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You are given a 0-indexed array nums and an integer target.A 0-indexed array infinite_nums is generated by infinitely appending the elements of nums to itself.Return the length of the shortest subarray of the array infinite_nums with a sum equal to target. If there is no such subarray return -1

Question

You are given a 0-indexed array nums and an integer target.A 0-indexed array infinite_nums is generated by infinitely appending the elements of nums to itself.Return the length of the shortest subarray of the array infinite_nums with a sum equal to target. If there is no such subarray return -1

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Solution

This problem can be solved using a sliding window approach in Python. Here is a step-by-step guide on how to do it:

  1. Initialize two pointers, start and end, to 0. These pointers will represent the start and end of the sliding window. Also, initialize a variable min_length to a large number (e.g., float('inf')) to keep track of the minimum length of the subarray.

  2. Create a variable current_sum to keep track of the sum of the elements in the current window.

  3. Start a while loop that continues until end is less than twice the length of nums. The reason for going up to twice the length is because the array is infinitely repeating, and any subarray with a sum equal to target must start within the first copy of nums and end within the first or second copy.

  4. Inside the loop, add the element at nums[end % len(nums)] to current_sum.

  5. If current_sum is less than target, move end to the right to include more elements in the window.

  6. If current_sum is greater than or equal to target, update min_length with the minimum of min_length and end - start + 1. Then, subtract the element at nums[start % len(nums)] from current_sum and move start to the right to exclude the leftmost element from the window.

  7. After the loop, if min_length is still a large number, return -1 because no subarray with a sum equal to target was found. Otherwise, return min_length.

Here is a Python code snippet that implements the above steps:

def minSubArrayLen(nums, target):
    start = end = current_sum = 0
    min_length = float('inf')
    while end < 2 * len(nums):
        current_sum += nums[end % len(nums)]
        while current_sum >= target:
            min_length = min(min_length, end - start + 1)
            current_sum -= nums[start % len(nums)]
            start += 1
        end += 1
    return -1 if min_length == float('inf') else min_length

This function takes as input a list of integers nums and an integer target, and returns the length of the shortest subarray of nums (repeated infinitely) with a sum equal to target, or -1 if no such subarray exists.

This problem has been solved

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