<p>You are given an array of integers <code>arr</code> and an integer <code>target</code>.</p>

<p>You have to find <strong>two non-overlapping sub-arrays</strong> of <code>arr</code> each with a sum equal <code>target</code>. There can be multiple answers so you have to find an answer where the sum of the lengths of the two sub-arrays is <strong>minimum</strong>.</p>

<p>Return <em>the minimum sum of the lengths</em> of the two required sub-arrays, or return <code>-1</code> if you cannot find such two sub-arrays.</p>

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

<pre>
<strong>Input:</strong> arr = [3,2,2,4,3], target = 3
<strong>Output:</strong> 2
<strong>Explanation:</strong> Only two sub-arrays have sum = 3 ([3] and [3]). The sum of their lengths is 2.
</pre>

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

<pre>
<strong>Input:</strong> arr = [7,3,4,7], target = 7
<strong>Output:</strong> 2
<strong>Explanation:</strong> Although we have three non-overlapping sub-arrays of sum = 7 ([7], [3,4] and [7]), but we will choose the first and third sub-arrays as the sum of their lengths is 2.
</pre>

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

<pre>
<strong>Input:</strong> arr = [4,3,2,6,2,3,4], target = 6
<strong>Output:</strong> -1
<strong>Explanation:</strong> We have only one sub-array of sum = 6.
</pre>

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

<ul>
	<li><code>1 &lt;= arr.length &lt;= 10<sup>5</sup></code></li>
	<li><code>1 &lt;= arr[i] &lt;= 1000</code></li>
	<li><code>1 &lt;= target &lt;= 10<sup>8</sup></code></li>
</ul>

from typing import List

class Solution:
    def minSumOfLengths(self, arr: List[int], target: int) -> int:
        n = len(arr)
        best = [float('inf')] * n  # Best length ending at each index
        best_so_far = float('inf')  # Best length seen so far
        curr_sum = 0  # Current sum in the sliding window
        left = 0  # Left pointer of the sliding window
        
        # Sliding window to find the best length ending at each index
        for right in range(n):
            curr_sum += arr[right]
            while curr_sum > target:
                curr_sum -= arr[left]
                left += 1
            
            if curr_sum == target:
                if left > 0 and best[left - 1] != float('inf'):
                    best_so_far = min(best_so_far, best[left - 1] + right - left + 1)
                best[right] = min(best[right - 1], right - left + 1)
            else:
                best[right] = best[right - 1]
        
        return -1 if best_so_far == float('inf') else best_so_far

# Example usage:
solution = Solution()
arr = [3, 2, 2, 4, 3]
target = 3
print(solution.minSumOfLengths(arr, target))  # Output: 2
30400