Find the minimal average of any slice containing at least two elements.

Task description

A non-empty array A consisting of N integers is given. A pair of integers (P, Q), such that 0 ≤ P < Q < N, is called a slice of array A (notice that the slice contains at least two elements). The average of a slice (P, Q) is the sum of A[P] + A[P + 1] + … + A[Q] divided by the length of the slice. To be precise, the average equals (A[P] + A[P + 1] + … + A[Q]) / (Q − P + 1).

Determine whether a given string of parentheses (multiple types) is properly nested

For example, array A such that: A[0] = 4 A[1] = 2 A[2] = 2 A[3] = 5 A[4] = 1 A[5] = 5 A[6] = 8

contains the following example slices:

  • slice (1, 2), whose average is (2 + 2) / 2 = 2;
  • slice (3, 4), whose average is (5 + 1) / 2 = 3;
  • slice (1, 4), whose average is (2 + 2 + 5 + 1) / 4 = 2.5.

The goal is to find the starting position of a slice whose average is minimal.

Write a function:

function solution(A);

that, given a non-empty array A consisting of N integers, returns the starting position of the slice with the minimal average. If there is more than one slice with a minimal average, you should return the smallest starting position of such a slice.

For example, given array A such that: A[0] = 4 A[1] = 2 A[2] = 2 A[3] = 5 A[4] = 1 A[5] = 5 A[6] = 8

the function should return 1, as explained above.

Write an efficient algorithm for the following assumptions:

  • N is an integer within the range [2..100,000];
  • each element of array A is an integer within the range [−10,000..10,000].
function solution(A) {
    let two = [];
    let three = [];
    let avg = Infinity;
    let index = -1;
    
    for(let i=1; i<A.length; i++) {
        two[i] = (A[i] + A[i-1])/2;
        if(two[i] < avg) {
            avg = two[i];
            index = i-1;
        }
        if(i>1) {
            three[i] = (A[i] + A[i-1] + A[i-2])/3;
            if(three[i] < avg) {
                avg = three[i];
                index = i-2;
            }
        }
    }
    
    return index;
}

Odd Occurrences In Array Find value odd number of elements.

More similar Questions:

Compute number of distinct values in an array.

Determine whether a given string of parentheses (multiple types) is properly nested

Compute the number of intersections in a sequence of discs.

N voracious fish are moving along a river. Calculate how many fish are alive.

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