In our embedded C++ runtime, each thread has a strictly limited stack frame (64KB). When traversing deeply skewed binary trees with millions of nodes, recursive DFS triggers a stack overflow, and allocating an explicit heap stack (std::vector) exceeds our device ...Read more
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In Floyd’s Cycle-Finding Algorithm (Tortoise and Hare), slow moves by 1 step and fast moves by 2 steps. If a cycle exists, they are guaranteed to meet. Then comes part 2: to find the start of the cycle (the loop origin), ...Read more
During deep learning training in PyTorch 2.x, my script crashed midway through an epoch with the error: RuntimeError: CUDA out of memory. Tried to allocate 512.00 MiB (GPU 0; 23.69 GiB total capacity; ...Read more
In standard textbook explanations of the 0/1 Knapsack problem, the solution uses a 2D table dp[n][W] where each cell represents the max value using a subset of items under capacity W. Then instructors show an optimization: ‘Just replace the 2D array ...Read more
We are building a distributed task build engine (similar to Bazel or Make) that resolves dependency trees across 500,000 code packages. Textbooks teach both Kahn’s algorithm (indegree BFS) and DFS post-order reversal. Why do production build systems almost universally prefer Kahn’s ...Read more
Abhay TiwariBegginer
I am indexing a table with 2,000,000 vectors (1,536 dimensions, OpenAI text-embedding-3-small) in PostgreSQL 16 using the pgvector extension. When executing: CREATE INDEX ON documents USING hnsw (embedding vector_cosine_ops) WITH (m = 16, ...Read more
The standard DP solution for Longest Increasing Subsequence (LIS) uses two nested loops: for each element i, scan all previous elements j < i. That takes O(N^2) time, which times out when N = 100,000. Everyone says the optimal solution is ...Read more
In our telemetry service, financial tick prices arrive at ~10,000 events/second. We need an online algorithm that can output the exact running median at any moment. Sorting the buffer on every tick is O(N log N), which is impossible at high ...Read more
When elements in an array appear twice except one, we can simply XOR all numbers together. But what if every element appears three times, except for a single number that appears once? The standard hash-map solution uses O(N) space. How can ...Read more