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N-Queens

hard
LeetCode Top 100backtracking

Problem

Given a number n, place n queens on an n by n chessboard so that no two attack each other, and return all distinct board configurations. Queens attack along rows, columns, and both diagonals.

Examples

Input: n = 4
Output: 2 distinct solutions
There are two ways to place four non-attacking queens.
Input: n = 1
Output: 1 solution
A single queen on a single cell.

Constraints

  • • 1 <= n <= 9
Hints(tap to reveal)
  • 1. Place one queen per row.
  • 2. Track occupied columns and diagonals for O(1) conflict checks.
Optimal approach(spoiler)
  1. Place queens row by row, choosing a safe column in each.
  2. Track used columns, and both diagonal directions in sets.
  3. Skip columns whose column or diagonal sets conflict.
  4. Record a full board when all rows are placed, then backtrack.
  5. Pruning keeps the search far below the naive bound.

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