# Deepest pit of an array

Following is based on a problem description from a Codility test, as a task in an interview.

## DeepestPit - problem description

A non-empty zero-indexed array B consisting of M integers is given. A pit in this array is any triplet of integers (X, Y, Z) such that:

• 0 ≤ X < Y < Z < M
• sequence [B[X], B[X+1], ..., B[Y]] is strictly decreasing, i.e. B[X] > B[X+1] > ... > B[Y]
• sequence B[Y], B[Y+1], ..., B[Z] is strictly increasing, i.e. B[Y] < B[Y+1] < ... < B[Z]

The depth of a pit (X, Y, Z) is the number min{B[X] − B[Y], B[Z] − B[Y]}.

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

B = 0
B = 2
B = 7
B = -4
B = 0
B = 4
B = 0
B = -6
B = 4
B = 6


Triplet (2, 3, 4) is one of pits in this array, because sequence [B, B] is strictly decreasing (7 > −4) and sequence [B, B] is strictly increasing (−4 < 0). Its depth is min{B − B, B − B} = 4. Triplet (2, 3, 5) is another pit with depth 8. Triplet (5, 7, 8) is yet another pit with depth 10. There is no pit in this array deeper (i.e. having depth greater) than 10.

Write a function:

function deepest_pit(B)


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

For example, for the above array B, the function should return 10, as explained above.

Write an efficient algorithm for the function.

Assume that:

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

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

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

Complexity:

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

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

My solution, as follows, gets a task score of 100% (100% for correctness and 100% for performance). (A previous version only got 26%, with 44% correctness and 0% performance.)

function deepest_pit(B) {
// write your code in JavaScript (Node.js 8.9.4)

var M = B.length,
depth = -1;

if (M < 3) {
return depth;
}

var X, Y, Z;
var i = 0, j, k;

while (i < M - 2) {
X = B[i];
// console.log("i = ", i, "X = ", X)
j = i + 1;
while (B[j] < B[j - 1] && j < M - 1) {
j++;
}
if (j === i + 1) {
i++;
continue;
}
j = j - 1;
Y = B[j];
// console.log("i = ", i, "Y = ", Y)
k = j + 1;
while (B[k] > B[k - 1] && k < M) {
k++;
}
if (k === j + 1) {
i++;
continue;
}
k = k - 1;
Z = B[k];
depth = Math.max(depth, Math.min(p - Y, Z - Y));
// console.log("depth is", depth)
i++;
}

return depth;
}


JSFiddle with the above code, plus tests.

• I think this could make a good Code Review question once the bugs have been resolved. Please finish debugging it and update the question with working code, then you'll likely get some good reviews. – Toby Speight Mar 5 at 8:41
• I have edited the while loops to check the previous element (j-1 and k-1, not q and r, respectively). I think this will work now. I will do some more testing. – James Ray Mar 5 at 23:50
• Edited accordingly, I am getting a 100% task score now: 100% for correctness and 100% for performance. – James Ray Mar 6 at 0:45
• The most recent edit implies that you don't want the question to be posted. – rolfl Mar 6 at 3:54