I have 2 cell of strings and I would like to order them according to the first one.
A = {'a';'b';'c'}
B = {'b';'a';'c'}
idx = [2,1,3] % TO FIND
B=B(idx);
I would like to find a way to find idx...
Use the second output of ismember. ismember tells you whether or not values in the first set are anywhere in the second set. The second output tells you where these values are located if we find anything. As such:
A = {'a';'b';'c'}
B = {'b';'a';'c'}
[~,idx] = ismember(A, B);
Note that there is a minor typo when you declared your cell arrays. You have a colon in between b and c for A and a and c for B. I placed a semi-colon there for both for correctness.
Therefore, we get:
idx =
2
1
3
Benchmarking
We have three very good algorithms here. As such, let's see how this performs by doing a benchmarking test. What I'm going to do is generate a 10000 x 1 random character array of lower case letters. This will then be encapsulated into a 10000 x 1 cell array, where each cell is a single character array. I construct A this way, and B is a random permutation of the elements in A. This is the code that I wrote to do this for us:
letters = char(97 + (0:25));
rng(123); %// Set seed for reproducibility
ind = randi(26, [10000, 1]);
lettersMat = letters(ind);
A = mat2cell(lettersMat, ones(10000,1), 1);
B = A(randperm(10000));
Now... here comes the testing code:
clear all;
close all;
letters = char(97 + (0:25));
rng(123); %// Set seed for reproducibility
ind = randi(26, [10000, 1]);
lettersMat = letters(ind);
A = mat2cell(lettersMat, 1, ones(10000,1));
B = A(randperm(10000));
tic;
[~,idx] = ismember(A,B);
t = toc;
fprintf('ismember: %f\n', t);
clear idx; %// Make sure test is unbiased
tic;
[~,idx] = max(bsxfun(#eq,char(A),char(B)'));
t = toc;
fprintf('bsxfun: %f\n', t);
clear idx; %// Make sure test is unbiased
tic;
[~, indA] = sort(A);
[~, indB] = sort(B);
idx = indB(indA);
t = toc;
fprintf('sort: %f\n', t);
This is what I get for timing:
ismember: 0.058947
bsxfun: 0.110809
sort: 0.006054
Luis Mendo's approach is the fastest, followed by ismember, and then finally bsxfun. For code compactness, ismember is preferred but for performance, sort is better. Personally, I think bsxfun should win because it's such a nice function to use ;).
This seems to be significantly faster than using ismember (although admittedly less clear than #rayryeng's answer). With thanks to #Divakar for his correction on this answer.
[~, indA] = sort(A);
[~, indB] = sort(B);
idx = indA(indB);
I had to jump in as it seems runtime performance could be a criteria here :)
Assuming that you are dealing with scalar strings(one character in each cell), here's my take that works even when you have not-commmon elements between A and B and uses the very powerful bsxfun and as such I am really hoping this would be runtime-efficient -
[v,idx] = max(bsxfun(#eq,char(A),char(B)'));
idx = v.*idx
Example -
A =
'a' 'b' 'c' 'd'
B =
'b' 'a' 'c' 'e'
idx =
2 1 3 0
For a specific case when you have no not-common elements between A and B, it becomes a one-liner -
[~,idx] = max(bsxfun(#eq,char(A),char(B)'))
Example -
A =
'a' 'b' 'c'
B =
'b' 'a' 'c'
idx =
2 1 3
Related
I am trying to convert a string of varchar to ascii. Then i'm trying to make it so any number that's not 3 digits has a 0 in front of it. then i'm trying to add a 1 to the very beginning of the string and then i'm trying to make it a large number that I can apply math to it.
I've tried a lot of different coding techniques. The closest I've gotten is below:
s = 'Ak'
for c in s:
mgk = (''.join(str(ord(c)) for c in s))
num = [mgk]
var = 1
num.insert(0, var)
mgc = lambda num: int(''.join(str(i) for i in num))
num = mgc(num)
print(num)
With this code I get the output: 165107
It's almost doing exactly what I need to do but it's taking out the 0 from the ord(A) which is 65. I want it to be 165. everything else seems to be working great. I'm using '%03d'% to insert the 0.
