<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:
        n = len(arr)
        num_to_indicies = defaultdict(list)
        for idx, num in enumerate(arr):
            num_to_indicies[num].append(idx)

        queue = [0]
        jumps = 0
        visited = set([0])
        while queue:
            new_queue = []
            while queue:
                pos = queue.pop(0)
                if pos == len(arr) - 1:
                    return jumps
                # visited.add(pos)
                num = arr[pos]
                for next_pos in num_to_indicies[num]:
                    if next_pos not in visited:
                        visited.add(next_pos)
                        new_queue.append(next_pos)
                
                if pos + 1 < len(arr) and pos + 1 not in visited:
                    visited.add(pos + 1)
                    new_queue.append(pos + 1)
                
                if 0 <= pos - 1 and pos - 1 not in visited:
                    visited.add(pos - 1)
                    new_queue.append(pos - 1)
            
            num_to_indicies[num].clear()
            queue.extend(new_queue)
            jumps += 1

# min(left + 1, right + 1, jump of any identical value + 1)

29976