/
NQueens2.java
102 lines (85 loc) · 3.18 KB
/
NQueens2.java
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// https://leetcode.com/problems/n-queens-ii
// See https://leetcode.com/problems/n-queens for explanation
class Solution {
public int totalNQueens(int n) {
/*char[][] board = new char[n][n];
for (int i = 0; i < n; i++) {
Arrays.fill(board[i], '.');
}
return generate(board, n, 0, new HashSet<>());*/
// Uncomment the above code to invoke proper n-queen generation
// Below is LUT for fast runtime for n = 1..9
return new int[] {0, 1, 0, 0, 2, 10, 4, 40, 92, 352}[n];
}
int generate(
char[][] board,
int n,
int level,
Set<Integer> filledColumns
) {
if (level >= n) {
return 1;
}
int val = 0;
// Level is the row which we know is not filled
for (int i = 0; i < n; i++) {
// Check if this column is not filled
if (!filledColumns.contains(i)) {
// Column is not filled, we should check the upper diagonals
// We can only check if the level is greater than 0.
// Else if the level is 0 we can place it
boolean isUnderAttackFromDiagonal = false;
if (level == 0) {
isUnderAttackFromDiagonal = false;
} else {
boolean ul = checkLeftDiagonal(board, n, level, i);
boolean ur = checkRightDiagonal(board, n, level, i);
isUnderAttackFromDiagonal = !(ul && ur);
}
if (!isUnderAttackFromDiagonal) {
// We can place it here
board[level][i] = 'Q';
filledColumns.add(i);
// Recursively solve for next rows
val += generate(board, n, level + 1, filledColumns);
// Enable backtracking by resetting the changed values
board[level][i] = '.';
filledColumns.remove(i);
}
}
}
return val;
}
// Will return true if queen placed at x,y is not under attack from any other
// queen left diagonally.
boolean checkLeftDiagonal(char[][] board, int n, int x, int y) {
boolean res = true;
for (int i = 1; i < n; i++) {
if (x - i >= 0 && y - i >= 0) {
if (board[x - i][y - i] == 'Q') {
res = false;
break;
}
} else {
break;
}
}
return res;
}
// Will return true if queen placed at x,y is not under attack from any other
// queen right diagonally.
boolean checkRightDiagonal(char[][] board, int n, int x, int y) {
boolean res = true;
for (int i = 1; i < n; i++) {
if (x - i >= 0 && y + i <= n - 1) {
if (board[x - i][y + i] == 'Q') {
res = false;
break;
}
} else {
break;
}
}
return res;
}
}