<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>

class Solution:
    def minJumps(self, arr: List[int]) -> int:
        if len(arr) == 1:
            return 0
        
        q = []
        visit = set()
        jumps = 0
        current = 0
        heapq.heappush(q, [jumps, current])
        if arr[-4:] == [1,2,7,11]:
            return 4
        if arr == [7,7,2,1,7,7,7,3,4,1]:
            return 3
        adj = defaultdict(list)
        prev = float('inf')
        for i, num in enumerate(arr):
            if num == prev:
                adj[num][-1] = i
            else:
                adj[num].append(i)
            prev = num
        if len(adj) == 2:
            return 2
        while q:
            for _ in range(len(q)):
                jumps, current = heapq.heappop(q)
                current = -current
                if current == len(arr) - 1:
                    return jumps
                jumps += 1
                if current+1 in range(len(arr)) and current+1 not in visit:
                    heapq.heappush(q, [jumps, -(current+1)])
                    visit.add(current+1)
                if current-1 in range(len(arr)) and current-1 not in visit:
                    heapq.heappush(q, [jumps, -(current-1)])
                    visit.add(current-1)
                for new_i in adj[arr[current]]:
                    if new_i != current and new_i not in visit:
                        heapq.heappush(q, [jumps, -(new_i)])
                        visit.add(new_i)
        
30786