How to find all occurrences of a non - contiguous substring in Python?

Question

Premise:

I am currently working on the following problem:

http://rosalind.info/problems/sseq/

I must find the index combinations of all occurrences of a substring in a string, where the substring is not necessarily contiguous.

My testing parameters:

Main_String = ACGGTTAACGTGACGGTTAAGSSGSSTSSTSSASSA
Substring = GGTTAA

Non-contiguous means that an occurrence of the Substring in the Main_String may look like this: GGSTTSAASSS where the substring is GGTTAA and the MAIN_STRING - GGSTTSAASSS .

The substring, although cut by random characters (S in our case) is still to be found in the main string. As such, a possible answer would be (format:Letter((index + 1) in Main_String)) G(1)G(2)T(4)T(5)A(7)A(8) = 1, 2, 4, 5, 7, 8. That is easy enough to get for the first match. I need to get all possible variations though, so if we use my testing parameters from above, correct answers would be:

3, 4, 5, 6, 7, 8 and 3, 12, 17, 18, 19, 20 and 3, 15, 17, 18, 19, 20 and so on up to 21, 24, 27, 30, 33, 36 .

Question:

I need an algorithm that can provide me with all possible variations of a non-contiguous substring in a given string.

Issue:

This is the code I have so far, which works to an extent, but does not return all possible variations, only some of them.

    dna = ''
counter = -1
dna_subseq = ''
dna_subseq_indexes = []


with open('Rosalind_dna.txt', 'r') as file:
    data = file.read().split('\n')
    for line in data:
        if line == '':
            continue
        if 'Rosalind' in line and counter < 1:
            counter += 1
            continue
        elif 'Rosalind' not in line and counter < 1:
            dna += line
        elif 'Rosalind' not in line and counter >= 1:
            dna_subseq += line

result = 0
dna_subseq_minus_start = dna_subseq[1:]


def find_next(start_parameter, base):
    result_func = dna.find(base, start_parameter)
    if result_func + 1 in dna_subseq_indexes_subcombo:
        if result_func + 1 == 0:
            return
        find_next(start_parameter + 1, base)
    else:
        dna_subseq_indexes_subcombo.append(result_func + 1)
        return


for index, value in enumerate(dna):
    global_start = index
    result = 0
    while result != -1:
        dna_subseq_indexes_subcombo = []
        if value == dna_subseq[0]:
            dna_subseq_indexes_subcombo.append(index + 1)
            Flag = True
            for base in dna_subseq_minus_start:
                if Flag:
                    start = global_start
                    Flag = False
                result = dna.find(base, start)
                if result + 1 in dna_subseq_indexes_subcombo:
                    find_next(start + 1, base)
                else:
                    dna_subseq_indexes_subcombo.append(result + 1)
                    start += 1
            dna_subseq_indexes.append(dna_subseq_indexes_subcombo)
            global_start += 1
        else:
            break


final_result = []
for x in dna_subseq_indexes:
    test = x.copy()
    test.sort()
    if test == x:
        final_result.append(x)
    else:
        continue
print(final_result)

Answer 1

I'm not sure your algorithm could find all solutions even if it would be fixed. I tried this logic instead : Find the initial sequence closest to the left of dna and search all declinations going from right to left recursively. This way the solutions are automatically sorted.

dna        = 'ACGGTTAACGTGACGGTTAAGSSGSSTSSTSSASSA'
dna_len    = len(dna)
dna_subseq = 'GGTTAA'
subseq_len = len(dna_subseq)
count      = 0
print_mode = True # Prints the solutions, set to False to collect them instead

# Finds a single solution starting from the previous one or from a null solution
def find_one_solution(prev_solution, subseq_start, dna_start):
    global dna, dna_subseq, subseq_len, count, mode
    searched   = dna_subseq[subseq_start]
    coll       = prev_solution[:subseq_start]
    subseq_idx = subseq_start

    for i in range(dna_start, len(dna), 1):
        letter = dna[i]
        if letter == searched:
            coll.append(i)
            subseq_idx += 1
        if (subseq_idx == subseq_len): break
        else: searched = dna_subseq[subseq_idx]
    if len(coll) < subseq_len: return None
    count += 1
    if (print_mode): print(coll)
    return coll

