Colon operator in List Slicing - list

mini_batch_X = shuffled_X[:, k * mini_batch_size:(k + 1) * mini_batch_size]
What is the semantics of the above line? what does the first colon mean?

Colon in a slicing operation will generate slice(None, None, None), in numpy it means take all indices for this dimension.
A slice is start:end:step, usually step is omitted writing only start:end, but you can also omit start :end that will slice from beginning, or start: that will end at the last index.

Related

Extracting numbers using Regex in Matlab

I would like to extract integers from strings from a cell array in Matlab. Each string contains 1 or 2 integers formatted as shown below. Each number can be one or two digits. I would like to convert each string to a 1x2 array. If there is only one number in the string, the second column should be -1. If there are two numbers then the first entry should be the first number, and the second entry should be the second number.
'[1, 2]'
'[3]'
'[10, 3]'
'[1, 12]'
'[11, 12]'
Thank you very much!
I have tried a few different methods that did not work out. I think that I need to use regex and am having difficulty finding the proper expression.
You can use str2num to convert well formatted chars (which you appear to have) to the correct arrays/scalars. Then simply pad from the end+1 element to the 2nd element (note this is nothing in the case there's already two elements) with the value -1.
This is most clearly done in a small loop, see the comments for details:
% Set up the input
c = { ...
'[1, 2]'
'[3]'
'[10, 3]'
'[1, 12]'
'[11, 12]'
};
n = cell(size(c)); % Initialise output
for ii = 1:numel(n) % Loop over chars in 'c'
n{ii} = str2num(c{ii}); % convert char to numeric array
n{ii}(end+1:2) = -1; % Extend (if needed) to 2 elements = -1
end
% (Optional) Convert from a cell to an Nx2 array
n = cell2mat(n);
If you really wanted to use regex, you could replace the loop part with something similar:
n = regexp( c, '\d{1,2}', 'match' ); % Match between one and two digits
for ii = 1:numel(n)
n{ii} = str2double(n{ii}); % Convert cellstr of chars to arrays
n{ii}(end+1:2) = -1; % Pad to be at least 2 elements
end
But there are lots of ways to do this without touching regex, for example you could erase the square brackets, split on a comma, and pad with -1 according to whether or not there's a comma in each row. Wrap it all in a much harder to read (vs a loop) cellfun and ta-dah you get a one-liner:
n = cellfun( #(x) [str2double( strsplit( erase(x,{'[',']'}), ',' ) ), -1*ones(1,1-nnz(x==','))], c, 'uni', 0 );
I'd recommend one of the loops for ease of reading and debugging.

Need help implementing a certain logic that will fill a text to a certain width.

