LeetCode-in-All
51. N-Queens
Hard
The n-queens puzzle is the problem of placing n queens on an n x n chessboard such that no two queens attack each other.
Given an integer n, return all distinct solutions to the n-queens puzzle. You may return the answer in any order.
Each solution contains a distinct board configuration of the n-queens’ placement, where 'Q' and '.' both indicate a queen and an empty space, respectively.
Example 1:
Input: n = 4
Output: [[“.Q..”,”…Q”,”Q…”,”..Q.”],[”..Q.”,”Q…”,”…Q”,”.Q..”]]
Explanation: There exist two distinct solutions to the 4-queens puzzle as shown above
Example 2:
Input: n = 1
Output: [[“Q”]]
Constraints:
1 <= n <= 9
Solution
func solveNQueens(n int) [][]string {
pos := make([]bool, n+2*n-1+2*n-1)
pos2 := make([]int, n)
ans := [][]string{}
helper(n, 0, pos, pos2, &ans)
return ans
}
func helper(n, row int, pos []bool, pos2 []int, ans *[][]string) {
if row == n {
construct(n, pos2, ans)
return
}
for i := 0; i < n; i++ {
index := n + 2*n - 1 + n - 1 + i - row
if pos[i] || pos[n+i+row] || pos[index] {
continue
}
pos[i] = true
pos[n+i+row] = true
pos[index] = true
pos2[row] = i
helper(n, row+1, pos, pos2, ans)
pos[i] = false
pos[n+i+row] = false
pos[index] = false
}
}
func construct(n int, pos []int, ans *[][]string) {
sol := []string{}
for r := 0; r < n; r++ {
queenRow := make([]byte, n)
for i := range queenRow {
queenRow[i] = '.'
}
queenRow[pos[r]] = 'Q'
sol = append(sol, string(queenRow))
}
*ans = append(*ans, sol)
}