How I want it to work is:
Get the ord() value from a string of numbers and letters.
if the ord() value is less than 100 (ex: A = 65, add a 0 to make it a 3 digit number)
take the ord() values and combine them into 1 number. 0 needs to stay in from of 65. then add a one to the list. so basically the output will look like:
1065107
I want to make sure I can take that number and apply math to it.
I have this code too:
s = 'Ak'
for c in s:
s = ord(c)
s = '%03d'%s
mgk = (''.join(str(s)))
s = [mgk]
var = 1
s.insert(0, var)
mgc = lambda s: int(''.join(str(i) for i in s))
s = mgc(s)
print(s)
but then it counts each letter as its own element and it will not combine them and I only want the one in front of the very first number.
When the number is converted to an integer, it
Is this what you want? I am kinda confused:
a = 'Ak'
result = '1' + ''.join(str(f'{ord(char):03d}') for char in a)
print(result) # 1065107
# to make it a number just do:
my_int = int(result)
I'm self-studying problem 32-1 in CLRS; part c), presents the following algorithm for string matching:
REPETITION-MATCHER(P, T)
m = P.length
n = T.length
k = 1 + ρ'(P)
q = 0
s = 0
while s <= n-m
if T[s+q+1] == P[q+1]
q = q+1
if q==m
print "Pattern occurs with shift" s
if q==m or T[s+q+1] != P[q+1]
s = s+max(1, ceil(q/k))
q = 0
Here, ρ'(P), which is a function of P only, is defined as the largest integer r such that some prefix P[1..i] = y^r, e.g. a substring y repeated r times.
This algorithm appears to be 95 percent similar to the naive brute-force string matcher. However, the one part which greatly confuses me, and which seems to be the centerpiece of the entire algorithm, is the second to last line. Here, q is the number of characters of P matched so far. What is the rationale behind ceil(q/k)? It is completely opaque to me. It would have made more sense if that line were something like s = s + max(1+q, 1+i), where i is the length of the prefix that gives rise to ρ'(P).
CLRS claims that this algorithm is due to Galil and Seiferas, but in the reference they provide, I cannot find anything that resembles the algorithm provided above. It appears that reference contains, if anything, a much more advanced version of what is here. Can someone explain this ceil(q/k) value, and/or point me toward a reference that describes this particular algorithm, instead of the more well-known main Galil Seiferas paper?
Example #1:
Match aaaa in aaaaab, here ρ' = 4. Consider state:
aaaa ab
^
We have a mismatch here, and we want to move forward by one symbol, no more, because we will match full pattern again (last line sets q to zero). q = 4 and k = 5, so ceil(q/k) = 1, that's all right.
Example #2: Match abcd.abcd.abcd.X in abcd.abcd.abcd.abcd.X. Consider state:
abcd.abcd.abcd. abcd.X
^
We have a mismatch here, and we would like to move forward by five symbols. q = 15 and k = 4, so ceil(q/k) = 4. That's ok, it is almost 5, we still can match our pattern. Had we bigger ρ', say 10, we would have ceil(50/(10+1)) = 5.
Yeh, algorithms skips forward less symbols than KMP does, in case ρ'=10 its running time is O(10n+m) while KMP has O(n+m).
I figured out the proof of correctness.
let k = ρ'(P) + 1, and ρ'(P) is the largest possible repetition factor out of all the prefixes of P.
Suppose T[s+1..s+q] = P[1..q], and either q=m or T[s+q+1] != P[q+1]
Then, for 1 <= j <= floor(q/k) (except for the case q=m and m mod k = 0, in which the upper limit must be ceil(m/k)), we have
T[s+1..s+j] = P[1..j]
T[s+j+1..s+2j] = P[j+1..2j]
T[s+2j+1..s+3j] = P[2j+1..3j]
...
T[s+(k-1)j+1..s+kj] = P[(k-1)j+1..kj]
where not every quantity on every line is equal, since k cannot be a repetition factor, since the largest possible repetition factor out of any prefix of P is k-1.
Suppose we now make a comparison at shift s' = s+j, so that we will make the following comparisons
T[s+j+1..s+2j] with P[1..j]
T[s+2j+1..s+3j] with P[j+1..2j]
T[s+3j+1..s+4j] with P[2j+1..3j]
...
