← Snowflake Interview Insights
The basic two-pointer approach I knew cold.
Start by explaining the sort + two-pointer algorithm: sort the array, then for each index i, use two pointers to find pairs that sum to -nums[i]. Emphasize the duplicate-skipping conditions for i and for the pointers, and prove correctness by analyzing edge cases like all zeros.
Pro tip: When discussing duplicate skipping, explicitly state the invariant that after skipping, the next element is strictly greater than the previous, ensuring no duplicate triplets. Also, mention that the algorithm is O(n^2) because sorting is O(n log n) and the two-pointer scan is O(n^2).
Sort the input array in non-decreasing order. This enables the two-pointer technique and makes duplicate skipping straightforward.
Loop over each element as the first element of the triplet. Skip duplicates for i by checking if nums[i] == nums[i-1] and i > 0.
For each i, set left = i+1 and right = n-1. While left < right, compute sum = nums[i] + nums[left] + nums[right]. If sum < 0, increment left; if sum > 0, decrement right; if sum == 0, record triplet and skip duplicates for left and right.
After finding a triplet, move left past all equal elements and right past all equal elements to avoid duplicate triplets. Also, skip duplicate i values at the start of the loop.
For an array of all zeros, show that the algorithm finds exactly one triplet [0,0,0] by skipping duplicates at i, left, and right. Argue that any duplicate triplet would require equal elements at different positions, which are skipped.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Generalizing to T is trivial, just subtract from the target as you fix each element.
Start by generalizing the classic 3-sum problem to an arbitrary target T, then extend to k-sum using recursion with sorting and pruning. Discuss the time complexity trade-offs and how to prevent integer overflow using safe arithmetic or wider data types.
Pro tip: Emphasize that pruning is key to reducing the search space in practice, and mention that using 64-bit integers or Python's arbitrary precision can prevent overflow, but be mindful of performance implications.
Explain how to modify the two-pointer approach for 3-sum to work with any target T by adjusting the sum comparison.
Describe a recursive function that reduces k-sum to (k-1)-sum by fixing one element and recursively solving for the remaining sum.
Discuss pruning techniques such as early termination when the smallest or largest possible sum exceeds the target, and skipping duplicates.
State that the time complexity is O(n^{k-1}) for the recursive approach, and explain how pruning can improve average-case performance.
Mention using 64-bit integers (long long in C++), Python's arbitrary precision, or checking for overflow before addition.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Start by clarifying the problem constraints and assumptions, then outline an external-memory algorithm that sorts the array and uses a streaming approach to find triplets, analyzing I/O complexity. If exact enumeration is infeasible, propose a probabilistic sketch like HyperLogLog to estimate the number of unique triplets, discussing trade-offs.
Pro tip: Emphasize that the choice of algorithm depends on the triplet definition (e.g., sum to zero, distinct values) and that you would validate the probabilistic estimate with a small-scale exact computation.
Ask clarifying questions about the triplet definition (e.g., sum to zero, distinct elements) and whether the array fits in memory. Confirm that 5 million elements (e.g., 8 bytes each) exceed 512 MB, necessitating external memory.
Propose sorting the array using external merge sort (O(N log N) I/O), then for each element, use two pointers to find pairs that form a triplet, streaming through the sorted data. Alternatively, use a hash-based approach with partitioning.
State that external sorting takes O(N log_{M/B} (N/B)) I/Os, and the two-pointer scan adds O(N) I/Os, so overall I/O complexity is dominated by sorting. Mention that if the array is already sorted, it's O(N) I/Os.
If exact enumeration is infeasible, suggest using a probabilistic sketch like HyperLogLog to estimate the number of unique triplets. Describe how to hash each triplet and feed into the sketch, noting that this requires generating triplets on the fly.
Compare exact vs. approximate methods in terms of time, space, and accuracy. Mention that the sketch provides an estimate with a small relative error, and suggest validating on a smaller dataset.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Favorite part of the whole interview, weirdly.
Iterate over pairs of distinct values (including the same value twice) from the frequency map, compute the required third value, and check its frequency to count valid triplets. Carefully handle cases where the third value equals one or both of the pair values by adjusting counts based on available frequencies.
Pro tip: Clarify whether triplets are counted by distinct value combinations or by multiplicities (i.e., number of index triplets). The frequency map approach naturally counts combinations of values; if multiplicities are needed, multiply frequencies appropriately.
Confirm that triplets are unordered and that values can repeat. Identify the three cases: all three distinct, two equal, and all three equal.
Use two nested loops over the distinct values (i from 0 to m-1, j from i to m-1) to consider all unordered pairs, including the same value twice.
For each pair (a, b), compute c = T - a - b. If c is in the frequency map, determine how many valid triplets can be formed based on the relative order and equality of a, b, and c.
For each case (all distinct, two equal, all equal), calculate the number of combinations using frequencies, ensuring no overcounting and that enough occurrences exist.
Accumulate the counts from all valid pairs and return the total number of unique triplets.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.