[Codility] GenomicRangeQuery

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:

vector<int> solution(string &S, vector<int> &P, vector<int> &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 a vector 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.

vector<int> solution(string &S, vector<int> &P, vector<int> &Q) {
    vector<int> ans;
    int A[S.length()+1];
    int C[S.length()+1];
    int G[S.length()+1];
    int T[S.length()+1];
    A[0] = 0;
    C[0] = 0;
    G[0] = 0;
    T[0] = 0;
    for (int i = 0; i < S.length(); i++)
    {
        A[i+1] = A[i];
        C[i+1] = C[i];
        G[i+1] = G[i];
        T[i+1] = T[i];
        switch (S[i])
        {
            case 'A':
                A[i+1] = A[i] + 1;
                break;
            case 'C':
                C[i+1] = C[i] + 1;
                break;
            case 'G':
                G[i+1] = G[i] + 1;
                break;
            case 'T':
                T[i+1] = T[i] + 1;
                break;
        }
    }
    for (int i = 0; i < P.size(); i++)
    {
        if (A[P[i]] < A[Q[i]+1])
        {
            ans.push_back(1);
            continue;
        }
        if (C[P[i]] < C[Q[i]+1])
        {
            ans.push_back(2);
            continue;
        }
        if (G[P[i]] < G[Q[i]+1])
        {
            ans.push_back(3);
            continue;
        }
        if (T[P[i]] < T[Q[i]+1])
        {
            ans.push_back(4);
            continue;
        }
    }
    return ans;
}

Detected time complexity: O(N + M)