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
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:
-
Initialize two pointers,
startandend, to 0. These pointers will represent the start and end of the sliding window. Also, initialize a variablemin_lengthto a large number (e.g.,float('inf')) to keep track of the minimum length of the subarray. -
Create a variable
current_sumto keep track of the sum of the elements in the current window. -
Start a while loop that continues until
endis less than twice the length ofnums. The reason for going up to twice the length is because the array is infinitely repeating, and any subarray with a sum equal totargetmust start within the first copy ofnumsand end within the first or second copy. -
Inside the loop, add the element at
nums[end % len(nums)]tocurrent_sum. -
If
current_sumis less thantarget, moveendto the right to include more elements in the window. -
If
current_sumis greater than or equal totarget, updatemin_lengthwith the minimum ofmin_lengthandend - start + 1. Then, subtract the element atnums[start % len(nums)]fromcurrent_sumand movestartto the right to exclude the leftmost element from the window. -
After the loop, if
min_lengthis still a large number, return -1 because no subarray with a sum equal totargetwas found. Otherwise, returnmin_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.
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