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GenomicRangeQuery (Lesson 5)

Instructions​

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:

function 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 and 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​

function solution(A) {
  let answer = 0;
  let accNum = (A[0] + A[1]) / 2;

  for (let i = 2, listLength = A.length; i < listLength; i++) {
    const preCurAvg = (A[i - 1] + A[i]) / 2;

    if (accNum > preCurAvg) {
      accNum = preCurAvg;
      answer = i - 1;
    }
    if (A[i + 1]) {
      const preCurNextAvg = (A[i - 1] + A[i] + A[i + 1]) / 3;

      if (accNum > preCurNextAvg) {
        accNum = preCurNextAvg;
        answer = i - 1;
      }
    }
  }

  return answer;
}

Review​

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References​