## Problem Fillomino is a logic puzzle where you fill an N x M grid so that every cell belongs to a connected region of cells, and each region's size equals the number written in any of its cells. Given a partially filled grid, write a solver that completes it. ```python def solve_fillomino(grid: list[list[int]]) -> list[list[int]]: # 0 = empty cell; non-zero = given clue # Returns completed grid, or raises if no solution exists pass def is_valid(grid: list[list[int]]) -> bool: # Validates a completed grid against Fillomino rules pass ``` **Example (4x4):** ``` Input: Output: [3, 0, 0, 2] [3, 3, 3, 2] [0, 0, 0, 2] [4, 4, 4, 2] [0, 0, 4, 0] [1, 4, 4, 4] [0, 0, 0, 0] [5, 5, 5, 5] ``` ## Follow-ups 1. What pruning strategies reduce backtracking? (Describe constraint propagation.) 2. How do you detect that two regions of the same number would need to merge, which is illegal? 3. What is the worst-case complexity of your backtracking solution? 4. How would you generate a valid Fillomino puzzle with a unique solution?

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Fillomino Puzzle: Solve and Validate a Fillomino Grid Using Backtracking

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Problem Fillomino is a logic puzzle where you fill an N x M grid so that every cell belongs to a connected region of cells, and each region's size equals the number written in any of its cells. Given a partially filled grid, write a solver that completes it. Example (4x4): Follow-ups What pruning strategies reduce backtracking? (Describe constraint propagation.) How do you detect that two regions of the same number would need to merge, which is illegal? What is the worst-case complexity of your…

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This is a candidate experience report from a waymo interview during the phone round.

It covers the following topics: Coding, Phone, Matrix, Backtracking .

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Fillomino Puzzle: Solve and Validate a Fillomino Grid Using Backtracking

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