genomic_range_query.py

#[Codility]
# A DNA sequence can be represented as a string consisting of the letters A, C, G and T, which correspond to the types of successive nucleotides in the sequence. Each nucleotide has an impact factor, which is an integer. Nucleotides of types A, C, G and T have impact factors of 1, 2, 3 and 4, respectively. You are going to answer several queries of the form: What is the minimal impact factor of nucleotides contained in a particular part of the given DNA sequence?

# The DNA sequence is given as a non-empty string S = S[0]S[1]...S[N-1] consisting of N characters. There are M queries, which are given in non-empty arrays P and Q, each consisting of M integers. The K-th query (0 ≤ K < M) requires you to find the minimal impact factor of nucleotides contained in the DNA sequence between positions P[K] and Q[K] (inclusive).

# For example, consider string S = CAGCCTA and arrays P, Q such that:

#     P[0] = 2    Q[0] = 4
#     P[1] = 5    Q[1] = 5
#     P[2] = 0    Q[2] = 6
# The answers to these M = 3 queries are as follows:

# The part of the DNA between positions 2 and 4 contains nucleotides G and C (twice), whose impact factors are 3 and 2 respectively, so the answer is 2.
# The part between positions 5 and 5 contains a single nucleotide T, whose impact factor is 4, so the answer is 4.
# The part between positions 0 and 6 (the whole string) contains all nucleotides, in particular nucleotide A whose impact factor is 1, so the answer is 1.
# Write a function:

# def solution(S, P, Q)

# that, given a non-empty string S consisting of N characters and two non-empty arrays P and Q consisting of M integers, returns an array consisting of M integers specifying the consecutive answers to all queries.

# Result array should be returned as an array of integers.

# For example, given the string S = CAGCCTA and arrays P, Q such that:

#     P[0] = 2    Q[0] = 4
#     P[1] = 5    Q[1] = 5
#     P[2] = 0    Q[2] = 6
# the function should return the values [2, 4, 1], as explained above.

# Write an efficient algorithm for the following assumptions:

# N is an integer within the range [1..100,000];
# M is an integer within the range [1..50,000];
# each element of arrays P, Q is an integer within the range [0..N − 1];
# P[K] ≤ Q[K], where 0 ≤ K < M;
# string S consists only of upper-case English letters A, C, G, T.

#==== Solution 1: correct but failling performance O(n*m)
# https://app.codility.com/demo/results/trainingSXFMWK-KJT/
def solution(S, P, Q):
    
    impact_dict = {"A":1, "C":2, "G":3, "T":4}

    ans = []

    for k in range(len(P)):
        i = P[k]
        j = Q[k]
        sub_sequence = S[i:j+1]
        min_impact = impact_dict[sub_sequence[0]]
        
        for letter in sub_sequence:
            if impact_dict[letter] < min_impact:
                min_impact = impact_dict[letter]
        ans.append(min_impact)
    
    return ans

#==== Using set in an attempt to improve performance - does not work 
# https://app.codility.com/demo/results/trainingSXFMWK-KJT/

def solution(S, P, Q):
    
    impact_dict = {"A":1, "C":2, "G":3, "T":4}

    ans = []

    m = len(P)

    if len(set(S)) == 1:
        ans = [impact_dict[S[0]]] * m
        return ans

    for k in range(len(P)):
        i = P[k]
        j = Q[k]
        sub_sequence = S[i:j+1]
        sub_sequence_set = set(sub_sequence) # 0(n)

        min_impact = impact_dict[sub_sequence[0]]
        
        for letter in sub_sequence_set: # O(n), max n = 4 since there are 4 letters
            if impact_dict[letter] < min_impact:
                min_impact = impact_dict[letter]
        ans.append(min_impact)
    
    return ans

#==== 100% Solution: O(n+m)
# https://app.codility.com/demo/results/training7TASPT-A6G/
def solution(S, P, Q):
    res = []
    for i in range(len(P)):
        if 'A' in S[P[i]:Q[i]+1]: #O(n)
            res.append(1)
        elif 'C' in S[P[i]:Q[i]+1]: #O(n)
            res.append(2)
        elif 'G' in S[P[i]:Q[i]+1]: #O(n)
            res.append(3)
        else:
            res.append(4)
    return res