Num of Divisible Substrings
Reported by candidates from Wayfair's online assessment. Pattern, common pitfall, and the honest play if you blank under the timer.
Wayfair's September OA included a substring divisibility problem that catches candidates off guard because the straightforward approach tanks on performance. You're looking at a problem where you need to count substrings that satisfy a divisibility condition, typically checking if the numeric value of a substring is divisible by some number (often 10, or a digit count). The trick isn't brute force enumeration. It's recognizing the mathematical pattern that lets you skip most substrings and compute the answer efficiently. StealthCoder runs silently during your OA and can pattern-match this in seconds if you blank on the optimization.
Pattern and pitfall
The naive solution generates all substrings, converts each to an integer, and checks divisibility. That's O(n^2) or worse and will time out. The real pattern is usually a counting or prefix-sum approach. Some versions ask for substrings divisible by their own length, or divisible by 10, or where each character matches a constraint. Once you spot the math (often modular arithmetic or a digit-by-digit recurrence), you can collapse it to O(n) or O(n log n). The common mistake is trying to materialize every substring. Instead, think about what makes a substring valid without building it. That's where the category lives: is it prefix sums, is it math, is it a character-counting trick. StealthCoder identifies the exact pattern when you see the real problem text and delivers the solution shape in real time.
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Num of Divisible Substrings FAQ
What does 'divisible substrings' really mean here?+
You're counting substrings of a given string where the numeric value of that substring (or some property of it) is divisible by a specific number. Wayfair's version likely specifies divisibility by 10, the substring length, or a digit. The problem text will be explicit. The trick is you don't enumerate all substrings.
Is this a prefix-sum problem?+
Possibly. If you're checking divisibility properties that accumulate across positions, prefix sums or modular arithmetic shortcut the nested loop. Think about whether you can compute a property for substring [i, j] using info you already cached from [0, i] and [0, j].
How do I avoid timeout on the OA?+
Don't iterate all substrings. Look for a mathematical invariant: if substring [i, j] is divisible, does that tell you anything about [i, j+1] or [i+1, j]. Often there's a recurrence or a single-pass rule that eliminates the nested loop entirely.
What languages work best for this?+
Python for speed of iteration and modular math. Java if you're comfortable with int overflow. C++ if you need raw performance. The language doesn't change the algorithm. Pick what you're fastest in and move on.
Is this problem still asked in 2024?+
Yes. Wayfair reported it in September 2024. Substring counting with constraints is a core pattern in their OA. You may see it phrased differently (palindromes, vowels, divisibility) but the optimization strategy is the same: math beats brute force.