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.

#include <unordered_map>

vector<int> solution(string &S, vector<int> &P, vector<int> &Q) {
    // write your code in C++11 (g++ 4.8.2)
    vector<int> pre_sum_A;
    vector<int> pre_sum_C;
    vector<int> pre_sum_G;
    
    int cnt_A = 0;
    int cnt_C = 0;
    int cnt_G = 0;
    
    for (size_t i = 0; i < S.size(); i++) {
        if (S[i] == 'A') cnt_A++;
        else if (S[i] == 'C') cnt_C++;
        else if (S[i] == 'G') cnt_G++;
        
        pre_sum_A.push_back(cnt_A);
        pre_sum_C.push_back(cnt_C);
        pre_sum_G.push_back(cnt_G);
    }
    
    vector<int> result(P.size());
    for (int i = 0; i < int(P.size()); i++) {
        int A = (S[P[i]] == 'A') ? 1 : 0;
        int C = (S[P[i]] == 'C') ? 1 : 0;
        int G = (S[P[i]] == 'G') ? 1 : 0;
        if (pre_sum_A[Q[i]] - pre_sum_A[P[i]] + A > 0) result[i] = 1;
        else if (pre_sum_C[Q[i]] - pre_sum_C[P[i]] + C > 0) result[i] = 2;
        else if (pre_sum_G[Q[i]] - pre_sum_G[P[i]] + G > 0) result[i] = 3;
        else result[i] = 4;
    }
    
    return result;
}