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Grokking the Coding Interview Patterns in Python

Solution: Minimum Moves to Spread Stones Over Grid

Explore how to solve the minimum moves problem for spreading stones across a 3x3 grid by applying backtracking. Understand how to use Manhattan distance to calculate moves and how to recursively try different stone placements to find the optimal solution. This lesson helps you implement backtracking effectively for grid-based distribution problems.

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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 ...