[Swift]LeetCode51. N皇后 | N-Queens
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➤微信公众号：山青咏芝（shanqingyongzhi）
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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 all distinct solutions to the n-queens puzzle.
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:
Input: 4 Output: [ [".Q..", // Solution 1 "...Q", "Q...", "..Q."], ["..Q.", // Solution 2 "Q...", "...Q", ".Q.."] ] Explanation: There exist two distinct solutions to the 4-queens puzzle as shown above.
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，返回所有不同的 n 皇后问题的解决方案。
每一种解法包含一个明确的 n 皇后问题的棋子放置方案，该方案中 'Q' 和 '.' 分别代表了皇后和空位。
示例:
输入: 4 输出: [ [".Q..", // 解法 1 "...Q", "Q...", "..Q."], ["..Q.", // 解法 2 "Q...", "...Q", ".Q.."] ] 解释: 4 皇后问题存在两个不同的解法。
24ms
1 class Solution { 2 func solveNQueens(_ n: Int) -> [[String]] { 3 guard n > 0 else { 4 return [] 5 } 6 var results = [[String]]() 7 var cols = [Int]() 8 cols.reserveCapacity(n) 9 dfsHelper(n, &cols, &results) 10 return results 11 } 12 13 fileprivate func dfsHelper(_ n: Int, _ cols: inout [Int], _ results: inout [[String]]) { 14 if cols.count == n { 15 results.append(draw(cols)) 16 return 17 } 18 19 for i in 0..<n { 20 guard isValid(cols, i) else { 21 continue 22 } 23 cols.append(i) 24 dfsHelper(n, &cols, &results) 25 cols.removeLast() 26 } 27 } 28 29 30 fileprivate func isValid(_ cols: [Int], _ colIndex: Int) -> Bool { 31 for rowIndex in 0..<cols.count { 32 if colIndex == cols[rowIndex] { 33 return false 34 } 35 if cols.count - rowIndex == colIndex - cols[rowIndex] { 36 return false 37 } 38 if rowIndex - cols.count == colIndex - cols[rowIndex] { 39 return false 40 } 41 } 42 return true 43 } 44 45 fileprivate func draw(_ cols: [Int]) -> [String] { 46 var result = [String]() 47 for rowIndex in 0..<cols.count { 48 var row = "" 49 for j in 0..<cols.count { 50 row += cols[rowIndex] == j ? "Q" : "." 51 } 52 result.append(row) 53 } 54 return result 55 } 56 }
48ms
1 class Solution { 2 func solveNQueens(_ n: Int) -> [[String]] { 3 var result = [[String]]() 4 var currB = Array(repeating:String(Array(repeating:".",count:n)),count:n) 5 var cols = Array(repeating:false,count:n) 6 var diagnal = Array(repeating:false,count:2*n-1) 7 var antidiagonal = Array(repeating:false,count:2*n-1) 8 9 helper(&result,&currB,n,0,&cols,&diagnal,&antidiagonal) 10 return result 11 } 12 13 func helper(_ result: inout [[String]], _ currB: inout [String], _ n: Int, _ row: Int, _ cols: inout [Bool], _ diagonal: inout [Bool], _ antiDiagonal: inout [Bool]) -> Void { 14 15 16 if(row==n) { 17 result.append(currB) 18 return 19 } 20 21 for col in 0..<n { 22 if(cols[col] || diagonal[row-col+n-1] || antiDiagonal[row+col]) { 23 continue 24 } 25 26 var curr = currB 27 28 29 cols[col] = true 30 diagonal[row-col+n-1] = true 31 antiDiagonal[row+col] = true 32 33 curr[row] = String(curr[row].prefix(col)) + String("Q") + String(curr[row].dropFirst(col + 1)) 34 helper(&result,&curr,n,row+1,&cols,&diagonal,&antiDiagonal) 35 cols[col] = false 36 diagonal[row-col+n-1] = false 37 antiDiagonal[row+col] = false 38 curr[row] = String(curr[row].prefix(col)) + String(".") + String(curr[row].dropFirst(col + 1)) 39 } 40 41 return 42 } 43 }
52ms
1 class Solution { 2 func solveNQueens(_ n: Int) -> [[String]] { 3 var result = [[String]]() 4 var answer = [String]() 5 nQueens(n: n, p: 0, l: 0, m: 0, r: 0, answer: &answer, result: &result) 6 return result 7 } 8 9 private func getNq(index: Int, n: Int) -> String { 10 var charArr = [Character](repeating: ".", count: n) 11 charArr[index] = "Q" 12 return String(charArr) 13 } 14 15 private func nQueens(n: Int, p: Int, l: Int, m: Int, r: Int, answer: inout [String], result: inout [[String]]) { 16 if p >= n { 17 result.append(answer) 18 return 19 } 20 let mask = l | m | r 21 var i = 0 22 var b = 1 23 while i < n { 24 if mask & b == 0 { 25 answer.append(getNq(index: i, n: n)) 26 nQueens(n: n, p: p+1, l: (l | b) >> 1, m: m | b, r: (r | b) << 1, answer: &answer, result: &result) 27 answer.removeLast() 28 } 29 i += 1 30 b <<= 1 31 } 32 } 33 }
56ms