# Recursive function
def find_all_solutions(solutions, solution, subseq_start, limit):
    global dna, dna_subseq, subseq_len, print_mode

    for start in range(subseq_len-1, limit-1, -1):
        # last element
        if start == subseq_len-1:
            while True:
                temp = find_one_solution(solution, start, solution[-1]+1)
                if temp == None: break
                else: solution = temp
                if (not print_mode): solutions.append(solution)
        # other elements
        else:
            # finds the next solution
            temp = find_one_solution(solution, start, solution[start]+1)
            if temp == None:
                continue
            else:
                solution = temp
                if (not print_mode): solutions.append(solution)
                # and restarts from end with subseq_start as the left limit
                find_all_solutions(solutions, solution, subseq_len-1, start)


def main():
    all_solutions       = []
    # Finds the initial solution
    initial_solution    = [0] * subseq_len
    initial_solution    = find_one_solution(initial_solution, 0, initial_solution[0])
    if initial_solution == None:
        print("No solution found")
    else:
        if (not print_mode): all_solutions.append(initial_solution)
        # Finds all other solutions
        find_all_solutions(all_solutions, initial_solution, subseq_len-1, 0)
        if (not print_mode): print(all_solutions)
        print("Total count:", count)


if __name__=="__main__":
    main()


#289 solutions found : [[2, 3, 4, 5, 6, 7], [2, 3, 4, 5, 6, 12], [2, 3, 4, 5, 6, 18], [2, 3, 4, 5, 6, 19], [2, 3, 4, 5, 6, 32], [2, 3, 4, 5, 6, 35], [2, 3, 4, 5, 7, 12], [2, 3, 4, 5, 7, 18], [2, 3, 4, 5, 7, 19], [2, 3, 4, 5, 7, 32], [2, 3, 4, 5, 7, 35], [2, 3, 4, 5, 12, 18], [2, 3, 4, 5, 12, 19], [2, 3, 4, 5, 12, 32], [2, 3, 4, 5, 12, 35], [2, 3, 4, 5, 18, 19], [2, 3, 4, 5, 18, 32], [2, 3, 4, 5, 18, 35], [2, 3, 4, 5, 19, 32], [2, 3, 4, 5, 19, 35], [2, 3, 4, 5, 32, 35], [2, 3, 4, 10, 12, 18], [2, 3, 4, 10, 12, 19], [2, 3, 4, 10, 12, 32], [2, 3, 4, 10, 12, 35], [2, 3, 4, 10, 18, 19], [2, 3, 4, 10, 18, 32], [2, 3, 4, 10, 18, 35], [2, 3, 4, 10, 19, 32], [2, 3, 4, 10, 19, 35], [2, 3, 4, 10, 32, 35], [2, 3, 4, 16, 18, 19], [2, 3, 4, 16, 18, 32], [2, 3, 4, 16, 18, 35], [2, 3, 4, 16, 19, 32], [2, 3, 4, 16, 19, 35], [2, 3, 4, 16, 32, 35], [2, 3, 4, 17, 18, 19], [2, 3, 4, 17, 18, 32], [2, 3, 4, 17, 18, 35], [2, 3, 4, 17, 19, 32], [2, 3, 4, 17, 19, 35], [2, 3, 4, 17, 32, 35], [2, 3, 4, 26, 32, 35], [2, 3, 4, 29, 32, 35], [2, 3, 5, 10, 12, 18], [2, 3, 5, 10, 12, 19], [2, 3, 5, 10, 12, 32], [2, 3, 5, 10, 12, 35], [2, 3, 5, 10, 18, 19], [2, 3, 5, 10, 18, 32], [2, 3, 5, 10, 18, 35], [2, 3, 5, 10, 19, 32], [2, 3, 5, 10, 19, 35], [2, 3, 5, 10, 32, 35], [2, 3, 5, 16, 18, 19], [2, 3, 5, 16, 18, 32], [2, 3, 5, 16, 18, 35], [2, 3, 5, 16, 19, 32], [2, 3, 5, 16, 19, 35], [2, 3, 5, 16, 32, 35], [2, 3, 5, 17, 18, 