1. GenomicRangeQuery (feat.PYTHON)

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.

 

풀이

문제는 위와 같으며 뉴클레오티드 영향 유형 A : 1 C : 2 G : 3 T : 4 의 충격 계수를 가집니다.

DNA서열인 문자열 S를 입력 받아 구간내의 충격 계수가 제일 작은 문자열 순서로 저장합니다.

def solution(S, P, Q):
    N, M = len(S), len(Q)

    answer = [0] * M
    Al, Cl, Gl = [0] * N, [0] * N, [0] * N
    A, C, G = -1, -1, -1

    for i, x in enumerate(S):
        if x == "A": A = i
        if x == "C": C = i
        if x == "G": G = i
        Al[i], Cl[i], Gl[i] = A, C, G

    for i in range(M):
        answer[i] = 4
        if Al[Q[i]] <= Q[i] and Al[Q[i]] >= P[i]:
            answer[i] = 1
            continue
        if Cl[Q[i]] <= Q[i] and Cl[Q[i]] >= P[i]:
            answer[i] = 2
            continue       
        if Gl[Q[i]] <= Q[i] and Gl[Q[i]] >= P[i]:
            answer[i] = 3
            continue

    return answer

print(solution("CAGCCTA", [2,5,0], [4,5,6]))

Prefix_sum 알고리즘을 모르면 풀지 못하는 문제로 누적합을 구하고 구간내의 갱신된 값이 

있는지로 검증하는 문제입니다.