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Solution: Continuous Subarray Sum

Explore how to determine if an integer array contains a subarray whose sum is a multiple of a given integer k. Learn to use cumulative sums and hash maps effectively to identify such subarrays, understand the importance of remainders, and implement an optimal O(n) time complexity solution.

Statement

Given an integer array nums and an integer k, determine if nums contains a good subarray. Return true if such a subarray exists; otherwise, return false.

A subarray of nums is considered good if:

  • Its length is at least 22.

  • The sum of its elements is a multiple of k.

Notes:

  • A subarray is defined as a contiguous sequence of elements within an array.

  • An integer x is a multiple of k if there exists an integer n such that x = n * k. Note that 0 is always considered a multiple of k.

Constraints:

  • 11 \leq nums.length 104\leq 10^4

  • ...