T[s+kj+1..s+(k+1)j] with P[(k-1)j+1..kj]
We claim that not every comparison can match, e.g. at least one of the above "with"s must be replaced with !=. We prove by contradiction. Suppose every "with" above is replaced by =. Then, comparing to the first set of comparisons we did, we would immediately have the following:
P[1..j] = P[j+1..2j]
P[j+1..2j] = [2j+1..3j]
...
P[(k-2)j+1..(k-1)j] = P[(k-1)j+1..kj]
However, this cannot be true, because k is not a repetition factor, hence a contradiction.
Hence, for any 1 <= j <= floor(q/k), testing a new shift s'=s+j is guaranteed to mismatch.
Hence, the smallest shift that is possible to result in a match is s + floor(q/k) + 1 >= ceil(q/k).
Note the code uses ceil(q/k) for simplicity, solely to deal with the case that q = m and m mod k = 0, in which case k * (floor(q/k)+1) would be greater than m, so only ceil(q/k) would do. However, when q mod k = 0 and q < m, then ceil(q/k) = floor(q/k), so is slightly suboptimal, since that shift is guaranteed to fail, and floor(q/k)+1 is the first shift that has any chance of matching.
For example, s1='abc', s2='kokoabckokabckoab'.
Output should be 3. (number of times s1 appears in s2).
Not allowed to use for or strfind. Can only use reshape,repmat,size.
I thought of reshaping s2, so it would contain all of the possible strings of 3s:
s2 =
kok
oko
koa
oab
.... etc
But I'm having troubles from here..
Assuming you have your matrix reshaped into the format you have in your post, you can replicate s1 and stack the string such that it has as many rows as there are in the reshaped s2 matrix, then do an equality operator. Rows that consist of all 1s means that we have found a match and so you would simply search for those rows where the total sum is equal to the total length of s1. Referring back to my post on dividing up a string into overlapping substrings, we can decompose your string into what you have posted in your question like so:
%// Define s1 and s2 here
s1 = 'abc';
len = length(s1);
s2 = 'kokoabckokabckoab';
%// Hankel starts here
c = (1 : len).';
r = (len : length(s2)).';
nr = length(r);
nc = length(c);
x = [ c; r((2:nr)') ]; %-- build vector of user data
cidx = (1:nc)';
ridx = 0:(nr-1);
H = cidx(:,ones(nr,1)) + ridx(ones(nc,1),:); % Hankel subscripts
ind = x(H); % actual data
%// End Hankel script
%// Now get our data
subseqs = s2(ind.');
%// Case where string length is 1
if len == 1
subseqs = subseqs.';
end
subseqs contains the matrix of overlapping characters that you have alluded to in your post. You've noticed a small bug where if the length of the string is 1, then the algorithm won't work. You need to make sure that the reshaped substring matrix consists of a single column vector. If we ran the above code without checking the length of s1, we would get a row vector, and so simply transpose the result if this is the case.
Now, simply replicate s1 for as many times as we have rows in subseqs so that all of these strings get stacked into a 2D matrix. After, do an equality operator.
eqs = subseqs == repmat(s1, size(subseqs,1), 1);
Now, find the column-wise sum and see which elements are equal to the length of your string. This will produce a single column vector where 1 indicates that we have found a match, and zero otherwise:
sum(eqs, 2) == len
ans =
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
Finally, to add up how many times the substring matched, you just have to add up all elements in this vector:
out = sum(sum(eqs, 2) == len)
out =
2
As such, we have two instances where abc is found in your string.
Here is another one,
s1='abc';
s2='bkcokbacaabcsoabckokabckoabc';
[a,b] = ismember(s2,s1);
b = [0 0 b 0 0];
a1=circshift(b,[0 -1]);
a2=circshift(b,[0 -2]);
sum((b==1)&(a1==2)&(a2==3))
It gives 3 for your input and 4 for my example, and it seems to work well if ismember is okey.
