Eight Queen Problem

This idea is from https://www.cnblogs.com/bigmoyan/p/4521683.html. It greatly reduces the space complexity compare to any 2D array solution.

public class EightQueen {
    // layer
    int n = 8;
    int[] r = new int[n];
    int count = 0;

    public void queen(int row) {
        if (row == n) {
            count++;
            return;
        }
        for (int i = 0; i < n; i++) {
            r[row] = i;
            if (isValid(row)) {
                queen(row + 1);
            }
        }
    }

    private boolean isValid(int row) {
        for (int i = 0; i < row; i++) {
            if (r[row] == r[i]  row - r[row] == i - r[i]  row + r[row] == i + r[i]) {
                return false;
            }
        }
        return true;
    }

    public static void main(String[] args) {
        EightQueen eq=new EightQueen();
        eq.queen(0);
        System.out.println(eq.count);
    }
}