continuous_subarray_sum.py

"""
https://leetcode.com/problems/continuous-subarray-sum

Given an integer array nums and an integer k, return true if nums has a continuous subarray of size at least two whose elements sum up to a multiple of k, or false otherwise.

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

Example 1:
Input: nums = [23,2,4,6,7], k = 6
Output: true
Explanation: [2, 4] is a continuous subarray of size 2 whose elements sum up to 6.

Example 2:
Input: nums = [23,2,6,4,7], k = 6
Output: true
Explanation: [23, 2, 6, 4, 7] is an continuous subarray of size 5 whose elements sum up to 42.
42 is a multiple of 6 because 42 = 7 * 6 and 7 is an integer.

Example 3:
Input: nums = [23,2,6,4,7], k = 13
Output: false

Constraints:
1 <= nums.length <= 105
0 <= nums[i] <= 109
0 <= sum(nums[i]) <= 231 - 1
1 <= k <= 231 - 1
"""

from typing import List, Type

def check_subarray_sum(nums: List[int], k: int) -> bool:    
    if type(nums) != list:
        raise TypeError("First argument must be of type list")
    elif  type(k) != int:
        raise TypeError("Second argument must be of type int")

    tracker = { 0: -1 }
    current_total = 0
    
    for i, num in enumerate(nums):
        current_total += num
        remainder = current_total % k
        
        if remainder not in tracker:
            tracker[remainder] = i
        elif i - tracker[remainder] > 1:
            if remainder in tracker and i - tracker[remainder] >= 2:
                return True
    
    return False