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Grokking the Coding Interview Patterns

Solution: Minimum Moves to Spread Stones Over Grid

Understand how to solve the problem of spreading stones over a 3x3 grid using backtracking. Explore how to handle extra stones, calculate moves with Manhattan distance, and recursively try all combinations to minimize moves. This lesson teaches applying backtracking to grid-based distribution problems effectively.

We'll cover the following...

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 ...