Hard data structure and algorithm practice puzzle.
Given a vector, a position, and theta, rotate the vector and return it, rounded to 4 decimals. Take the values in pairs (x, y) and rotate each pair by the angle position x theta: the new x is x cos - y sin, and the new y is x sin + y cos. Rotary position embeddings use this so a model can tell how far apart two tokens are.
Solve it three ways: snap the jigsaw pieces together, fill in the blanks, or type it from scratch against the tests. This one is free.
Every line of the solution comes with a note explaining why it is there, and a step by step replay shows the code running. At level 3, where you type it yourself, you can ask for an AI mock interview on this problem that ends with a hiring manager's scorecard.
Then grow it into a real project with the Software Engineer button: this puzzle becomes the Request Tile Exporter, a pipeline you can run and download. See every Software Engineer project.
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