<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>

# BFS
from collections import deque, defaultdict
class Solution:
    def minJumps(self, arr: List[int]) -> int:
        self.arr = arr
        if len(arr) == 1:
             return 0

        self.graph = defaultdict(set)
        for i, num in enumerate(arr):
            self.graph[num].add(i)
        # print(self.graph)

        queue = deque([0])
        visited = set([0])
        step = 0 
        while queue:
            step += 1
            for _ in range(len(queue)):
                cur = queue.popleft()
                for ne in self.get_neighbors(cur):
                    if ne == len(arr) - 1:
                        return step
                    if ne in visited:
                        continue
                    visited.add(ne)
                    queue.append(ne)
                self.graph.pop(self.arr[cur])
        return -1
    
    def get_neighbors(self, idx):
        res = self.graph[self.arr[idx]]
        if idx in res:
            res.remove(idx)
        if idx - 1 > -1:
            res.add(idx - 1)
        if idx + 1 < len(self.arr):
            res.add(idx + 1)
        # print(self.graph[self.arr[idx]], res)
        return res

        
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