9 digit combos

What would be the algorithm that produces all of the nine digit combinations using numbers 1 through 9, in which there are no repeating numbers and using a 3x3 array set up as depicted, once the number is used it can’t be used again.

 

To generate all nine-digit combinations using the numbers 1 through 9 without repeating any number, arranged in a 3x3 grid, we can use a backtracking algorithm. Backtracking is a recursive algorithm that tries to build a solution incrementally and abandons a path as soon as it determines that this path cannot lead to a valid solution. Here's a step-by-step outline of the algorithm:

1. Initialize the 3x3 grid: Start with an empty 3x3 grid.
2. Track used numbers: Use a boolean array to keep track of which numbers from 1 to 9 have been used.
3. Backtracking function:
   • If the grid is completely filled, print the grid or store the combination.
   • Otherwise, for each cell in the grid (iterate row by row and column by column):
     • Try placing each number from 1 to 9 in the current cell if it hasn't been used.
     • Mark the number as used and place it in the cell.
     • Recursively attempt to fill the next cell.
     • If the recursive call fails to fill the grid, backtrack by removing the number from the current cell and marking it as unused.
4. Terminate the recursion: When all cells are filled, a valid 3x3 grid is obtained.

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