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NQueens.java
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77 lines (74 loc) · 1.86 KB
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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.
*
* For example,
*
* There exist two distinct solutions to the 4-queens puzzle:
*
* [
* [".Q..", // Solution 1
* "...Q",
* "Q...",
* "..Q."],
*
* ["..Q.", // Solution 2
* "Q...",
* "...Q",
* ".Q.."]
* ]
*/
import java.util.ArrayList;
public class NQueens {
public ArrayList<String[]> solveNQueens(int n) {
ArrayList<String[]> ret = new ArrayList<String[]>();
if (n == 0)
return ret;
StringBuffer line = new StringBuffer();
for (int i = 0; i < n; i++) {
line.append('.');
}
StringBuffer[] sol = new StringBuffer[n];
for (int i = 0; i < n; i++) {
sol[i] = new StringBuffer(line.toString());
}
boolean[] cols = new boolean[n];
int[] row = new int[n];
findSolutions(n, 0, ret, sol, row, cols);
return ret;
}
private void findSolutions(int n, int start, ArrayList<String[]> ret,
StringBuffer[] sol, int[] row, boolean[] cols) {
if (start == n) {
String[] newSol = new String[n];
for (int i = 0; i < n; i++) {
newSol[i] = sol[i].toString();
}
ret.add(newSol);
} else {
for (int i = 0; i < n; i++) {
if (cols[i])
continue;
boolean ok = true;
for (int j = 0; j < start; j++) {
if (Math.abs(start - j) == Math.abs(i - row[j])) {
ok = false;
break;
}
}
if (ok) {
cols[i] = true;
sol[start].setCharAt(i, 'Q');
row[start] = i;
findSolutions(n, start + 1, ret, sol, row, cols);
row[start] = 0;
sol[start].setCharAt(i, '.');
cols[i] = false;
}
}
}
}
}