<p>Given an array of&nbsp;integers <code>arr</code> and an integer <code>d</code>. In one step you can jump from index <code>i</code> to index:</p>

<ul>
	<li><code>i + x</code> where:&nbsp;<code>i + x &lt; arr.length</code> and <code> 0 &lt;&nbsp;x &lt;= d</code>.</li>
	<li><code>i - x</code> where:&nbsp;<code>i - x &gt;= 0</code> and <code> 0 &lt;&nbsp;x &lt;= d</code>.</li>
</ul>

<p>In addition, you can only jump from index <code>i</code> to index <code>j</code>&nbsp;if <code>arr[i] &gt; arr[j]</code> and <code>arr[i] &gt; arr[k]</code> for all indices <code>k</code> between <code>i</code> and <code>j</code> (More formally <code>min(i,&nbsp;j) &lt; k &lt; max(i, j)</code>).</p>

<p>You can choose any index of the array and start jumping. Return <em>the maximum number of indices</em>&nbsp;you can visit.</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>
<img alt="" src="https://assets.leetcode.com/uploads/2020/01/23/meta-chart.jpeg" style="width: 633px; height: 419px;" />
<pre>
<strong>Input:</strong> arr = [6,4,14,6,8,13,9,7,10,6,12], d = 2
<strong>Output:</strong> 4
<strong>Explanation:</strong> You can start at index 10. You can jump 10 --&gt; 8 --&gt; 6 --&gt; 7 as shown.
Note that if you start at index 6 you can only jump to index 7. You cannot jump to index 5 because 13 &gt; 9. You cannot jump to index 4 because index 5 is between index 4 and 6 and 13 &gt; 9.
Similarly You cannot jump from index 3 to index 2 or index 1.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> arr = [3,3,3,3,3], d = 3
<strong>Output:</strong> 1
<strong>Explanation:</strong> You can start at any index. You always cannot jump to any index.
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> arr = [7,6,5,4,3,2,1], d = 1
<strong>Output:</strong> 7
<strong>Explanation:</strong> Start at index 0. You can visit all the indicies. 
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= arr.length &lt;= 1000</code></li>
	<li><code>1 &lt;= arr[i] &lt;= 10<sup>5</sup></code></li>
	<li><code>1 &lt;= d &lt;= arr.length</code></li>
</ul>

class Solution:
    def maxJumps(self, arr: List[int], d: int) -> int:
        

        
        graph = defaultdict(list)
        indegree = defaultdict(int)
        
        
        # connect nodes if prev_val < cur_val and cur_index - prev_index <= d
        stack = []
        for ind, num in enumerate(arr):
            
            while stack and ind - stack[-1] <= d and arr[stack[-1]] < num:
                popped = stack.pop()
                graph[ind].append(popped)
                indegree[popped] += 1
                
            stack.append(ind)
        
        # perform the same operation backwards from the end
        stack = []
        for ind in range(len(arr) - 1, -1, -1):
            num = arr[ind]
            while stack and stack[-1] - ind <= d and arr[stack[-1]] < num: 
                popped = stack.pop()
                graph[ind].append(popped)
                indegree[popped] += 1
            
            stack.append(ind)
        
        
        # topological sorting
        queue = deque()
        for node in range(len(arr)):
            if not indegree[node]:
                queue.append(node)
            
        jumps = 0
        while queue:
            for _ in range(len(queue)):
                cur = queue.popleft()
                
                for neigh in graph[cur]:
                    indegree[neigh] -= 1
                    if  not indegree[neigh]:
                        queue.append(neigh)
                        
            jumps += 1
             
            
        return jumps
        
        
147