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December 2010

PrefixSet edition (2010-10)

Calculate the shortest adjacent sequence for given array A.

A non-empty zero-indexed array A consisting of N integers is given. Two integers P and Q are called *adjacent in array A* if there exists an index 0 ≤ K < N−1 such that:

- P = A[K] and Q = A[K+1], or
- Q = A[K] and P = A[K+1].

A non-empty zero-indexed sequence B consisting of M integers is called *adjacent in array A* if the following conditions hold:

- B[0] = A[0];
- B[M−1] = A[N−1];
- B[K] and B[K+1] are adjacent in A for 0 ≤ K < M−1.

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

The following sequences are adjacent in array A:

- [1, 10, 6, 5, 10, 7, 5, 2];
- [1, 10, 7, 5, 2];
- [1, 10, 6, 5, 10, 6, 5, 10, 7, 5, 2];
- [1, 10, 5, 2].

The last sequence is the shortest possible sequence adjacent in array A.

Write a function

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

that, given a non-empty zero-indexed array A consisting of N integers, returns the length of the shortest sequence adjacent in array A.

For example, given array A such that:

the function should return 4, as explained above.

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

- N is an integer within the range [1..100,000];
- each element of array A is an integer within the range [−2,147,483,648..2,147,483,647].

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