<p>Given an array of&nbsp;integers <code>arr</code>, you are initially positioned at the first index of the array.</p>

<p>In one step you can jump from index <code>i</code> to index:</p>

<ul>
	<li><code>i + 1</code> where:&nbsp;<code>i + 1 &lt; arr.length</code>.</li>
	<li><code>i - 1</code> where:&nbsp;<code>i - 1 &gt;= 0</code>.</li>
	<li><code>j</code> where: <code>arr[i] == arr[j]</code> and <code>i != j</code>.</li>
</ul>

<p>Return <em>the minimum number of steps</em> to reach the <strong>last index</strong> of the array.</p>

<p>Notice that you can not jump outside of the array at any time.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> arr = [100,-23,-23,404,100,23,23,23,3,404]
<strong>Output:</strong> 3
<strong>Explanation:</strong> You need three jumps from index 0 --&gt; 4 --&gt; 3 --&gt; 9. Note that index 9 is the last index of the array.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> arr = [7]
<strong>Output:</strong> 0
<strong>Explanation:</strong> Start index is the last index. You do not need to jump.
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> arr = [7,6,9,6,9,6,9,7]
<strong>Output:</strong> 1
<strong>Explanation:</strong> You can jump directly from index 0 to index 7 which is last index of the array.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= arr.length &lt;= 5 * 10<sup>4</sup></code></li>
	<li><code>-10<sup>8</sup> &lt;= arr[i] &lt;= 10<sup>8</sup></code></li>
</ul>

from collections import deque
from collections import defaultdict

class Solution:
    def minJumps(self, arr):
        val_visited, idx_visited = set(), set()
        val_d = defaultdict(list)
        for i in range(len(arr)-1, -1, -1):
            val_d[arr[i]].append(i)
        
        frontier = deque()
        frontier.append((0,0))
        while len(frontier) != 0:
            cur, dist = frontier.popleft()
            if cur == len(arr)-1:
                return dist
            if cur in idx_visited:
                continue
            idx_visited.add(cur)
            if cur > 0 and cur-1 not in idx_visited:
                frontier.append((cur-1,dist+1))
            if cur < len(arr)-1 and cur+1 not in idx_visited:
                frontier.append((cur+1, dist+1))
            if arr[cur] not in val_visited:
                for v in val_d[arr[cur]]:
                    frontier.append((v,dist+1))
                val_visited.add(arr[cur])
        return -1
            

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