<p>You are given a <strong>0-indexed</strong> array of integers <code>nums</code> of length <code>n</code>. You are initially positioned at <code>nums[0]</code>.</p>

<p>Each element <code>nums[i]</code> represents the maximum length of a forward jump from index <code>i</code>. In other words, if you are at <code>nums[i]</code>, you can jump to any <code>nums[i + j]</code> where:</p>

<ul>
	<li><code>0 &lt;= j &lt;= nums[i]</code> and</li>
	<li><code>i + j &lt; n</code></li>
</ul>

<p>Return <em>the minimum number of jumps to reach </em><code>nums[n - 1]</code>. The test cases are generated such that you can reach <code>nums[n - 1]</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> nums = [2,3,1,1,4]
<strong>Output:</strong> 2
<strong>Explanation:</strong> The minimum number of jumps to reach the last index is 2. Jump 1 step from index 0 to 1, then 3 steps to the last index.
</pre>

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

<pre>
<strong>Input:</strong> nums = [2,3,0,1,4]
<strong>Output:</strong> 2
</pre>

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

<ul>
	<li><code>1 &lt;= nums.length &lt;= 10<sup>4</sup></code></li>
	<li><code>0 &lt;= nums[i] &lt;= 1000</code></li>
	<li>It&#39;s guaranteed that you can reach <code>nums[n - 1]</code>.</li>
</ul>

class Solution:
    def jump(self, nums: List[int]) -> int:
        # backtrack from the end to start - check how one canget to the end

        min_jumps = inf
        def backtrack(nums, current_position_index: int = len(nums) - 1, current_jumps: int | float = 0):
            nonlocal min_jumps
            #print("current pos", current_position_index)
            if current_position_index <= 0:
                #print("current jumps", current_jumps)
                min_jumps = min(min_jumps, current_jumps)
                return 

            # from which positions we could have got to the current possition?
            previous_longest_jump = None
            for i in range(current_position_index):
                min_jump_distance = current_position_index - i
                if nums[i] >= min_jump_distance:
                    previous_longest_jump = i
                    break
    
            #print("prev longest?", previous_longest_jump, nums[i])
            if previous_longest_jump is not None:
                backtrack(nums, previous_longest_jump, current_jumps + 1)
        
        backtrack(nums)
        
        return min_jumps if min_jumps != inf else 0

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