The task is to justify text within a certain width.
user inputs: Hello my name is Harrry. This is a sample text input that nobody
will enter.
output: What text width do you want?
user inputs: 15
output: |Hello my name|
|is Harrry. This|
|is a sample|
|text that|
|nobody will|
|enter. |
Basically, the line has to be 15 spaces wide including blank spaces. Also, if the next word in the line cant fit into 15, it will skip entirely. If there are multiple words in a line, it will try to distribute the spaces evenly between each word. See the line that says "Is a sample" for example.
I created a vector using getline(...) and all that and the entire text is saved in a vector. However, I'm kind of stuck on moving forward. I tried using multiple for loops, but I just cant seem to skip lines or even out the spacing at all.
Again, not looking or expecting anyone to solve this, but I'd appreciate it if you could guide me into the right direction in terms of logic/algorithm i should think about.
You should consider this Dynamic programming solution.
Split text into “good” lines
Since we don't know where we need to break the line for good justification, we start guessing where the break to be done to the paragraph. (That is we guess to determine whether we should break between two words and make the second word as start of the next line).
You notice something? We brutefore!
And note that if we can't find a word small enought to fit in the remaining space in the current line, we insert spaces inbetween the words in the current line. So, the space in the current line depends on the words that might go into the next or previous line. That's Dependency!
You are bruteforcing and you have dependency,there comes the DP!
Now lets define a state to identify the position on our path to solve this problem.
State: [i : j] ,which denotes line of words from ith word to jth word in the original sequence of words given as input.
Now, that you have state for the problem let us try to define how these states are related.
Since all our sub-problem states are just a pile of words, we can't just compare the words in each state and determine which one is better. Here better delineates to the use of line's width to hold maximum character and minimum spaces between the words in the particular line. So, we define a parameter, that would measure the goodness of the list of words from ith to jth words to make a line. (recall our definition of subproblem state). This is basically evaluating each of our subproblem state.
A simple comparison factor would be :
Define badness(i, j) for line of words[i : j].
For example,
Infinity if total length > page width,
else (page width − total length of words in current line)3
To make things even simple consider only suffix of the given text and apply this algorithm. This would reduce the DP table size from N*N to N.
So, For finishing lets make it clear what we want in DP terms,
subproblem = min. badness for suffix words[i :]
=⇒ No.of subproblems = Θ(n) where n = no of words
guessing = where to end first line, say i : j
=⇒ no. of choices for j = n − i = O(n)
recurrence relation between the subproblem:
• DP[i] = min(badness (i, j) + DP[j] for j in range (i + 1, n + 1))
• DP[n] = 0
=⇒ time per subproblem = Θ(n)
so, total time = Θ(n^2).
Also, I'll leave it to you how insert spaces between words after determining the words in each line.
Logic would be:
1) Put words in array
2) Loop though array of words
3) Count the number of chars in each word, and check until they are the text width or less (skip if more than textwidth). Remember the number of words that make up the total before going over 15 (example remember it took 3 words to get 9 characters, leaving space for 6 spaces)
4) Divide the number of spaces required by (number of words - 1)
5) Write those words, writing the same number of spaces each time.
Should give the desired effect I hope.
You obviously have some idea how to solve this, as you have already produced the sample output.
Perhaps re-solve your original problem writing down in words what you do in each step....
e.g.
Print text asking for sentence.
Take input
Split input into words.
Print text asking for width.
...
If you are stuck at any level, then expand the details into sub-steps.
I would look to separate the problem of working out a sequence of words which will fit onto a line.
Then how many spaces to add between each of the words.
Below is an example for printing one line after you find how many words to print and what is the starting word of the line.
std::cout << "|";
numOfSpaces = lineWidth - numOfCharsUsedByWords;
/*
* If we have three words |word1 word2 word3| in a line
* ideally the spaces to print between then are 1 less than the words
*/
int spaceChunks = numOfWordsInLine - 1;
/*
* Print the words from starting point to num of words
* you can print in a line
*/
for (j = 0; j < numOfWordsInLine; ++j) {
/*
* Calculation for the number of spaces to print
* after every word
*/
int spacesToPrint = 0;
if (spaceChunks <= 1) {
/*
* if one/two words then one
* chunk of spaces between so fill then up
*/
spacesToPrint = numOfSpaces;
} else {
/*
* Here its just segmenting a number into chunks
* example: segment 7 into 3 parts, will become 3 + 2 + 2
* 7 to 3 = (7%3) + (7/3) = 1 + 2 = 3
* 4 to 2 = (4%2) + (4/2) = 0 + 2 = 2
* 2 to 1 = (2%1) + (2/1) = 0 + 2 = 2
*/
spacesToPrint = (numOfSpaces % spaceChunks) + (numOfSpaces / spaceChunks);
}
numOfSpaces -= spacesToPrint;
spaceChunks--;
cout << words[j + lineStartIdx];
for (int space = 0; space < spacesToPrint; space++) {
std::cout << " ";
}
}
std::cout << "|" << std::endl;
Hope this code helps. Also you need to consider what happens if you set width less then the max word size.

