NQueens

//成功地把GeeksForGeeks中的只输出一个解的解法改为了输出所有结果的解法。20181118.
//参考了此解法https://blog.csdn.net/H_JinXian/article/details/51088752

/* Java program to solve N Queen Problem using
backtracking */
public class Solution
{
final static int N = 4;
static int res = 0;
public static int board[][] = new int[N][N];

 

/* A utility function to print solution */

static void printSolution(int board[][])
{
for (int i = 0; i < N; i++)
{
for (int j = 0; j < N; j++)
System.out.print(board[i][j]
+ " ");
System.out.println();
}
System.out.println();
}

 

/* A utility function to check if a queen can
be placed on board[row][col]. Note that this
function is called when "col" queens are already
placeed in columns from 0 to col -1. So we need
to check only left side for attacking queens */
static boolean isSafe(int board[][], int row, int col)
{
int i, j;

/* Check this row on left side */
for (i = 0; i < col; i++)
if (board[row][i] == 1)
return false;

/* Check upper diagonal on left side */
for (i=row, j=col; i>=0 && j>=0; i--, j--)
if (board[i][j] == 1)
return false;

/* Check lower diagonal on left side */
for (i=row, j=col; j>=0 && i<N; i++, j--)
if (board[i][j] == 1)
return false;

return true;
}

/* A recursive utility function to solve N
Queen problem */
static void solveNQUtil(int board[][], int col)
{
/* base case: If all queens are placed
then return true */
if (col >= N) {
res++;
System.out.print("方案"+res+":\n");
printSolution(board);
return;
}
/* Consider this column and try placing
this queen in all rows one by one */
for (int i = 0; i < N; i++)
{
/* Check if the queen can be placed on
board[i][col] */
if (isSafe(board, i, col))
{
/* Place this queen in board[i][col] */
board[i][col] = 1;

/* recur to place rest of the queens */
solveNQUtil(board, col + 1);
//return;

/* If placing queen in board[i][col]
doesn't lead to a solution then
remove queen from board[i][col] */
board[i][col] = 0; // BACKTRACK
}
}

/* If the queen can not be placed in any row in
this colum col, then return false */
//return false;
}

/* This function solves the N Queen problem using
Backtracking. It mainly uses solveNQUtil () to
solve the problem. It returns false if queens
cannot be placed, otherwise, return true and
prints placement of queens in the form of 1s.
Please note that there may be more than one
solutions, this function prints one of the
feasible solutions.*/

/*boolean solveNQ()
{
int board[][] = null;
for(int i = 0; i < N; i++)
for(int j = 0; j < N; j++)
board[i][j] = 0;


int board[][] = {{0, 0, 0, 0},
{0, 0, 0, 0},
{0, 0, 0, 0},
{0, 0, 0, 0},
};

int board[][] = {{0, 0, 0, 0,0},
{0, 0, 0, 0, 0},
{0, 0, 0, 0, 0},
{0, 0, 0, 0, 0},
{0, 0, 0, 0, 0},
};

solveNQUtil(board, 0);
System.out.println();

if (solveNQUtil(board, 0) == false)
{
System.out.print("Solution does not exist");
return false;
}

//printSolution(board);
System.out.println();
return true;
}*/

// driver program to test above function
public static void main(String args[])
{
Solution Queen = new Solution();
//Queen.solveNQ();
Solution.solveNQUtil(board, 0);
System.out.println();
System.out.println(Queen.N+"皇后问题共有："+Queen.res+"种可能");
}
}