equivalent of this syntax:
foo[0][0][[8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30],0]
Instead of
foo[0][0][8::30][0]
try
foo[0, 0, 8:30, 0]
The foo[0][0] part is the same as foo[0, 0, :, :], selecting a 2d array (35 x 51). But foo[0][0][8::30] selects a subset of those rows
Consider what happens when is use 0::30 on 2d array:
In [490]: np.zeros((35,51))[0::30].shape
Out[490]: (2, 51)
In [491]: np.arange(35)[0::30]
Out[491]: array([ 0, 30])
The 30 is the step, not the stop value of the slice.
the last [0] then picks the first of those rows. The end result is the same as foo[0,0,0,:].
It is better, in most cases, to index multiple dimensions with the comma syntax. And if you want the first 30 rows use 0:30, not 0::30 (that's basic slicing notation, applicable to lists as well as arrays).
As for:
foo[0][0][[8::30],0]
simplify it to x[[8::30], 0]. The Python interpreter accepts [1:2:3, 0], translating it to tuple(slice(1,2,3), 0) and passing it to a __getitem__ method. But the colon syntax is accepted in a very specific context. The interpreter is treating that inner set of brackets as a list, and colons are not accepted there.
foo[0,0,[1,2,3],0]
is ok, because the inner brackets are a list, and the numpy getitem can handle those.
numpy has a tool for converting a slice notation into a list of numbers. Play with that if it is still confusing:
In [495]: np.r_[8:30]
Out[495]:
array([ 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24,
25, 26, 27, 28, 29])
In [496]: np.r_[8::30]
Out[496]: array([0])
In [497]: np.r_[8:30:2]
Out[497]: array([ 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28])
I am new in python. I have asked another question How to arrange three lists in such a way that the sum of corresponding elements if greater then appear first? Now the problem is following:
I am working with a large text file, in which there are 419040 rows and 6 columns containing floats. Among them I am taking first 3 columns to generate those three lists. So the lists I am actually working with has 419040 entries in each. While I was running the python code to extract the three columns into three lists the python shell was not responding, I suspected the large number of entries for this, I used this code:
file=open("file_location","r")
a=[]
b=[]
c=[]
for lines in file:
x=lines.split(" ")
a.append(float(x[0]))
b.append(float(x[1]))
c.append(float(x[2]))
Note: for small file this code was running perfectly.
To avoid this problem I am using the following code:
import numpy as np
a = []
b = []
c = []
a,b,c = np.genfromtxt('file_location',usecols = [0,1,2], unpack=True)
So when I am running the code given in answers to my previous question the same problem is happening. So what will be the corresponding code using numpy? Or, any other solutions?
If you're going to use numpy, then I suggest using ndarrays, rather than lists. You can use loadtxt since you don't have to handle missing data. I assume it'll be faster.
a = np.loadtxt('file.txt', usecols=(0, 1, 2))
a is now a two-dimensional array, stored as an np.ndarray datatype. It should look like:
>>> a
array([[ 1, 20, 400],
[ 5, 30, 500],
[ 3, 50, 100],
[ 2, 40, 300],
[ 4, 10, 200]])
However, you now need to re-do what you did in the previous question, but using numpy arrays rather than lists. This can be easily achieved like so:
>>> b = a.sum(axis=1)
>>> b
Out[21]: array([535, 421, 342, 214, 153])
>>> i = np.argsort(b)[::-1]
>>> i
Out[26]: array([0, 1, 2, 3, 4])
>>> a[i, :]
Out[27]:
array([[ 5, 30, 500],
[ 1, 20, 400],
[ 2, 40, 300],
[ 4, 10, 200],
[ 3, 50, 100]])
The steps involved are described in a little greater detail here.
I have an array that is already sorted in partitions of 4:
2, 23, 45, 55, 1, 4, 23, 74545, 75, 234, 323, 9090, 2, 43, 6342, 323452
What would be the most efficient way to sort this array? Note: the array size is always even and the program knows that every 4 elements are sorted.
I think you can use merge sort for problems like this.
You might be able to use strand sort for this.