package top100liked

import (
	"fmt"
	"strings"
	"testing"
)

// https://leetcode.cn/problems/n-queens/description/?envType=study-plan-v2&envId=top-100-liked

func solveNQueens(n int) [][]string {
	res := [][]string{}
	path := []string{}
	// 同列/同对角线共享一个不变量，用三个独立数组各标记一条线是否被占。
	// 列：col；主对角线（↘）：row-col 为常数，+n-1 偏移成非负下标；
	// 副对角线（↙）：row+col 为常数，本身非负。行约束不需要（每行只放一个）。
	cols := make([]bool, n)     // cols[col]：第 col 列是否被占
	diag1 := make([]bool, 2*n-1) // diag1[row-col+n-1]：↘ 对角线是否被占
	diag2 := make([]bool, 2*n-1) // diag2[row+col]：↙ 对角线是否被占

	var helper func()
	helper = func() {
		row := len(path)
		if row == n {
			cp := make([]string, len(path))
			copy(cp, path)
			res = append(res, cp)
			return
		}
		for col := range n {
			d1 := row - col + n - 1 // ↘ 对角线下标
			d2 := row + col         // ↙ 对角线下标
			if !cols[col] && !diag1[d1] && !diag2[d2] {
				path = append(path, strings.Repeat(".", col)+"Q"+strings.Repeat(".", n-col-1))
				cols[col] = true
				diag1[d1] = true
				diag2[d2] = true
				helper()
				cols[col] = false
				diag1[d1] = false
				diag2[d2] = false
				path = path[:len(path)-1]
			}
		}
	}

	helper()

	return res
}

func Test(t *testing.T) {
	fmt.Printf("%+v\n", solveNQueens(4))
}

func Test2(t *testing.T) {
	fmt.Printf("%+v\n", solveNQueens(1))
}