19], [2, 3, 5, 17, 18, 32], [2, 3, 5, 17, 18, 35], [2, 3, 5, 17, 19, 32], [2, 3, 5, 17, 19, 35], [2, 3, 5, 17, 32, 35], [2, 3, 5, 26, 32, 35], [2, 3, 5, 29, 32, 35], [2, 3, 10, 16, 18, 19], [2, 3, 10, 16, 18, 32], [2, 3, 10, 16, 18, 35], [2, 3, 10, 16, 19, 32], [2, 3, 10, 16, 19, 35], [2, 3, 10, 16, 32, 35], [2, 3, 10, 17, 18, 19], [2, 3, 10, 17, 18, 32], [2, 3, 10, 17, 18, 35], [2, 3, 10, 17, 19, 32], [2, 3, 10, 17, 19, 35], [2, 3, 10, 17, 32, 35], [2, 3, 10, 26, 32, 35], [2, 3, 10, 29, 32, 35], [2, 3, 16, 17, 18, 19], [2, 3, 16, 17, 18, 32], [2, 3, 16, 17, 18, 35], [2, 3, 16, 17, 19, 32], [2, 3, 16, 17, 19, 35], [2, 3, 16, 17, 32, 35], [2, 3, 16, 26, 32, 35], [2, 3, 16, 29, 32, 35], [2, 3, 17, 26, 32, 35], [2, 3, 17, 29, 32, 35], [2, 3, 26, 29, 32, 35], [2, 9, 10, 16, 18, 19], [2, 9, 10, 16, 18, 32], [2, 9, 10, 16, 18, 35], [2, 9, 10, 16, 19, 32], [2, 9, 10, 16, 19, 35], [2, 9, 10, 16, 32, 35], [2, 9, 10, 17, 18, 19], [2, 9, 10, 17, 18, 32], [2, 9, 10, 17, 18, 35], [2, 9, 10, 17, 19, 32], [2, 9, 10, 17, 19, 35], [2, 9, 10, 17, 32, 35], [2, 9, 10, 26, 32, 35], [2, 9, 10, 29, 32, 35], [2, 9, 16, 17, 18, 19], [2, 9, 16, 17, 18, 32], [2, 9, 16, 17, 18, 35], [2, 9, 16, 17, 19, 32], [2, 9, 16, 17, 19, 35], [2, 9, 16, 17, 32, 35], [2, 9, 16, 26, 32, 35], [2, 9, 16, 29, 32, 35], [2, 9, 17, 26, 32, 35], [2, 9, 17, 29, 32, 35], [2, 9, 26, 29, 32, 35], [2, 11, 16, 17, 18, 19], [2, 11, 16, 17, 18, 32], [2, 11, 16, 17, 18, 35], [2, 11, 16, 17, 19, 32], [2, 11, 16, 17, 19, 35], [2, 11, 16, 17, 32, 35], [2, 11, 16, 26, 32, 35], [2, 11, 16, 29, 32, 35], [2, 11, 17, 26, 32, 35], [2, 11, 17, 29, 32, 35], [2, 11, 26, 29, 32, 35], [2, 14, 16, 17, 18, 19], [2, 14, 16, 17, 18, 32], [2, 14, 16, 17, 18, 35], [2, 14, 16, 17, 19, 32], [2, 14, 16, 17, 19, 35], [2, 14, 16, 17, 32, 35], [2, 14, 16, 26, 32, 35], [2, 14, 16, 29, 32, 35], [2, 14, 17, 26, 32, 35], [2, 14, 17, 29, 32, 35], [2, 14, 26, 29, 32, 35], [2, 15, 16, 17, 18, 19], [2, 15, 16, 17, 18, 32], [2, 15, 16, 17, 18, 35], [2, 15, 16, 17, 19, 32], [2, 15, 16, 17, 19, 35], [2, 15, 16, 17, 32, 35], [2, 15, 16, 26, 32, 35], [2, 15, 16, 29, 32, 35], [2, 15, 17, 26, 32, 35], [2, 15, 17, 29, 32, 35], [2, 15, 26, 29, 32, 35], [2, 20, 26, 29, 32, 35], [2, 23, 26, 29, 32, 35], [3, 9, 10, 16, 18, 19], [3, 9, 10, 16, 18, 32], [3, 9, 10, 16, 18, 35], [3, 9, 10, 16, 19, 32], [3, 9, 10, 16, 19, 35], [3, 9, 10, 16, 32, 35], [3, 9, 10, 17, 18, 19], [3, 9, 10, 17, 18, 32], [3, 9, 10, 17, 18, 35], [3, 9, 10, 17, 19, 32], [3, 9, 10, 17, 19, 35], [3, 9, 10, 17, 32, 35], [3, 9, 10, 26, 32, 35], [3, 9, 10, 29, 32, 35], [3, 9, 16, 17, 18, 19], [3, 9, 16, 17, 18, 32], [3, 9, 16, 17, 18, 35], [3, 9, 16, 17, 19, 32], [3, 9, 16, 17, 19, 35], [3, 9, 16, 17, 32, 35], [3, 9, 16, 26, 32, 35], [3, 9, 16, 29, 32, 35], [3, 9, 17, 26, 32, 35], [3, 9, 17, 29, 32, 35], [3, 9, 26, 29, 32, 35], [3, 11, 16, 17, 18, 19], [3, 11, 16, 17, 18, 32], [3, 11, 16, 17, 18, 35], [3, 11, 16, 17, 19, 32], [3, 11, 16, 17, 