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Grokking the Coding Interview Patterns in C#

Solution: Minimum Moves to Spread Stones Over Grid

Explore how to use the backtracking technique to solve the problem of distributing stones on a 3x3 grid with minimal moves. Understand how to identify empty cells and extra stones, calculate moves using Manhattan distance, and recursively try all combinations to find the optimal solution. This lesson helps you grasp the application of backtracking to complex grid problems with clear time and space complexity insights.

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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 ...