##### Short Problem Definition:

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.

##### Link

##### Complexity:

time complexity is O(NlogN)

space complexity is O(N)

##### Execution:

This is a graph problem, the shortest adjacent sequence is basically a shortest path in a bidirectional graph.

To calculate the shortest path I am using Breath-first-search or Dijkstra’s algorithm.

I don’t agree with the problem specification of one of the extreme cases such as [1,2,1]. I believe that the shortest path is 3, since the beginning and end are not adjacent. But it seems that Codility expects 1.

##### Solution:

```
from collections import defaultdict
def bfs_shortest_path(paths, start, end):
q = [(start, 1)]
visited_paths = set()
visited_paths.add(start)
while q:
key, distance = q.pop(0)
new_distance = distance + 1
for path in paths[key]:
if path == end:
return new_distance
elif path not in visited_paths:
visited_paths.add(path)
q.append((path, new_distance))
def solution(A):
if len(A) <= 2:
return len(A)
# I dont agree with this edge case based on the problem statement
if A[0] == A[-1]:
return 1
paths = defaultdict(set)
paths[A[0]].add(A[1])
paths[A[-1]].add(A[-2])
for i in range(1, len(A)-1):
paths[A[i]].add(A[i-1])
paths[A[i]].add(A[i+1])
return bfs_shortest_path(paths, A[0], A[-1])
```

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