♛ N-Queens — Backtracking

Search space (n = 6)

brute (nⁿ)46,656

one/column (n!)720

backtracking nodes32

Pruning avoids the exponential blow-up by rejecting attacks early.

Backtracking Pseudocode

1solve(row):
2  if row == n: return true   // all placed
3  for col in 0 .. n−1:
4    if not safe(row, col): skip
5    place queen at (row, col)
6    if solve(row+1): return true
7    remove queen  (backtrack)

Speed: 60%Board size: 6×6

N-Queens Visualizer: Backtracking Search You Can Watch and Play

This N-Queens simulator makes backtracking tangible. Press Play and queens drop into the board row by row; the moment a partial board has a conflict the search prunes that branch and backtracks, visibly removing a queen — with attacked squares shaded red so you see exactly why. A search-space card contrasts the brute-force nn boards and the n! column permutations against the handful of nodes backtracking actually visits (for n = 8 that's ~16.7 million versus a couple thousand). The signature interaction: switch to Solve-It-Yourself and place queens by clicking squares, with attacking pairs turning red in real time and a success banner when you arrange n queens with no shared row, column, or diagonal. A synced pseudocode panel highlights the try, place, and backtrack lines as the search runs.

What you can do in this simulation

Watch backtracking place queens and undo them at dead ends, with attacked squares shaded so pruning is visible
Switch to Solve-It-Yourself and click squares to place queens — attacking pairs turn red instantly and the board celebrates a valid solution
Read the search-space card: brute force nn versus n! versus the nodes backtracking actually visits
Press Play, Pause, or Step to run the search at any speed, with a pseudocode panel highlighting try / place / backtrack
Resize the board from 4x4 to the classic 8x8 and complete missions for finding a solution, witnessing a backtrack, and solving it by hand

Concepts covered

backtracking · n-queens problem · constraint satisfaction · search tree pruning · recursion · exponential search space · depth-first search

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1solve(row):

2 if row == n: return true // all placed

3 for col in 0 .. n−1:

4 if not safe(row, col): skip

5 place queen at (row, col)

6 if solve(row+1): return true

7 remove queen (backtrack)

N-Queens Visualizer: Backtracking Search You Can Watch and Play

What you can do in this simulation

Watch backtracking place queens and undo them at dead ends, with attacked squares shaded so pruning is visible

Switch to Solve-It-Yourself and click squares to place queens — attacking pairs turn red instantly and the board celebrates a valid solution

Read the search-space card: brute force nn versus n! versus the nodes backtracking actually visits

Press Play, Pause, or Step to run the search at any speed, with a pseudocode panel highlighting try / place / backtrack

Resize the board from 4x4 to the classic 8x8 and complete missions for finding a solution, witnessing a backtrack, and solving it by hand