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December 2010

PrefixSet edition (2010-10)

Calculate the number of slices in which (maximum - minimum <= K).

An integer K and a non-empty array A consisting of N integers are given.

A pair of integers (P, Q), such that 0 ≤ P ≤ Q < N, is called a *slice* of array A.

A *bounded slice* is a slice in which the difference between the maximum and minimum values in the slice is less than or equal to K. More precisely it is a slice, such that max(A[P], A[P + 1], ..., A[Q]) − min(A[P], A[P + 1], ..., A[Q]) ≤ K.

The goal is to calculate the number of bounded slices.

For example, consider K = 2 and array A such that:

There are exactly nine bounded slices: (0, 0), (0, 1), (1, 1), (1, 2), (1, 3), (2, 2), (2, 3), (3, 3), (4, 4).

Write a function:

class Solution { public int solution(int K, int[] A); }

that, given an integer K and a non-empty array A of N integers, returns the number of bounded slices of array A.

If the number of bounded slices is greater than 1,000,000,000, the function should return 1,000,000,000.

For example, given:

the function should return 9, as explained above.

Write an ** efficient** algorithm for the following assumptions:

- N is an integer within the range [1..100,000];
- K is an integer within the range [0..1,000,000,000];
- each element of array A is an integer within the range [−1,000,000,000..1,000,000,000].

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