Given an array of integers arr, you are initially positioned at the first index of the array.
In one step you can jump from index i to index:
i + 1 where: i + 1 < arr.length.
i - 1 where: i - 1 >= 0.
j where: arr[i] == arr[j] and i != j.
Return the minimum number of steps to reach the last index of the array.
Notice that you can not jump outside of the array at any time.
Example 1:
Input: arr = [100,-23,-23,404,100,23,23,23,3,404]
Output: 3
Explanation: You need three jumps from index 0 --> 4 --> 3 --> 9. Note that index 9 is the last index of the array.
Example 2:
Input: arr = [7]
Output: 0
Explanation: Start index is the last index. You don't need to jump.
Example 3:
Input: arr = [7,6,9,6,9,6,9,7]
Output: 1
Explanation: You can jump directly from index 0 to index 7 which is last index of the array.
Example 4:
Input: arr = [6,1,9]
Output: 2
Example 5:
Input: arr = [11,22,7,7,7,7,7,7,7,22,13]
Output: 3
Constraints:
1 <= arr.length <= 5 * 10^4
-10^8 <= arr[i] <= 10^8
class Solution:
  def minJumps(self, arr):
    nei = collections.defaultdict(list)
    _ = [nei[x].append(i) for i, x in enumerate(arr)]

    frontier = collections.deque([(0,0)])
    num_met, pos_met = set(), set()
    while frontier:
        pos, step = frontier.popleft() # state: position, step
        if pos == len(arr) - 1: return step
        num = arr[pos]
        pos_met.add(pos) # track explored positions

        for p in [pos - 1, pos + 1] + nei[num] * (num not in num_met):
            if p in pos_met or not 0 <= p < len(arr): continue
            frontier.append((p, step + 1))

        num_met.add(num) # track explored values
class Solution:
  def minJumps(self, arr):
    nei = collections.defaultdict(list)
    _ = [nei[x].append(i) for i, x in enumerate(arr)]

    frontier = collections.deque([(0,0)])
    num_met, pos_met = set(), set()
    while frontier:
        pos, step = frontier.popleft() # state: position, step
        if pos == len(arr) - 1: return step
        num = arr[pos]
        pos_met.add(pos) # track explored positions

        for p in [pos - 1, pos + 1] + nei[num] * (num not in num_met):
            if p in pos_met or not 0 <= p < len(arr): continue
            frontier.append((p, step + 1))

        num_met.add(num) # track explored values