#0300

N-Queens Count

HardDSA40 min25 XP

Problem

Return the number of valid ways to place n queens on an n x n board so no two queens share a row, column, or diagonal.

Why This Matters

N-Queens is the classic backtracking constraint problem with columns and diagonals as state.

Function Signature

def total_n_queens(n):

Examples

Example 1

Inputn = 4

Output2

A 4x4 board has exactly two valid N-Queens arrangements.

Constraints

Return the exact requested value.
Handle edge cases cleanly.
Use the intended DSA pattern when brute force would scale poorly.

CodePython

def total_n_queens(n):
    """
    Input example: n = 4
    Return: 2
    Return the value from the function so the tests can compare it. Do not print unless the prompt asks.
    """
    # write your code here
    return 0

def total_n_queens(n):
    """
    Input example: n = 4
    Return: 2
    Return the value from the function so the tests can compare it. Do not print unless the prompt asks.
    """
    # write your code here
    return 0

Visible browser tests run here when available.

Testcases2 visible / 3 hidden categories

Four queens

Input4

Expected2

The classic 4x4 case has two solutions.

One queen

Input1

Expected1

A single queen can be placed in one way.

Hidden Test Categories

n = 2n = 3n = 5