Try it!

I'm trying to animate Dancing Links by Donald Knuth, using the Eight Queens Puzzle

The clever choice of options ordering is too smart in QUEENS-DLX by Knuth. No backtracking occurs below n=16. I decided to start with a naive order. Now backtracking happens a lot even for n=8.

Mandatory. All rows and all columns must be covered exactly once

• RA..RH rows (8)
• CA..CH columns (8)

Not mandatory. Diagonals can be covered at most once

• AA..AO left diagonals (15)
• BA..BO right diagonals (15)

The four corner diagonals, AA, AO, BA and BO have only one option, so they are actually not needed. No risk for two queens on these.

• a1..h1 first row, RA
• a8..h8 last row, RH
• a1..a8 first column, CA
• h1..h8 last column, CH
• a1..a1 first left diagonal, AA
• h8..h8 last left diagonal, AO
• a8..a8 first right diagonal, BA
• h1..h1 last right diagonal, BO

When all queens are placed on the board and in legal positions, the first solution has been found. This viewer only shows the first solution.

• Texts in yellow are mouse aware
• Hold the mouse over item names, e.g. CA
• Hold the mouse over a chess square, e.g. a1
• Click on one of the snapshots in the list to the right

• Down Arrow: go to next snapshot
• Up Arrow: go to previous snapshot
• Space: Compact or Expanded View

8queens.json is generated by 037-DLX. Simplified extract:

options: "a1 a2 a3 a4 a5 a6 a7 a8 b1 b2 b3 b4 b5 b6 b7 b8 c1 c2 c3 c4 c5 c6 c7 c8 d1 d2 d3 d4 d5 d6 d7 d8 e1 e2 e3 e4 e5 e6 e7 e8 f1 f2 f3 f4 f5 f6 f7 f8 g1 g2 g3 g4 g5 g6 g7 g8 h1 h2 h3 h4 h5 h6 h7 h8"
items: "CA CB CC CD CE CF CG CH R1 R2 R3 R4 R5 R6 R7 R8 AA AB AC AD AE AF AG AH AI AJ AK AL AM AN AO BA BB BC BD BE BF BG BH BI BJ BK BL BM BN BO"
snapshots: 
  choices: "" entries: {...}
  choices: "a1" entries: {...}
  choices: "a1 b3" entries: {...}
  choices: "a1 b3 c5" entries: {AE:"d2" AF:"e2" AH:"e4 g2" AI:"f4 h2" ...}
  ...

• Stanford Lecture: Don Knuth—"Dancing Links" (2018)
• Original paper
• Knuth's Algorithm X
• Exact Cover
• Dancing Links