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All topics›JavaScript›Advanced backtracking

N-Queens — Count the Solutions

advancedlayer A10 · Advanced backtracking5 tests

On an n × n chessboard, place n queens so that no two attack each other. Return how many distinct arrangements exist.

  • Two queens attack each other if they share a row, a column, or a diagonal
  • Reflections and rotations count as distinct arrangements
  • n = 4 has 2 solutions; n = 2 and n = 3 have none
  • n = 8 — the classic board — has 92, and must finish quickly, so prune as you go rather than generating all placements and filtering

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