Solving a linear equation in one variable

What would be the most efficient algorithm to solve a linear equation in one variable given as a string input to a function? For example, for input string:
"x + 9 – 2 - 4 + x = – x + 5 – 1 + 3 – x"
The output should be 1.
I am considering using a stack and pushing each string token onto it as I encounter spaces in the string. If the input was in polish notation then it would have been easier to pop numbers off the stack to get to a result, but I am not sure what approach to take here.
It is an interview question.
Solving the linear equation is (I hope) extremely easy for you once you've worked out the coefficients a and b in the equation a * x + b = 0.
So, the difficult part of the problem is parsing the expression and "evaluating" it to find the coefficients. Your example expression is extremely simple, it uses only the operators unary -, binary -, binary +. And =, which you could handle specially.
It is not clear from the question whether the solution should also handle expressions involving binary * and /, or parentheses. I'm wondering whether the interview question is intended:
to make you write some simple code, or
to make you ask what the real scope of the problem is before you write anything.
Both are important skills :-)
It could even be that the question is intended:
to separate those with lots of experience writing parsers (who will solve it as fast as they can write/type) from those with none (who might struggle to solve it at all within a few minutes, at least without some hints).
Anyway, to allow for future more complicated requirements, there are two common approaches to parsing arithmetic expressions: recursive descent or Dijkstra's shunting-yard algorithm. You can look these up, and if you only need the simple expressions in version 1.0 then you can use a simplified form of Dijkstra's algorithm. Then once you've parsed the expression, you need to evaluate it: use values that are linear expressions in x and interpret = as an operator with lowest possible precedence that means "subtract". The result is a linear expression in x that is equal to 0.
If you don't need complicated expressions then you can evaluate that simple example pretty much directly from left-to-right once you've tokenised it[*]:
x
x + 9
// set the "we've found minus sign" bit to negate the first thing that follows
x + 7 // and clear the negative bit
x + 3
2 * x + 3
// set the "we've found the equals sign" bit to negate everything that follows
3 * x + 3
3 * x - 2
3 * x - 1
3 * x - 4
4 * x - 4
Finally, solve a * x + b = 0 as x = - b/a.
[*] example tokenisation code, in Python:
acc = None
for idx, ch in enumerate(input):
if ch in '1234567890':
if acc is None: acc = 0
acc = 10 * acc + int(ch)
continue
if acc != None:
yield acc
acc = None
if ch in '+-=x':
yield ch
elif ch == ' ':
pass
else:
raise ValueError('illegal character "%s" at %d' % (ch, idx))
Alternative example tokenisation code, also in Python, assuming there will always be spaces between tokens as in the example. This leaves token validation to the parser:
return input.split()
ok some simple psuedo code that you could use to solve this problem
function(stinrgToParse){
arrayoftokens = stringToParse.match(RegexMatching);
foreach(arrayoftokens as token)
{
//now step through the tokens and determine what they are
//and store the neccesary information.
}
//Use the above information to do the arithmetic.
//count the number of times a variable appears positive and negative
//do the arithmetic.
//add up the numbers both positive and negative.
//return the result.
}
The first thing is to parse the string, to identify the various tokens (numbers, variables and operators), so that an expression tree can be formed by giving operator proper precedences.
Regular expressions can help, but that's not the only method (grammar parsers like boost::spirit are good too, and you can even run your own: its all a "find and recourse").
The tree can then be manipulated reducing the nodes executing those operation that deals with constants and by grouping variables related operations, executing them accordingly.
This goes on recursively until you remain with a variable related node and a constant node.
At the point the solution is calculated trivially.
They are basically the same principles that leads to the production of an interpreter or a compiler.
Consider:
from operator import add, sub
def ab(expr):
a, b, op = 0, 0, add
for t in expr.split():
if t == '+': op = add
elif t == '-': op = sub
elif t == 'x': a = op(a, 1)
else : b = op(b, int(t))
return a, b
Given an expression like 1 + x - 2 - x... this converts it to a canonical form ax+b and returns a pair of coefficients (a,b).
Now, let's obtain the coefficients from both parts of the equation:
le, ri = equation.split('=')
a1, b1 = ab(le)
a2, b2 = ab(ri)
and finally solve the trivial equation a1*x + b1 = a2*x + b2:
x = (b2 - b1) / (a1 - a2)
Of course, this only solves this particular example, without operator precedence or parentheses. To support the latter you'll need a parser, presumable a recursive descent one, which would be simper to code by hand.

