Counting bounded slice codility

Question

I have recently attended a programming test in codility, and the question is to find the Number of bounded slice in an array..

I am just giving you breif explanation of

Answer 1

Now codility release their golden solution with O(N) time and space. https://codility.com/media/train/solution-count-bounded-slices.pdf

if you still confused after read the pdf, like me.. here is a very nice explanation

The solution from the pdf:

def boundedSlicesGolden(K, A):
N = len(A)

maxQ = [0] * (N + 1)
posmaxQ = [0] * (N + 1)
minQ = [0] * (N + 1)
posminQ = [0] * (N + 1)

firstMax, lastMax = 0, -1
firstMin, lastMin = 0, -1
j, result = 0, 0

for i in xrange(N):
    while (j < N):
        # added new maximum element
        while (lastMax >= firstMax and maxQ[lastMax] <= A[j]):
            lastMax -= 1
        lastMax += 1
        maxQ[lastMax] = A[j]
        posmaxQ[lastMax] = j

        # added new minimum element
        while (lastMin >= firstMin and minQ[lastMin] >= A[j]):
            lastMin -= 1
        lastMin += 1
        minQ[lastMin] = A[j]
        posminQ[lastMin] = j

        if (maxQ[firstMax] - minQ[firstMin] <= K):
            j += 1
        else:
            break
    result += (j - i)
    if result >= maxINT:
        return maxINT
    if posminQ[firstMin] == i:
        firstMin += 1
    if posmaxQ[firstMax] == i:
        firstMax += 1
return result