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This is the question from a Codility test, as a task in an interview:

DeepestPit - problem description

A non-empty zero-indexed array A consisting of N integers is given. A pit in this array is any triplet of integers (P, Q, R) such that:

·         0 ≤ P < Q < R
< N;

·        
sequence [A[P], A[P+1], ..., A[Q]] is strictly decreasing,
i.e.
A[P] > A[P+1] > ... >
A[Q];

·         sequence
A[Q], A[Q+1], ..., A[R] is strictly increasing,
i.e. A[Q] <
A[Q+1] < ... < A[R].

The depth of a pit (P, Q, R) is the number min{A[P] − A[Q], A[R] − A[Q]}.

For example, consider array A consisting of 10 elements such that:

A[0] = 0

A[1] = 1

A[2] = 3

A[3] = -2

A[4] = 0

A[5] = 1

A[6] = 0

A[7] = -3

A[8] = 2

A[9] = 3

Triplet (2, 3, 4) is one of pits in this array, because sequence [A[2], A[3]] is strictly decreasing (3 > −2) and sequence [A[3], A[4]] is strictly increasing (−2 < 0). Its depth is min{A[2] − A[3], A[4] − A[3]} = 2. Triplet (2, 3, 5) is another pit with depth 3. Triplet (5, 7, 8) is yet another pit with depth 4. There is no pit in this array deeper (i.e. having depth greater) than 4.

Write a function:

function solution(A)

that, given a non-empty zero-indexed array A consisting of N integers, returns the depth of the deepest pit in array A. The function should return −1 if there are no pits in array A.

For example, for the above array A, the function should return 4, as explained above.

Assume that:

• N is an integer within the range [1..1,000,000];
  
  


• each element of array A is an integer within the range
  [−100,000,000..100,000,000].

Write an efficient algorithm for the function.

(A previous test instead stated the complexity conditions as follows.)

Complexity:

·         expected worst-case time complexity is O(N);

·         expected worst-case space complexity is O(N), beyond input storage (not counting the storage required for input arguments).

My solution, as follows, got a score of 26%, with 44% for correctness and 0% for performance. I'd like to improve it to get a 100% score. Unfortunately I can't find where to do a rerun of the task, so it will have to be verified in other ways e.g. via JSFiddle and JSPerf.

// you can write to stdout for debugging purposes, e.g.

// console.log('this is a debug message');



function solution(A) {

    // write your code in JavaScript (Node.js 8.9.4)

    // A.sort((a, b) => (a - b))



    var n = A.length,

        depth = -1;



    if (n < 3) {

        return depth;

    }



    var p, q, r;

    var i = 0, j, k;



    while (i < n - 2) {

        p = A[i];

        // console.log("i = ", i, "p = ", p)

        j = i + 1;

        while (A[j] < p) {

            j++;

        }

        if (j === i + 1) {

            i++;

            continue;

        }

        j = j - 1;

        q = A[j];

        // console.log("i = ", i, "q = ", q)

        k = j + 1;

        while (A[k] > q) {

            k++;

        }

        if (k === j + 1) {

            i++;

            continue;

        }

        k = k - 1;

        r = A[k];

        current_depth = Math.min(p - q, r - q);

        if (current_depth > depth) {

            depth = current_depth;

        }

        // console.log("depth is", depth)

        i++;

    }



    return depth;

}