/*
 * @lc app=leetcode id=51 lang=java
 *
 * [51] N-Queens
 */

// @lc code=start

import java.util.ArrayList;

class Solution {
    public List<List<String>> solveNQueens(int n) {
        int[][] m = createMap(n);
        List<List<String>> r = new ArrayList<>();
        dfsNQueen(r, m, 0, n, 0);
        return r;
    }

    private void dfsNQueen(List<List<String>> r, int[][] m, int i, int n, int p) {
        if(i == n && pass(m, n, i)) {
            r.add(buildRetStr(m));
            return;
        } else if (i>=n) {
            return;
        }
        if(!pass(m,n, i)) {
            return;
        }
        for(int j = p; j<n*n; j++) {
            int x = j / n;
            int y = j % n;
            if(m[x][y] == 0) {
                m[x][y] = 1;
                dfsNQueen(r, m, i+1, n, j+1);
                m[x][y] = 0;
            }
        }
    }

    private boolean pass(int[][] m , int n, int i) {
        // todo: check logic
        return checkRow(m, n, i) && checkColumn(m, n) && checkLeftSlash(m,n) && checkRightSlash(m,n);
    }

    private boolean checkRow(int[][] m, int n, int s) {
        for(int i=0; i<n; i++) {
            if(!checkWithStrategy(m, new Point(i, 0), n, pos->{
                return new Point(pos.x, pos.y+1);
            })) {
                return false;
            }
            if(i < s && !checkRowNotEmpty(m, n, i)) {
                return false;
            }
        }
        return true;
    }

    private boolean checkRowNotEmpty(int[][] m, int n, int s) {
        for(int i=0; i<n; i++) {
            if(m[s][i] != 0) {
                return true;
            }
        }
        return false;
    }
    
    private boolean checkColumn(int[][] m, int n) {
        for(int i = 0; i<n; i++) {
            if(!checkWithStrategy(m, new Point(0, i), n, pos->{
                return new Point(pos.x+1, pos.y);
            })) {
                return false;
            }
        }
        return true;
    }

    private boolean checkLeftSlash(int[][] m, int n) {
        for(int i = 0; i<n; i++) {
            if(!checkWithStrategy(m, new Point(i, 0), n, pos->{
                return new Point(pos.x+1, pos.y+1);
            })) {
                return false;
            }
            if(!checkWithStrategy(m, new Point(0, i), n, pos->{
                return new Point(pos.x+1, pos.y+1);
            })) {
                return false;
            }
        }
        return true;
    }

    private boolean checkRightSlash(int[][] m, int n) {
        for(int i = 0; i<n; i++) {
            if(!checkWithStrategy(m, new Point(0, i), n, pos->{
                return new Point(pos.x+1, pos.y-1);
            })) {
                return false;
            }
            if(!checkWithStrategy(m, new Point(i, n-1), n, pos->{
                return new Point(pos.x+1, pos.y-1);
            })) {
                return false;
            }
        }
        return true;
    }


    private boolean checkWithStrategy(int[][] m, Point pos, int n,Function<Point, Point> incrStrategy) {
        int c = 0;
        if(m[pos.x][pos.y] !=0) {
            c++;
        }
        for(int i=0;i<n-1;i++) {
            pos = incrStrategy.apply(pos);
            if(pos.x >=n || pos.y>= n || pos.x <0 || pos.y <0) {
                break;
            }
            if(m[pos.x][pos.y] != 0) {
                c++;
                if(c>1) {
                    return false;
                }
            }
        }
        return true;
    }

    private int[][] createMap(int n) {
        int[][] r = new int[n][n];
        zset(r);
        return r;
    }

    private void zset(int[][] m) {
        if(m == null) {
            return;
        }
        for (int i = 0; i < m.length; i++) {
            if(m[i]==null) {
                continue;
            }
            for(int j = 0; j < m[i].length; j++) {
                m[i][j] = 0;
            }
        }
    }

    private List<String> buildRetStr(int[][] m) {
        List<String> r = new ArrayList<String>();
        if(m == null) {
            return r;
        }
        for(int i = 0; i<m.length; i++) {
            int[] t = m[i];
            if(t == null) {
                r.add("");
                continue;
            }
            StringBuilder sbd = new StringBuilder();
            for(int j = 0; j<t.length; j++) {
                sbd.append(t[j]==0?".":"Q");
            }
            r.add(sbd.toString());
        }
        return r;
    }

    public static class Point {
        public int x;
        public int y;

        public Point(int x, int y) {
            this.x = x;
            this.y = y;
        }
    }
}
// @lc code=end