Just for the fun of it: this can be done with nlfilter from the Image Processing Toolbox (I just discovered this function today and am eager to apply it!):
ds1 = double(s1);
ds2 = double(s2);
result = sum(nlfilter(ds2, [1 numel(ds1)], #(x) all(x==ds1)));
Consider the following function on a string:
int F(string S)
{
int N = S.size();
int T = 0;
for (int i = 0; i < N; i++)
for (int j = i + 1; j < N; j++)
if (S[i] > S[j])
T++;
return T;
}
A string S0 of length N with all pairwise distinct characters has a total of N! unique permutations.
For example "bac" has the following 6 permutations:
bac
abc
cba
bca
acb
cab
Consider these N! strings in lexicographical order:
abc
acb
bac
bca
cab
cba
Now consider the application of F to each of these strings:
F("abc") = 0
F("acb") = 1
F("bac") = 1
F("bca") = 2
F("cab") = 2
F("cba") = 3
Given some string S1 of this set of permutations, we want to find the next string S2 in the set, that has the following relationship to S1:
F(S2) == F(S1) + 1
For example if S1 == "acb" (F = 1) than S2 == "bca" (F = 1 + 1 = 2)
One way to do this would be to start at one past S1 and iterate through the list of permutations looking for F(S) = F(S1)+1. This is unfortunately O(N!).
By what O(N) function on S1 can we calculate S2 directly?
Suppose length of S1 is n, biggest value for F(S1) is n(n-1)/2, if F(S1) = n(n-1)/2, means it's a last function and there isn't any next for it, but if F(S1) < n(n-1)/2, means there is at least one char x which is bigger than char y and x is next to y, find such a x with lowest index, and change x and y places. let see it by example:
S1 == "acb" (F = 1) , 1 < 3 so there is a char x which is bigger than another char y and its index is bigger than y, here smallest index x is c, and by first try you will replace it with a (which is smaller than x so algorithm finishes here)==> S2= "cab", F(S2) = 2.
Now let test it with S2, cab: x=b, y=a, ==> S3 = "cba".\
finding x is not hard, iterate the input, and have a variable name it min, while current visited character is smaller than min, set min as newly visited char, and visit next character, first time you visit a character which is bigger than min stop iteration, this is x:
This is pseudocode in c# (but I wasn't careful about boundaries e.g in input.Substring):
string NextString(string input)
{
var min = input[0];
int i=1;
while (i < input.Length && input[i] < min)
{
min = input[i];
i++;
}
if (i == input.Length) return "There isn't next item";
var x = input[i], y=input[i-1];
return input.Substring(0,i-2) + x + y + input.Substring(i,input.Length - 1 - i);
}
Here's the outline of an algorithm for a solution to your problem.
I'll assume that you have a function to directly return the n-th permutation (given n) and its inverse, ie a function to return n given a permutation. Let these be perm(n) and perm'(n) respectively.
If I've figured it correctly, when you have a 4-letter string to permute the function F goes like this:
F("abcd") = 0
F("abdc") = 1
F(perm(3)) = 1
F(...) = 2
F(...) = 2
F(...) = 3
F(perm(7)) = 1
F(...) = 2
F(...) = 2
F(...) = 3
F(...) = 3
F(...) = 4
F(perm(13)) = 2
F(...) = 3
F(...) = 3
F(...) = 4
F(...) = 4
F(...) = 5
F(perm(19)) = 3
F(...) = 4
F(...) = 4
F(...) = 5
F(...) = 5
F(perm(24)) = 6
In words, when you go from 3 letters to 4 you get 4 copies of the table of values of F, adding (0,1,2,3) to the (1st,2nd,3rd,4th) copy respectively. In the 2nd case, for example, you already have one derangement by putting the 2nd letter in the 1st place; this simply gets added to the other derangements in the same pattern as would be true for the original 3-letter strings.
From this outline it shouldn't be too difficult (but I haven't got time right now) to write the function F. Strictly speaking the inverse of F isn't a function as it would be multi-valued, but given n, and F(n) there are only a few cases for finding m st F(m)==F(n)+1. These cases are:
n == N! where N is the number of letters in the string, there is no next permutation;
F(n+1) < F(n), the sought-for solution is perm(n+(N-1)!), ;
F(n+1) == F(n), the solution is perm(n+2);
F(n+1) > F(n), the solution is perm(n+1).
