How do you solve Minimum Size Subarray in Infinite Array on LeetCode?

Minimum Size Subarray in Infinite Array (LeetCode #2875) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(n) space complexity. Key insight: Understanding how to leverage prefix sums can greatly reduce the complexity of array problems.

What is the time complexity of Minimum Size Subarray in Infinite Array?

The optimal solution for Minimum Size Subarray in Infinite Array runs in O(n) time and uses O(n) space. This complexity arises because we compute prefix sums in linear time and use a hash map to store them, which also takes linear space.

What is the brute force solution for Minimum Size Subarray in Infinite Array?

The brute force approach for Minimum Size Subarray in Infinite Array is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach involves checking every possible subarray in the infinite array to see if it sums to the target. This is straightforward but inefficient, especially for larger arrays. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Minimum Size Subarray in Infinite Array?

Minimum Size Subarray in Infinite Array uses the following concepts: Array, Hash Table, Sliding Window, Prefix Sum. The recommended patterns to study are: Hash Map, Array.

What are the interview tips for Minimum Size Subarray in Infinite Array?

Always consider edge cases, such as when the target is less than the smallest element in the array. Discuss your thought process out loud to help the interviewer understand your approach. If you get stuck, try to simplify the problem or break it down into smaller parts.

What are common mistakes when solving Minimum Size Subarray in Infinite Array?

Failing to account for the wrapping nature of the infinite array when calculating indices. Not using a hash map effectively to track previously seen prefix sums.

#2875

Minimum Size Subarray in Infinite Array

Medium

ArrayHash TableSliding WindowPrefix SumHash MapArray

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n)
Space	O(1)	O(n)

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Intuition

Time O(n)Space O(n)

The optimal solution leverages prefix sums and a hash map to efficiently find the shortest subarray that sums to the target. By calculating prefix sums, we can quickly determine the sum of any subarray.

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Algorithm

3 steps

1Step 1: Calculate the prefix sums of the nums array and store them in a list.
2Step 2: Use a hash map to track the first occurrence of each prefix sum modulo the total sum of nums.
3Step 3: Iterate through the prefix sums, checking if the difference between the current prefix sum and target can be found in the hash map, and update the minimum length accordingly.

solution.py22 lines

1# Full working Python code
2
3def min_size_subarray(nums, target):
4    n = len(nums)
5    total_sum = sum(nums)
6    prefix_sum = [0] * (2 * n + 1)
7    for i in range(1, 2 * n + 1):
8        prefix_sum[i] = prefix_sum[i - 1] + nums[(i - 1) % n]
9
10    min_length = float('inf')
11    prefix_map = {0: -1}
12
13    for i in range(2 * n):
14        current_sum = prefix_sum[i + 1]
15        needed_sum = current_sum - target
16
17        if needed_sum in prefix_map:
18            min_length = min(min_length, i - prefix_map[needed_sum])
19
20        prefix_map[current_sum % total_sum] = i
21
22    return min_length if min_length != float('inf') else -1

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Complexity note: This complexity arises because we compute prefix sums in linear time and use a hash map to store them, which also takes linear space.

1Understanding how to leverage prefix sums can greatly reduce the complexity of array problems.
2Recognizing that the infinite nature of the array can be handled with modular arithmetic is crucial.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.