[Matthew Zhang] - Backtracking Algorithm with number constraints

[caspinprince]

Overview:

Implemented a Sudoku Solving algorithm using backtracking. Used arrays to represent rows, columns and sub-boxes of the grid to make checking for valid operations more efficient.

Time Complexity Explanation:

The time complexity of this algorithm is difficult to determine exactly as it depends on the input puzzle. Technically we can say it is constant, but the constant is very large so it may be worth analyzing the exact number of operations. In the worst case, the algorithm starts with an empty grid and tries every possible combination, which would result in O(9^(n^2)) for an n*n grid (n=9 for standard Sudoku). However, the average case is much better due to early stopping when an invalid state is reached.