1. Board filled
Placing a queen on every row yields one valid arrangement.
if (row === n)Typorithm · hard
N-Queens
▷ Interactive algorithm labn-queensbacktrackingconstraintsdiagonalschoose-explore-undo
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Full lesson · 8 learning steps Open any exercise for focused practice
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Step 1 of 8 · intro card
Learn N-Queens
Backtracking
Place one queen per row, rejecting squares attacked on a column or diagonal, with sets as O(1) guards.
One queen goes in each row, so the search only chooses a column per row.
A square is safe unless its column, its row-minus-col diagonal, or its row-plus-col anti-diagonal is taken.
Three sets make each safety check O(1); add on place and delete on undo.
Preparing algorithm lab…
01
One queen per row.
02
Track col, row-col, and row+col.
03
Add to place, delete to undo.
function totalNQueens(n) {
let count = 0;
const cols = new Set();
const diag = new Set();
const anti = new Set();
function backtrack(row) {
if (row === n) {
count += 1;
return;
}
for (let col = 0; col < n; col += 1) {
if (cols.has(col) || diag.has(row - col) || anti.has(row + col)) {
continue;
}
cols.add(col);
diag.add(row - col);
anti.add(row + col);
backtrack(row + 1);
cols.delete(col);
diag.delete(row - col);
anti.delete(row + col);
}
}
backtrack(0);
return count;
}Read the implementation
Connect each part of the code to the concept before you type.
2. Attack check
Reject a square attacked on its column or either diagonal.
if (cols.has(col) || diag.has(row - col) || anti.has(row + col))3. Place queen
Mark the column and both diagonals as occupied.
cols.add(col)4. Next row
Move to the next row to place the following queen.
backtrack(row + 1)5. Remove (undo)
Free the column and diagonals before trying another square.
cols.delete(col)A complete learning loop
01
Understand
Read the concept map and follow the code breakdown.
02
Reconstruct
Type the implementation, repair mistakes and work through every recall exercise.
03
Verify
Use the final check without hints; revisit weak concepts in short practice sessions.