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Grokking the Coding Interview Patterns

Solution: Minimum Moves to Spread Stones Over Grid

Explore a backtracking method to determine the minimum number of moves needed to distribute stones evenly across a 3x3 grid. Learn how to assess empty and extra stone cells, calculate moves using Manhattan distance, and use recursion with backtracking to find the optimal solution for stone placement.

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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 ...