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Grokking the Coding Interview Patterns in Python

Solution: Minimum Moves to Spread Stones Over Grid

Explore how to determine the minimum number of moves to place exactly one stone in each cell of a 3x3 grid by using backtracking. Understand how to track extra stones, empty cells, and calculate moves with Manhattan distance. This lesson helps you solve complex grid rearrangement problems efficiently.

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Statement

Given a 2D grid of integers of size (3×33 \times 3), where each value represents the number of stones in the given cell, return the minimum number of moves required to place exactly one stone in each grid cell.

Constraints:

  • Only one stone can be moved in one move.

  • Stone from a cell can only be moved to another cell if they are adjacent (share a side).

  • The sum of all stones in the grid must be equal to 99.

  • grid.length, grid[i].length ...