I suspect that some of this might only work for 4 letter strings, that some of these terms will have to be adjusted for K-letter permutations.
This is not O(n), but it is at least O(n²) (where n is the number of elements in the permutation, in your example 3).
First, notice that whenever you place a character in your string, you already know how much of an increase in F that's going to mean -- it's however many characters smaller than that one that haven't been added to the string yet.
This gives us another algorithm to calculate F(n):
used = set()
def get_inversions(S1):
inv = 0
for index, ch in enumerate(S1):
character = ord(ch)-ord('a')
cnt = sum(1 for x in range(character) if x not in used)
inv += cnt
used.add(character)
return inv
This is not much better than the original version, but it is useful when inverting F. You want to know the first string that is lexicographically smaller -- therefore, it makes sense to copy your original string and only change it whenever mandatory. When such changes are required, we should also change the string by the least amount possible.
To do so, let's use the information that the biggest value of F for a string with n letters is n(n-1)/2. Whenever the number of required inversions would be bigger than this amount if we didn't change the original string, this means we must swap a letter at that point. Code in Python:
used = set()
def get_inversions(S1):
inv = 0
for index, ch in enumerate(S1):
character = ord(ch)-ord('a')
cnt = sum(1 for x in range(character) if x not in used)
inv += cnt
used.add(character)
return inv
def f_recursive(n, S1, inv, ign):
if n == 0: return ""
delta = inv - (n-1)*(n-2)/2
if ign:
cnt = 0
ch = 0
else:
ch = ord(S1[len(S1)-n])-ord('a')
cnt = sum(1 for x in range(ch) if x not in used)
for letter in range(ch, len(S1)):
if letter not in used:
if cnt < delta:
cnt += 1
continue
used.add(letter)
if letter != ch: ign = True
return chr(letter+ord('a'))+f_recursive(n-1, S1, inv-cnt, ign)
def F_inv(S1):
used.clear()
inv = get_inversions(S1)
used.clear()
return f_recursive(len(S1), S1, inv+1, False)
print F_inv("acb")
It can also be made to run in O(n log n) by replacing the innermost loop with a data structure such as a binary indexed tree.
Did you try to swap two neighbor characters in the string? It seems that it can help to solve the problem. If you swap S[i] and S[j], where i < j and S[i] < S[j], then F(S) increases by one, because all other pairs of indices are not affected by this permutation.
If I'm not mistaken, F calculates the number of inversions of the permutation.
I've a string like this "FBECGHD" and i need to use MATLAB and generate all the required possible permutations? In there a specific MATLAB function that does this task or should I define a custom MATLAB function that perform this task?
Use the perms function. A string in matlab is a list of characters, so it will permute them:
A = 'FBECGHD';
perms(A)
You can also store the output (e.g. P = perms(A)), and, if A is an N-character string, P is a N!-by-N array, where each row corresponds to a permutation.
If you are interested in unique permutations, you can use:
unique(perms(A), 'rows')
to remove duplicates (otherwise something like 'ABB' would give 6 results, instead of the 3 that you might expect).
As Richante answered, P = perms(A) is very handy for this. You may also notice that P is of type char and it's not convenient to subset/select individual permutation. Below worked for me:
str = 'FBECGHD';
A = perms(str);
B = cellstr(reshape(A,7,[])');
C = unique(B);
It also appears that unique(A, 'rows') is not removing duplicate values:
>> A=[11, 11];
>> unique(A, 'rows')
ans =
11 11
However, unique(A) would:
>> unique(A)
ans =
11
I am not a matlab pro by any means and I didn't investigate this exhaustively but at least in some cases it appears that reshape is not what you want. Notice that below gives 999 and 191 as permutations of 199 which isn't true. The reshape function as written appears to operate "column-wise" on A:
>> str = '199';
A = perms(str);
B = cellstr(reshape(A,3,[])');
C = unique(B);
>> C
C =
'191'
'199'
'911'
'919'
'999'
Below does not produce 999 or 191:
B = {};
index = 1;
while true
try
substring = A(index,:);
B{index}=substring;
index = index + 1;
catch
break
end
end
C = unique(B)
C =
'199' '919' '991'