Which problem can be effectively solved using backtracking?

The N-Queens problem can be effectively solved using backtracking because it involves finding a way to place N queens on an N×N chessboard so that no two queens threaten each other. The backtracking algorithm systematically explores all possible configurations of the queens by placing them one by one in different columns and checking for conflicts with already-placed queens.

If a conflict occurs, the algorithm backtracks and attempts the next possible position for the most recently placed queen. This process continues until all queens are successfully placed or all possibilities have been tried. Backtracking is particularly suited to this kind of problem where constraints must be met and trial-and-error is required to find a valid configuration.

Other options mention problems that are typically solved with different methodologies. The Traveling Salesperson Problem is best approached with optimization algorithms or heuristics rather than straightforward backtracking due to the exponential growth of permutations. The Minimum Spanning Tree problem is efficiently solved through greedy algorithms like Prim's or Kruskal's algorithm. The Graph Coloring problem can also be tackled with backtracking, but its effective solutions often involve specific heuristic approaches or algorithms designed for specific types of graphs. Nonetheless, the N-Queens problem is a classic example of utilizing backtracking effectively.