LeetCode Online Judge 题目C# 练习 - N-Queens
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.
For example,
There exist two distinct solutions to the 4-queens puzzle:
[
[".Q..", // Solution 1
"...Q",
"Q...",
"..Q."],
["..Q.", // Solution 2
"Q...",
"...Q",
".Q.."]
]
1 public static List<List<string>> NQueens(int n) 2 { 3 //solution is the List of map 4 List<List<int>> solution = new List<List<int>>(); 5 //map is for Q index on each row, for example ["..Q."] map[row] = 2; 6 List<int> map = new List<int>(); 7 //initial map for later 8 for (int i = 0; i < n; i++) 9 map.Add(0); 10 NQueensHelper(solution, map, 0, n); 11 12 List<List<string>> ret = new List<List<string>>(); 13 14 //Construct the ret with solution 15 for (int i = 0; i < solution.Count; i++) 16 { 17 List<string> board = new List<string>(); 18 string temp = ""; 19 for (int j = 0; j < n; j++) 20 { 21 for(int k = 0; k < n; k++) 22 { 23 if (k == solution[i][j]) 24 temp += "Q"; 25 else 26 temp += "."; 27 } 28 board.Add(temp); 29 temp = ""; 30 } 31 ret.Add(board); 32 } 33 34 return ret; 35 } 36 37 public static void NQueensHelper(List<List<int>> solutions, List<int> map, int row, int n) 38 { 39 if(n == 1) 40 { 41 map[0] = 0; 42 solutions.Add(map); 43 return; 44 } 45 46 if (row >= n) 47 { 48 solutions.Add(new List<int>(map)); 49 return; 50 } 51 52 for (int i = 0; i < n; i++) 53 { 54 if (row == 0) 55 { 56 map[row] = i; 57 NQueensHelper(solutions, map, row + 1, n); 58 } 59 else 60 { 61 bool valid = true; 62 for (int j = row - 1; j >= 0; j--) 63 { 64 //check if Q can be placed on this position 65 //Critical Algorithm here... 66 if (i == map[j] || Math.Abs(i - map[j]) == row - j) 67 { 68 valid = false; 69 break; 70 } 71 } 72 73 if (valid) 74 { 75 map[row] = i; 76 NQueensHelper(solutions, map, row + 1, n); 77 } 78 } 79 } 80
代码分析：
N皇后，经典的递归题。第一次写不出来，，第二次复习的时候居然跌跌撞撞的写出来了。O(n3)。
这种要求所有可能的解的题目，递归比DP好，很多时候DP未必能做出来。
下面把我贴到LEETCODE上跑的C++的代码也贴一下，以后好复习C++跟C#的区别
1 vector<vector<string> > solveNQueens(int n) { 2 // Start typing your C/C++ solution below 3 // DO NOT write int main() function 4 vector<vector<int> > solution;// = new List<List<int>>(); 5 vector<int> map;// = new List<int>(); 6 for (int i = 0; i < n; i++) 7 map.push_back(0); 8 NQueensHelper(solution, map, 0, n); 9 10 vector<vector<string> > ret;// = new List<List<string>>(); 11 12 for (int i = 0; i < solution.size(); i++) 13 { 14 vector<string> board;// = new List<string>(); 15 string temp = ""; 16 for (int j = 0; j < n; j++) 17 { 18 for(int k = 0; k < n; k++) 19 { 20 if (k == solution[i][j]) 21 temp += "Q"; 22 else 23 temp += "."; 24 } 25 board.push_back(temp); 26 temp = ""; 27 } 28 ret.push_back(board); 29 } 30 31 return ret; 32 } 33 34 void NQueensHelper(vector<vector<int> > &solutions, vector<int> &map, int row, int n) 35 { 36 if(n == 1) 37 { 38 map[0] = 0; 39 solutions.push_back(map); 40 return; 41 } 42 43 if (row >= n) 44 { 45 solutions.push_back(vector<int>(map)); 46 return; 47 } 48 49 for (int i = 0; i < n; i++) 50 { 51 if (row == 0) 52 { 53 map[row] = i; 54 NQueensHelper(solutions, map, row + 1, n); 55 } 56 else 57 { 58 bool valid = true; 59 for (int j = row - 1; j >= 0; j--) 60 { 61 if (i == map[j] || abs(i - map[j]) == row - j) 62 { 63 valid = false; 64 break; 65 } 66 } 67 68 if (valid) 69 { 70 map[row] = i; 71 NQueensHelper(solutions, map, row + 1, n); 72 } 73 } 74 } 75 }