19, 35], [3, 11, 16, 17, 32, 35], [3, 11, 16, 26, 32, 35], [3, 11, 16, 29, 32, 35], [3, 11, 17, 26, 32, 35], [3, 11, 17, 29, 32, 35], [3, 11, 26, 29, 32, 35], [3, 14, 16, 17, 18, 19], [3, 14, 16, 17, 18, 32], [3, 14, 16, 17, 18, 35], [3, 14, 16, 17, 19, 32], [3, 14, 16, 17, 19, 35], [3, 14, 16, 17, 32, 35], [3, 14, 16, 26, 32, 35], [3, 14, 16, 29, 32, 35], [3, 14, 17, 26, 32, 35], [3, 14, 17, 29, 32, 35], [3, 14, 26, 29, 32, 35], [3, 15, 16, 17, 18, 19], [3, 15, 16, 17, 18, 32], [3, 15, 16, 17, 18, 35], [3, 15, 16, 17, 19, 32], [3, 15, 16, 17, 19, 35], [3, 15, 16, 17, 32, 35], [3, 15, 16, 26, 32, 35], [3, 15, 16, 29, 32, 35], [3, 15, 17, 26, 32, 35], [3, 15, 17, 29, 32, 35], [3, 15, 26, 29, 32, 35], [3, 20, 26, 29, 32, 35], [3, 23, 26, 29, 32, 35], [9, 11, 16, 17, 18, 19], [9, 11, 16, 17, 18, 32], [9, 11, 16, 17, 18, 35], [9, 11, 16, 17, 19, 32], [9, 11, 16, 17, 19, 35], [9, 11, 16, 17, 32, 35], [9, 11, 16, 26, 32, 35], [9, 11, 16, 29, 32, 35], [9, 11, 17, 26, 32, 35], [9, 11, 17, 29, 32, 35], [9, 11, 26, 29, 32, 35], [9, 14, 16, 17, 18, 19], [9, 14, 16, 17, 18, 32], [9, 14, 16, 17, 18, 35], [9, 14, 16, 17, 19, 32], [9, 14, 16, 17, 19, 35], [9, 14, 16, 17, 32, 35], [9, 14, 16, 26, 32, 35], [9, 14, 16, 29, 32, 35], [9, 14, 17, 26, 32, 35], [9, 14, 17, 29, 32, 35], [9, 14, 26, 29, 32, 35], [9, 15, 16, 17, 18, 19], [9, 15, 16, 17, 18, 32], [9, 15, 16, 17, 18, 35], [9, 15, 16, 17, 19, 32], [9, 15, 16, 17, 19, 35], [9, 15, 16, 17, 32, 35], [9, 15, 16, 26, 32, 35], [9, 15, 16, 29, 32, 35], [9, 15, 17, 26, 32, 35], [9, 15, 17, 29, 32, 35], [9, 15, 26, 29, 32, 35], [9, 20, 26, 29, 32, 35], [9, 23, 26, 29, 32, 35], [11, 14, 16, 17, 18, 19], [11, 14, 16, 17, 18, 32], [11, 14, 16, 17, 18, 35], [11, 14, 16, 17, 19, 32], [11, 14, 16, 17, 19, 35], [11, 14, 16, 17, 32, 35], [11, 14, 16, 26, 32, 35], [11, 14, 16, 29, 32, 35], [11, 14, 17, 26, 32, 35], [11, 14, 17, 29, 32, 35], [11, 14, 26, 29, 32, 35], [11, 15, 16, 17, 18, 19], [11, 15, 16, 17, 18, 32], [11, 15, 16, 17, 18, 35], [11, 15, 16, 17, 19, 32], [11, 15, 16, 17, 19, 35], [11, 15, 16, 17, 32, 35], [11, 15, 16, 26, 32, 35], [11, 15, 16, 29, 32, 35], [11, 15, 17, 26, 32, 35], [11, 15, 17, 29, 32, 35], [11, 15, 26, 29, 32, 35], [11, 20, 26, 29, 32, 35], [11, 23, 26, 29, 32, 35], [14, 15, 16, 17, 18, 19], [14, 15, 16, 17, 18, 32], [14, 15, 16, 17, 18, 35], [14, 15, 16, 17, 19, 32], [14, 15, 16, 17, 19, 35], [14, 15, 16, 17, 32, 35], [14, 15, 16, 26, 32, 35], [14, 15, 16, 29, 32, 35], [14, 15, 17, 26, 32, 35], [14, 15, 17, 29, 32, 35], [14, 15, 26, 29, 32, 35], [14, 20, 26, 29, 32, 35], [14, 23, 26, 29, 32, 35], [15, 20, 26, 29, 32, 35], [15, 23, 26, 29, 32, 35], [20, 23, 26, 29, 32, 35]]

To test the validity of the algorithm, I used a simpler sequence from which all the solutions are easy to find manually :

dna = 'AAAAAAAA'
dna_subseq = 'AAAA'

Note that I worked with zero based indices because it's simpler, but you could easily add 1 to all results if you need it.