The knight visits every square once. Each candidate shows its Warnsdorff degree (onward unvisited moves); the rule picks the lowest. Watch the path fill with order numbers and backtracking fire on dead ends.
The board is the knight graph drawn as a grid. The knight symbol ♞ marks the current square. Each candidate square shows a small orange number in its corner: that is its Warnsdorff degree — how many unvisited squares it could reach next.
On a score step, all candidates light up with their degrees. On a choose step, the minimum-degree candidate is outlined in green (ties go to the square farther from the center). On a move step, the knight jumps there and the square is stamped with its visit-order number. On a backtrack step, a failed branch flashes red and the search undoes the last move to try the next candidate.
The Search state panel tracks squares filled, moves made, backtracks, and nodes expanded. On a well-behaved board (try N = 6 or N = 8 from a corner), backtracks stay at 0 — Warnsdorff's first path completes the whole tour. Increase N or change the start to watch where the heuristic occasionally needs the backtracking safety net.
Tip: lower the Speed slider for a slow, readable walk; raise it to watch a large board fill quickly. Use Step to inspect a single decision at a time.
Why the lowest degree? A square with few onward moves is about to become a trap: every move you make elsewhere can only reduce its remaining exits, never add one. Visiting the most-constrained square first keeps the rest of the board flexible — that single idea is what turns an exponential search into a near-linear one.
Remember: this is a heuristic, not a guarantee. The backtracking fallback (the red flashes) is what makes the search always correct when the greedy choice stumbles.
junior.md, middle.md, and professional.md for the heuristic's intuition, tie-breaking, existence theorems, and why it carries no completeness guarantee.