Created
May 27, 2018 06:38
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public class NQueensBT { | |
public int[][] solution; | |
public NQueensBT(int N) { | |
solution = new int[N][N]; | |
for (int i = 0; i < N; i++) { | |
for (int j = 0; j < N; j++) { | |
solution[i][j] = 0; | |
} | |
} | |
} | |
public void solve(int N) { | |
if(placeQueens(0, N)){ | |
//print the result | |
for (int i = 0; i < N; i++) { | |
for (int j = 0; j < N; j++) { | |
System.out.print(" " + solution[i][j]); | |
} | |
System.out.println(); | |
} | |
}else{ | |
System.out.println("NO SOLUTION EXISTS"); | |
} | |
} | |
public boolean placeQueens(int queen, int N) { | |
// will place the Queens one at a time, for column wise | |
if(queen==N){ | |
//if we are here that means we have solved the problem | |
return true; | |
} | |
for (int row = 0; row < N; row++) { | |
// check if queen can be placed row,col | |
if (canPlace(solution, row, queen)) { | |
// place the queen | |
solution[row][queen] = 1; | |
// solve for next queen | |
if(placeQueens(queen+1, N)){ | |
return true; | |
} | |
//if we are here that means above placement didn't work | |
//BACKTRACK | |
solution[row][queen]=0; | |
} | |
} | |
//if we are here that means we haven't found solution | |
return false; | |
} | |
// check if queen can be placed at matrix[row][column] | |
public boolean canPlace(int[][] matrix, int row, int column) { | |
// since we are filling one column at a time, | |
// we will check if no queen is placed in that particular row | |
for (int i = 0; i < column; i++) { | |
if (matrix[row][i] == 1) { | |
return false; | |
} | |
} | |
// we are filling one column at a time,so we need to check the upper and | |
// diagonal as well | |
// check upper diagonal | |
for (int i = row, j = column; i >= 0 && j >= 0; i--, j--) { | |
if (matrix[i][j] == 1) { | |
return false; | |
} | |
} | |
// check lower diagonal | |
for (int i = row, j = column; i < matrix.length && j >= 0; i++, j--) { | |
if (matrix[i][j] == 1) { | |
return false; | |
} | |
} | |
// if we are here that means we are safe to place Queen at row,column | |
return true; | |
} | |
public static void main(String[] args) { | |
int N = 4; | |
NQueensBT q = new NQueensBT(N); | |
q.solve(N); | |
} | |
} |
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