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Solution: Minimum Moves to Spread Stones Over Grid

Explore how to solve the minimum moves problem on a 3x3 grid by applying backtracking techniques. Understand how to identify empty cells and extra stones, use recursion to test configurations, and compute move costs with Manhattan distance. This lesson helps you develop an approach to efficiently distribute stones with minimal moves through systematic exploration of all possibilities.

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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 =3 = 3

  • 0≤0 \le grid[i][j] ≤9 \le 9

Solution

This solution works by trying different combinations of moving extra stones around the grid until each empty cell has at least one stone. ...