python bitwise_xor

I am having a problem with an xor search.
I have an array composed of binary values. My list contains 1000 distinct binary values, and I want to time how long it takes for a double loop to find an element in the list. Therefore for a double loop search, I expect it to go through the loop [(1) + (2) +(3)+...+(1000)] = 500500 times. [n(n+1) / 2]
I use the bitwise_xor in the following code
from numpy import bitwise_xor
count = 0
for word1 in listOutTextnoB:
for word2 in listOutTextnoB:
count+=1
if bitwise_xor(word1,word2)==0:
break
print "count"
Unfortunately, when I print count, I get count = 1,000,000
If I change the if statement to
if bitwise_xor(word1,word2):
break
count is 1000
I also tried to do:
if word1^word2==0:
break
but it gives me "TypeError: unsupported operand type(s) for ^: 'str' and 'str'"
A working example would be:
1101110111010111011101101110110010111100101111001 XOR 1101110111010111011101101110110010111100101111001
it should give me 0 and exit the inner loop
What is wrong with code?
^ works on integers, not arrays, so that is not surprising.
I don't know why you used strings but:
from numpy import bitwise_xor
listOutTextnoB = range(1000)
count = 0
for word1 in listOutTextnoB:
for word2 in listOutTextnoB:
count+=1
if bitwise_xor(word1,word2)==0:
break
print "count", count
prints
count 500500
as you predict.
EDIT: yes, you should be doing
if int(word1) ^ int(word2) == 0:
break
bitwise_xor is actually returning 'NotImplemented' for every string, string input.
Your error shows the problem: the values in your list are strings, not numbers. I'm not sure what bitwise_xor does to them, but I'm pretty sure it won't convert them to numbers first. If you do this manually (bitwise_xor (int (word1), int (word2))), I think it should work.

Finding all possible common substrings from a file consisting of strings using c++

I am trying to find all possible common strings from a file consisting of strings of various lengths. Can anybody help me out?
E.g input file is sorted:
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAC
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAG
AAAAAAAATTAGGCTGGG
AAAAAAAATTGAAACATCTATAGGTC
AAAAAAACTCTACCTCTCT
AAAAAAACTCTACCTCTCTATACTAATCTCCCTACA
and my desired output is:
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAC
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAG
AAAAAAAATTAGGCTGGG
AAAAAAAATTGAAACATCTATAGGTC
AAAAAAACTCTACCTCTCTATACTAATCTCCCTACA
[EDIT] Each line which is a substring of any other line should be removed.
Basically for each line, compare it with the next line to see if the next line is shorter or if the next line's substring is not equal to the current line. If this is true, the line is unique. This can be done with a single linear pass because the list is sorted: any entry which contains a substring of the entry will follow that entry.
A non-algorithmic optimization (micro-optimization) is to avoid the use of substr which creates a new string. We can simply compare the other string as though it was truncated without actually creating a truncated string.
vector<string> unique_lines;
for (unsigned int j=0; j < lines.size() - 2; ++j)
{
const string& line = lines[j];
const string& next_line = lines[j + 1];
// If the line is not a substring of the next line,
// add it to the list of unique lines.
if (line.size() >= next_line.size() ||
line != next_line.substr(0, line .size()))
unique_lines.push_back(line);
}
// The last line is guaranteed to not be a substring of any
// previous line as the lines are sorted.
unique_lines.push_back(lines.back());
// The desired output will be contained in 'unique_lines'.
What I understand is you want to find substring and wanted to remove such string which is substring of any string.
For that you can use strstr method to find if a string is a substring of another string.
Hope this will help..
Well, that's probably not the fastest solution to solve your problem, but seems easy to implement. You just keep a histogram of chars that will represent a signature of a string. For each string that you read (separated for spaces), you count the numbers of each char and just stores it on your answer if there isn't any other string with the same numbers of each char. Let me illustrate it:
aaa bbb aabb ab aaa
Here we have just two possible input letters, so, we just need an histogram of size 2.
aaa - hist[0] = 3, hist[1] = 0 : New one - add to the answer
bbb - hist[0] = 0, hist[1] = 3 : New one - add to the answer
aabb - hist[0] = 2, hist[1] = 2 : New one - add to the answer
ab - hist[0] = 1, hist[1] = 1 : New one - add to the answer
aaa - hist[0] = 3, hist[1] = 0 : Already exists! Don't add to the answer.
The bottleneck of your implementation will be the histogram comparisons, and there are a lot of possible implementations for it.
The simplest one would be a simple linear search, iterating through all your previous answer and comparing with the current histogram, wich would be O(1) to store and O(n) to search. If you have a big file, it would take hours to finish.
A faster one, but a lot more troublesome to implement, would use a hash table to store your answer, and use the histogram signature to generate the hash code. Would be to troublesome to explain this approach here.