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Trace Path: Why Net Displacement Fails and Axis-Split Interval Tracking Works

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A DEV Community walkthrough examines the GeeksforGeeks Trace Path grid problem, rated Easy and tagged Matrix. The article argues that checking only net displacement against grid size is a flawed shortcut, because the question concerns every cell visited rather than just the endpoint. It shows that horizontal and vertical moves are independent, so the grid decomposes into two one-dimensional problems solvable by tracking a shrinking interval per axis in O(|s|) time. The explanation is presented as an interview transcript that walks through clarifying questions, incorrect proposals, and corrections. The author also reports testing the solution on 20,000 random inputs with U and D swapped, finding that the answer never changed.

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