Use a sliding window with a hash map to track the last seen index of each character, expanding the right pointer and shrinking the left pointer when a duplicate is found. This yields an O(n) time and O(min(n, alphabet)) space solution. Clearly explain the invariant that the window always contains distinct characters.
Pro tip: After presenting the optimal solution, mention the brute-force O(n^2) approach and why it's inefficient, then discuss edge cases like empty string, all unique characters, and all same characters. This shows you think about trade-offs and robustness.
Confirm that the substring must be contiguous and characters are case-sensitive. Ask about input constraints (e.g., ASCII vs Unicode) to decide on data structures.
Briefly outline the O(n^2) approach of checking all substrings for uniqueness, and explain why it's suboptimal for large inputs.
Introduce the sliding window technique with two pointers (left and right) and a hash map to store the last index of each character. Explain how the window expands and contracts.
Trace the algorithm on a sample string like 'abcabcbb' to demonstrate how the window updates and the maximum length is tracked.
State O(n) time and O(min(n, alphabet)) space. Mention edge cases: empty string, single character, all unique, all duplicates, and strings with spaces or special characters.
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Start by clarifying the problem scope and assumptions (e.g., binary labels, feature matrix shape, no regularization). Then outline the logistic regression model, loss function, and gradient derivation, and finally walk through the implementation of fit (batch gradient descent), predict_proba (sigmoid), and predict (thresholding).
Pro tip: Mention numerical stability techniques like clipping the sigmoid output or using the log-sum-exp trick, and discuss convergence criteria (e.g., gradient norm tolerance) to show production-level awareness.
Confirm input/output formats, binary classification, and that only batch gradient descent is allowed. Discuss initialization (zeros) and stopping criteria (max iterations or gradient tolerance).
Write the sigmoid function and log-likelihood loss. Derive the gradient of the loss with respect to weights and bias, showing that it simplifies to X^T (sigmoid(Xw+b) - y) / m.
Initialize weights and bias, then loop for a fixed number of iterations or until convergence. In each iteration, compute predictions, gradient, and update parameters using learning rate.
predict_proba returns the sigmoid of the linear combination. predict applies a threshold (e.g., 0.5) to the probabilities to output binary labels.
Mention vectorization for efficiency, handling large datasets, and potential improvements like stochastic gradient descent or regularization, while noting the constraint of batch GD.
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Start by clarifying the problem scope and assumptions, then outline the training and prediction phases. Emphasize the need for Laplace smoothing to handle unseen words, log-space computation to avoid underflow, and a strategy for unknown tokens at test time. Walk through the algorithm step-by-step, discussing trade-offs and edge cases.
Pro tip: Mention that you would use a defaultdict for counts and apply Laplace smoothing with alpha=1 by default, but be prepared to discuss how to tune alpha. Also, highlight that handling unknown tokens can be done by either ignoring them or mapping to a special <UNK> token if the training data included it.
Ask about the dataset size, number of classes, and whether tokenization is provided. Confirm that Laplace smoothing is required and that unknown tokens should be handled gracefully.
Compute class priors and conditional probabilities for each word given each class. Use Laplace smoothing to avoid zero probabilities, and store log probabilities to prevent underflow.
For a test document, sum the log priors and log likelihoods of its tokens for each class, then choose the class with the highest score. Handle unknown tokens by skipping them or using a predefined <UNK> probability.
Discuss how to handle empty documents, tokens not seen in training, and potential numerical stability issues. Mention that log-sum-exp can be used if probabilities are needed.
Compare multinomial vs. Bernoulli Naive Bayes, discuss time and space complexity, and note that smoothing parameter alpha can be tuned via cross-validation.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.