<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

        indexLookup: Dict[int, List[int]] = {}
        for index, val in enumerate(arr):
            if val not in indexLookup:
                indexLookup[val] = []
            indexLookup[val].append(index)

        firstVisited: Dict[int, int] = {}
        firstVisited[0] = 0

        minSteps = inf
        queue = [(0, 0)]

        while queue:
            current = queue.pop(0)
            steps = current[1]
            if steps >= minSteps:
                continue
            
            position = current[0]

            if position - 1 >= 0:
                if (position - 1 not in firstVisited or firstVisited[position - 1] > steps + 1) and steps + 1 <= minSteps:
                    firstVisited[position - 1] = steps + 1
                    queue.append((position - 1, steps + 1))
            if position + 1 < len(arr):
                if position + 1 == len(arr) - 1:
                    minSteps = min(minSteps, steps + 1)
                elif (position + 1 not in firstVisited or firstVisited[position + 1] > steps + 1) and steps + 1 <= minSteps:
                    firstVisited[position + 1] = steps + 1
                    queue.append((position + 1, steps + 1))
            if arr[position] in indexLookup and len(indexLookup[arr[position]]) > 1:
                for equiv in indexLookup[arr[position]]:
                    if equiv != position:
                        if equiv == len(arr) - 1:
                            minSteps = min(minSteps, steps + 1)
                        elif (equiv not in firstVisited or firstVisited[equiv] > steps + 1) and steps + 1 <= minSteps:
                            firstVisited[equiv] = steps + 1
                            queue.append((equiv, steps + 1))
                del indexLookup[arr[position]]

        return minSteps
1285