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Simplex Method: One Pivot Step is a hard coding interview question covering linear programming, math — the kind asked at FAANG (Facebook/Meta, Apple, Amazon, Netflix, Google) and AI-first companies like Anthropic, OpenAI, and Nvidia.
Implement one iteration of the Simplex method for linear programming.
Given a maximization LP in standard form with a tableau (objective row + constraint rows), perform one pivot:
1. Entering variable: column with most positive coefficient in the objective row 2. Leaving variable: row with minimum positive ratio b[i] / a[i][pivot_col] (ratio test) 3. Pivot: divide pivot row by pivot element, eliminate pivot column from all other rows
If no positive coefficients in objective row: optimal. If ratio test fails (all ratios negative/zero): unbounded.
Return updated tableau and status.
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