51.N-Queens

51. N Queens

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https://leetcode.com/problems/n-queens/

https://www.lintcode.com/problem/n-queens/description

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The n-queens puzzle is the problem of placing n queens on an nร—n chessboard such that no two queens attack each other(Any two queens can't be in the same row, column, diagonal line).

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 '.' each indicate a queen and an empty space respectively.

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Approach 1: Recursion

Time: O(N!) Space: O(N)

class Solution {
    public List<List<String>> solveNQueens(int n) {
        List<List<String>> ans = new ArrayList();
        if (n <= 0) return ans;

        List<Integer> cols = new ArrayList();
        dfs(ans, cols, n);   

        return ans;
    }

    private void dfs(List<List<String>> ans, List<Integer> cols, int n) {
        if (cols.size() == n) {
            ans.add(output(cols));
            return;
        }


        for (int col = 0; col < n; col++) {
            if (isValid(cols, col)) {
                cols.add(col);
                dfs(ans, cols, n);
                cols.remove(cols.size() - 1);
            }
        }
    }

    private boolean isValid(List<Integer> cols, int col) {
        int row = cols.size();
        for (Integer r = 0; r < row; r++) {
            Integer c = cols.get(r);
            if (c == col) return false;
            if (row - col == r - c)  return false;
            if (row + col == r + c) return false;
        }
        return true;
    }

    private List<String> output(List<Integer> cols) {
        List<String> ans = new ArrayList();
        int n = cols.size();
        for (int r = 0; r < n; r++) {
            StringBuilder sb = new StringBuilder();
            for (int c = 0; c < n; c++) {
                if (c == cols.get(r)) {
                    sb.append("Q");
                } else {
                    sb.append(".");
                }
            }
            ans.add(sb.toString());
        }

        return ans;
    }
}

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