<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:
    """
    At each index, you can jump forward or backward or to another index where it's the same number
    Minimum jumps happen by exploiting same number indices

    Construct a graph by finding out the same indices
    """
    def minJumps(self, arr: List[int]) -> int:
        group = defaultdict(list)
        # maps 100 to 0, 4, -23 to 1, 2 etc .. 
        for i in range(len(arr)):
            group[arr[i]].append(i)
        
        queue = [0] # start at index 0
        visited = [False] * len(arr)
        levels = 0
        while queue:
            # add accessible nodes that is not visited
            curr_len = len(queue)
            for i in range(curr_len):
                current_index = queue.pop(0)
                if current_index == len(arr) - 1:
                    return levels
                visited[current_index] = True
            
            # add forward, back indices
                backward_index = current_index - 1
                if backward_index >= 0 and not visited[backward_index]:
                    queue.append(backward_index)
            
                forward_index = current_index + 1
                if forward_index < len(arr) and not visited[forward_index]:
                    queue.append(forward_index)

            # add jumps based on groupings
                for node_index in group[arr[current_index]]:
                    if not visited[node_index]:
                        queue.append(node_index)
                        visited[node_index] = True
                
                group[arr[current_index]].clear()
            

            levels += 1
        
        
1157