Calculus & gradients + DSA Bit Manipulation kickoff

Interview questions to prep

1. Why does XOR-all give the unique element when others appear twice?
2. How does this generalize when others appear three times (LC 137)?

Interview questions to prep

1. Walk me through the bit trick used here, bit by bit on a small input.
2. Why XOR / AND / shift specifically — what property of that operation does the problem exploit?
3. What's the complexity in terms of bits (often O(32) → O(1)), and where could that break for big-int?

Interview questions to prep

1. Walk me through the bit trick used here, bit by bit on a small input.
2. Why XOR / AND / shift specifically — what property of that operation does the problem exploit?
3. What's the complexity in terms of bits (often O(32) → O(1)), and where could that break for big-int?

Interview questions to prep

1. Derive the chain rule for f(g(x)) and apply it to a 2-layer neural network.
2. What's the difference between a partial derivative and a directional derivative?

Interview questions to prep

1. What does the gradient vector represent geometrically?
2. When would you need the full Jacobian or Hessian in ML?
3. Why do second-order methods (Newton) rarely scale to deep nets?

Interview questions to prep

1. Explain backpropagation as the chain rule applied to a computation graph.
2. Why do vanishing gradients happen, and how do ReLU / residual connections help?