Dense Vector Dot Product
Reported by candidates from Cerebras's online assessment. Pattern, common pitfall, and the honest play if you blank under the timer.
The detail that matters in this Cerebras OA, reported August 2026, is the 64-bit note buried in the statement. Two vectors, multiply pairwise, sum. That's the whole problem. It's an array problem with one trap: with values up to 10^6, a single product hits 10^12 and overflows a 32-bit int. If you've got an invite and 48 hours, this one is about not tripping on types, not about cleverness. If you blank on the setup during the live OA, StealthCoder runs invisibly on your desktop and gives you the solution in real time as a safety net.
The problem
Given two equal-length integer vectors first and second, return their dot product. The dot product is the sum of first[i] * second[i] over every index. Use 64-bit arithmetic for each product and for the accumulated result. Function dotProduct(first: int[], second: int[]) → long Examples Example 1 first = [1,2,3] second = [4,5,6] return = 32 The dot product is 1 * 4 + 2 * 5 + 3 * 6 = 32. Example 2 first = [0,-3,5,0] second = [7,2,-4,9] return = -26 Only the middle entries contribute: -3 * 2 + 5 * -4 = -26. Example 3 first = [1000000,1000000] second = [1000000,-1000000] return = 0 The two products are 10^12 and -10^12, so they cancel. Constraints 1 ≤ first.length = second.length ≤ 2 * 10^5. -10^6 ≤ first[i], second[i] ≤ 10^6. The result fits in a signed 64-bit integer.
Reported by candidates. Source: FastPrep
Pattern and pitfall
The algorithm is a single pass. Loop i from 0 to n-1, multiply first[i] by second[i], add to a running total. That's O(n) time and O(1) space, and nothing faster exists since you must read every element. The pitfall is overflow. Each element fits in 32 bits, but the product reaches 10^12, so you must cast to long before multiplying, not after. In Java or C++, write (long) first[i] * second[i]. Casting the finished product is too late, because the overflow has already happened. In Python this doesn't matter. Example 3 is the tell: 10^12 and -10^12 cancel to 0, and a 32-bit overflow would give garbage. With n up to 2 * 10^5, no tricks are needed. If you freeze on the cast detail during the live OA, StealthCoder is the hedge that shows the correct typed version.
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Dense Vector Dot Product FAQ
How hard is the Cerebras Dense Vector Dot Product problem really?+
It's very easy. One loop, one accumulator. The only way to lose points is integer overflow. If you handle the 64-bit cast correctly, you pass. Spend your prep time on edge handling and clean code, not on algorithms.
What's the trick in this problem?+
Cast to a 64-bit type before multiplying. Each product can reach 10^12, which overflows a 32-bit int. The accumulated sum also needs 64 bits. The statement tells you this directly, so treat it as the whole trap.
Do I need to worry about time complexity?+
No. Length is capped at 2 * 10^5, and a single O(n) pass handles that easily. There's no way to beat linear because every pair must be read. Don't overthink it with sorting or hashing.
Which edge cases should I test?+
Test negative values, zeros, and the max magnitude case from Example 3 where products are 10^12 and -10^12. Also test length 1. These cover sign handling, overflow, and the minimum input size allowed by the constraints.
How do I prepare for this in 48 hours?+
Write the loop in your OA language and confirm how your language handles widening to 64-bit. Run Example 3 to check for overflow. That takes minutes. Then spend remaining time on harder array and hash-table problems, since the rest of the OA may be tougher.