Graph Theory37 sections · 1633 units
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Knight's Tour - Analysis

Backtracking with heuristics.

Pattern recognition:

  • Visit every vertex once = Hamiltonian path
  • Graph is implicit (knight move graph)
  • 6464 vertices, too many for bitmask DP (2642^{64})

Solution: Backtracking with Warnsdorff's heuristic.

Warnsdorff's rule: From current position, move to the square with the fewest onward moves (lowest degree among unvisited neighbors).

This greedy heuristic dramatically reduces backtracking and usually finds a solution quickly.