The n-queens puzzle is the problem of placing n queens on an n×n chessboard such that no two queens attack each other.
Given an integer n, return the number of distinct solutions to the n-queens puzzle.
Example:
Input: 4 Output: 2 Explanation: There are two distinct solutions to the 4-queens puzzle as shown below. [ [".Q..", // Solution 1 "...Q", "Q...", "..Q."], ["..Q.", // Solution 2 "Q...", "...Q", ".Q.."] ]
n 皇后问题研究的是如何将 n 个皇后放置在 n×n 的棋盘上，并且使皇后彼此之间不能相互攻击。
上图为 8 皇后问题的一种解法。
给定一个整数 n，返回 n 皇后不同的解决方案的数量。
示例:
输入: 4 输出: 2 解释: 4 皇后问题存在如下两个不同的解法。 [ [".Q..", // 解法 1 "...Q", "Q...", "..Q."], ["..Q.", // 解法 2 "Q...", "...Q", ".Q.."] ]
8ms
1 class Solution { 2 func totalNQueens(_ n: Int) -> Int { 3 if n == 0 { 4 return 0 5 } 6 var answer = 0 7 var limit = (1<<n) - 1 8 dfs(h: 0, r: 0, l: 0, answer: &answer, limit: &limit) 9 return answer 10 } 11 private func dfs(h: Int, r: Int, l: Int, answer: inout Int, limit: inout Int) { 12 if h == limit { 13 answer += 1 14 return 15 } 16 var position = limit & (~(h|r|l)) 17 while position > 0 { 18 let p = position & (-position) 19 position -= p 20 dfs(h: h+p, r: (r+p)<<1, l: (l+p)>>1, answer: &answer, limit: &limit) 21 } 22 } 23 }
20ms
1 class Solution { 2 var placeArr : [Int]! 3 var totalN : Int = 0 4 func canPlace(_ row:Int , _ col:Int) -> Bool{ 5 6 var colInRow : Int = 0 7 var offset : Int = 0 8 for idx in 0 ..< row { 9 colInRow = placeArr[idx] 10 11 if colInRow == col { 12 return false 13 } 14 offset = row - idx 15 if colInRow == col - offset{ 16 return false 17 } 18 if colInRow == col + offset{ 19 return false 20 } 21 } 22 return true 23 } 24 25 var count : Int = 0 26 func place(_ row:Int) -> (){ 27 if row == totalN { 28 count += 1 29 }else{ 30 for col in 0..<totalN { 31 if canPlace(row,col) { 32 placeArr[row] = col 33 place(row + 1) 34 } 35 } 36 } 37 } 38 39 func totalNQueens(_ n: Int) -> Int { 40 totalN = n 41 placeArr = Array(repeating : 0 , count : totalN) 42 43 place(0) 44 return count 45 } 46 }
28ms
1 class Solution { 2 func totalNQueens(_ n: Int) -> Int { 3 var board = [[Bool]](repeating: [Bool](repeating: false, count: n), count: n) 4 var result = 0 5 backtrack(&board, 0, &result) 6 return result 7 } 8 9 private func backtrack(_ board: inout [[Bool]], _ row: Int, _ result: inout Int) { 10 if row == board.count { 11 result += 1 12 } else { 13 for col in 0..<board.count where canPlaceQueen(board, row, col) { 14 board[row][col] = true 15 backtrack(&board, row + 1, &result) 16 board[row][col] = false 17 } 18 } 19 } 20 21 private func canPlaceQueen(_ board: [[Bool]], _ row: Int, _ col: Int) -> Bool { 22 let n = board.count 23 24 for i in 0..<row where board[i][col] { 25 return false 26 } 27 28 var i = row - 1 29 var j = col - 1 30 while i >= 0 && j >= 0 { 31 if board[i][j] { 32 return false 33 } 34 i -= 1 35 j -= 1 36 } 37 38 i = row - 1 39 j = col + 1 40 while i >= 0 && j < n { 41 if board[i][j] { 42 return false 43 } 44 i -= 1 45 j += 1 46 } 47 48 return true 49 } 50 }
32ms
1 class Solution { 2 var placeArr : [Int]! 3 var totalN : Int = 0 4 func canPlace(_ row:Int , _ col:Int) -> Bool{ 5 6 var colInRow : Int = 0 7 var offset : Int = 0 8 for idx in 0 ..< row { 9 colInRow = placeArr[idx] 10 11 if colInRow == col { 12 return false 13 } 14 offset = row - idx 15 if colInRow == col - offset{ 16 return false 17 } 18 if colInRow == col + offset{ 19 return false 20 } 21 } 22 return true 23 } 24 25 var count : Int = 0 26 func place(_ row:Int) -> (){ 27 if row == totalN { 28 count += 1 29 }else{ 30 for col in 0..<totalN { 31 if canPlace(row,col) { 32 placeArr[row] = col 33 place(row + 1) 34 } 35 } 36 } 37 } 38 39 func totalNQueens(_ n: Int) -> Int { 40 totalN = n 41 placeArr = Array(repeating : 0 , count : totalN) 42 43 place(0) 44 return count 45 } 46 }
44ms
1 class Solution { 2 3 func totalNQueens(_ n: Int) -> Int { 4 var result = 0 5 var cols = [Int]() 6 cols.reserveCapacity(n) 7 queensDFS(n, &cols, &result) 8 return result 9 } 10 11 fileprivate func queensDFS(_ n: Int, _ cols: inout [Int], _ counter: inout Int) { 12 if cols.count == n { 13 counter += 1 14 return 15 } 16 17 for colIndex in 0..<n { 18 guard isValid(cols, colIndex) else { 19 continue 20 } 21 cols.append(colIndex) 22 queensDFS(n, &cols, &counter) 23 cols.removeLast() 24 } 25 } 26 27 fileprivate func isValid(_ cols: [Int], _ colIndex: Int) -> Bool { 28 for rowIndex in 0..<cols.count { 29 if colIndex == cols[rowIndex] { 30 return false 31 } 32 if abs(colIndex - cols[rowIndex]) == abs(cols.count - rowIndex) { 33 return false 34 } 35 } 36 return true 37 } 38 }