Is Valid Subarrays With Matching Sum Digits I easy or hard?

The problem is rated Medium because the brute force idea is simple but recognizing the frequency-counting optimization requires pattern recognition. Once you reduce the condition to matching digit sums at the endpoints, the optimal O(n) hash map solution becomes straightforward.

Valid Subarrays With Matching Sum Digits I Python/Java solution

The implementation typically computes digit sums with a helper function, then iterates through the array while maintaining a hash map of frequencies. Python uses a dictionary or collections.Counter, Java uses HashMap , and C++ uses unordered_map for O(1) average lookup.

How to solve Valid Subarrays With Matching Sum Digits I in O(n)?

Precompute the digit sum of each element. Traverse the array and maintain a hash map where the key is the digit sum and the value is the number of times it has appeared so far. For the current element with digit sum d, add freq[d] to the answer and then increment freq[d]. This counts all subarrays ending at the current index whose endpoints share the same digit sum.

What is the best approach for Valid Subarrays With Matching Sum Digits I?

The most efficient approach converts every number into its digit sum and counts how often each digit sum appears. Using a hash map, every time the same digit sum appears again it forms new valid subarrays with previous occurrences. This reduces the problem to a frequency counting pattern and runs in O(n) time with O(n) extra space.

Is Valid Subarrays With Matching Sum Digits I asked at Google/Amazon/Meta?

Problems using digit manipulation and hash-map frequency counting appear frequently in interviews at companies like Amazon, Google, and Meta. While the exact question may vary, the pattern of transforming values and counting equal pairs or endpoints is common in coding interviews.

What data structure is used in Valid Subarrays With Matching Sum Digits I?

A hash map (dictionary) is the primary data structure. It stores frequencies of digit sums encountered so far. This allows constant-time lookups to determine how many valid subarrays can end at the current index.

What is the time complexity of Valid Subarrays With Matching Sum Digits I?

The optimal solution runs in O(n) time. Each element is processed once to compute its digit sum and update a hash map storing frequencies of previously seen digit sums. The brute force approach checks every subarray and takes O(n^2) time.

Description Hints 3 Solution Video 5:32

3969. Valid Subarrays With Matching Sum Digits I

Medium46.8% acceptance1 company

You are given an integer array nums and an integer digit x.

A subarray nums[l..r] is considered valid if the sum of its elements satisfies both of the following conditions:

The first digit of the sum is equal to x.
The last digit of the sum is equal to x.

Return the number of valid subarrays.

Example 1:

Input: nums = [1,100,1], x = 1

Output: 4

Explanation:

The valid subarrays are:

nums[0..0]: sum = 1
nums[0..1]: sum = 1 + 100 = 101
nums[1..2]: sum = 100 + 1 = 101
nums[2..2]: sum = 1

Thus, the answer is 4.

Example 2:

Input: nums = [1], x = 2

Output: 0

Explanation:

The only subarray is nums[0..0] with a sum of 1, which does not satisfy the conditions.

Thus, the answer is 0.

Constraints:

1 <= nums.length <= 1500
1 <= nums[i] <= 10⁹
1 <= x <= 9

Asked at 1 company

Microsoft

Topics

Hints open one at a time

Hint 1

Enumerate all subarrays with two loops. Since nums.length <= 1500, checking all O(n²) subarrays is acceptable.

Hint 2

You can use prefix sums so the sum of any nums[l..r] can be computed in constant time. Alternatively, you can enumerate the starting index i, then extend the ending index j while maintaining the running sum of nums[i..j].

Hint 3

For each subarray sum, check whether its last digit is x, then repeatedly divide by 10 to get its first digit.

5:32

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