1 class Solution { 2 func solveNQueens(_ n: Int) -> [[String]] { 3 var res = [[String]]() 4 var curr = Array(repeating: 0, count: n) 5 var usedColumn = Array(repeating: false, count: n) 6 var usedDiagonals = Array(repeating: false, count: n * 2 - 1) 7 var usedRevDiagonals = Array(repeating: false, count: n * 2 - 1) 8 generateSolution(n , 0, &curr, &res, &usedColumn, &usedDiagonals, &usedRevDiagonals) 9 return res 10 } 11 12 13 private func generateSolution(_ n: Int, _ row: Int, _ curr: inout [Int], _ res: inout [[String]], _ usedColumn: inout [Bool], _ usedDiagonals: inout [Bool], _ usedRevDiagonals: inout [Bool]) { 14 if row == n { 15 res.append(toList(n, curr)) 16 return 17 } 18 19 for i in 0..<n { 20 if isValid(n, row, i, usedColumn, usedDiagonals, usedRevDiagonals) { 21 mark(n, row, i, &usedColumn, &usedDiagonals, &usedRevDiagonals) 22 curr[row] = i 23 generateSolution(n , row + 1, &curr, &res, &usedColumn, &usedDiagonals, &usedRevDiagonals) 24 unMark(n, row, i, &usedColumn, &usedDiagonals, &usedRevDiagonals) 25 } 26 } 27 } 28 29 30 private func mark(_ n: Int, _ row: Int, _ column: Int, _ usedColumn: inout [Bool], _ usedDiagonals: inout [Bool], _ usedRevDiagonals: inout [Bool]) { 31 usedColumn[column] = true 32 usedDiagonals[row + column] = true 33 usedRevDiagonals[row - column + n - 1] = true 34 } 35 36 37 private func unMark(_ n: Int, _ row: Int, _ column: Int, _ usedColumn: inout [Bool], _ usedDiagonals: inout [Bool], _ usedRevDiagonals: inout [Bool]) { 38 usedColumn[column] = false 39 usedDiagonals[row + column] = false 40 usedRevDiagonals[row - column + n - 1] = false 41 } 42 43 44 private func isValid(_ n: Int, _ row: Int, _ column: Int, _ usedColumn: [Bool], _ usedDiagonals: [Bool], _ usedRevDiagonals: [Bool]) -> Bool { 45 return !usedColumn[column] && !usedDiagonals[row + column] && !usedRevDiagonals[row - column + n - 1] 46 } 47 48 49 private func toList(_ n: Int, _ curr: [Int]) -> [String] { 50 var res = [String]() 51 for num in curr { 52 var tmp = Array(repeating: ".", count: n) 53 tmp[num] = "Q" 54 var string = String() 55 for s in tmp { 56 string += s 57 } 58 res.append(string) 59 } 60 return res 61 } 62 }
68ms
1 class Solution { 2 func solveNQueens(_ n: Int) -> [[String]] { 3 var board = [[Character]](repeating: [Character](repeating: ".", count: n), count: n) 4 var result = [[String]]() 5 backtrack(&board, 0, &result) 6 return result 7 } 8 9 private func backtrack(_ board: inout [[Character]], _ row: Int, _ result: inout [[String]]) { 10 if row == board.count { 11 result.append(board.map { String($0) }) 12 } else { 13 for col in 0..<board.count where canPlaceQueen(board, row, col) { 14 board[row][col] = "Q" 15 backtrack(&board, row + 1, &result) 16 board[row][col] = "." 17 } 18 } 19 } 20 21 private func canPlaceQueen(_ board: [[Character]], _ row: Int, _ col: Int) -> Bool { 22 let n = board.count 23 24 for i in 0..<row where board[i][col] == "Q" { 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] == "Q" { 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] == "Q" { 42 return false 43 } 44 i -= 1 45 j += 1 46 } 47 48 return true 49 } 50 }
224ms
1 class Solution { 2 func solveNQueens(_ n: Int) -> [[String]] { 3 var result = [[String]]() 4 var currB = Array(repeating:String(Array(repeating:".",count:n)),count:n) 5 6 helper(&result,&currB,n,0) 7 return result 8 } 9 10 func canPlace( _ row: Int, _ col: Int, _ board: [String]) -> Bool { 11 var c = -1 12 for i in 0..<row { 13 for j in 0..<board[0].characters.count { 14 if charAt(board[i], j) == "Q" { 15 c = j 16 break 17 } 18 } 19 20 // check col 21 if c == col { 22 return false 23 } 24 25 // check diagnol 26 if abs(c - col) == abs(i - row) { 27 return false 28 } 29 } 30 31 return true 32 } 33 34 func charAt(_ str: String, _ index: Int) -> Character { 35 return str[str.index(str.startIndex, offsetBy: index)] 36 } 37 38 39 func helper(_ result: inout [[String]], _ currB: inout [String], _ n: Int, _ row: Int) { 40 41 if(row>=n) { 42 var curr = currB 43 result.append(curr) 44 return 45 } 46 47 for col in 0..<n { 48 if(canPlace(row,col,currB)) { 49 //print("Placing Q at row:",row,"col:",col) 50 currB[row] = String(currB[row].prefix(col)) + String("Q") + String(currB[row].dropFirst(col + 1)) 51 helper(&result,&currB,n,row+1) 52 //Backtrack 53 currB[row] = String(currB[row].prefix(col)) + String(".") + String(currB[row].dropFirst(col + 1)) 54 } 55 56 } 57 58 return 59 } 60 }
