【LeetCode】N-Queens && 【九度】题目1140：八皇后
N-Queens
Total Accepted: 3171 Total Submissions: 12620 My Submissions
The n-queens puzzle is the problem of placing n queens on an n×n chessboard such that no two queens attack each other.
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 '.' both indicate a queen and an empty space respectively.
For example,
There exist two distinct solutions to the 4-queens puzzle:
[
[".Q..", // Solution 1
"...Q",
"Q...",
"..Q."],
["..Q.", // Solution 2
"Q...",
"...Q",
".Q.."]
]
著名的N皇后问题，经典的DFS，我发现BFS也可以过。BFS比DFS慢了140ms。
和九度题目1140：八皇后解法一致。
Java DFS AC
public class Solution {
public ArrayList<String[]> solveNQueens(int n) {
list = new ArrayList<String[]>();
if(n <= 0){
return list;
}
int []queen = new int[n + 1];
for(int i = 1; i < n+1 ; i++){
queen[1] = i;
dfs(queen,2,n);
}
return list;
}
public ArrayList<String[]> list;
public void dfs(int queen[], int line, int n) {
if(line == n+1){
String[] tempArr = new String[n];
for(int i = 1; i < n+1; i++){
StringBuffer sb = new StringBuffer();
for (int j = 1; j < n+1; j++) {
if (queen[i] == j) {
sb.append("Q");
}else {
sb.append(".");
}
}
tempArr[i-1] = sb.toString();
}
list.add(tempArr);
return;
}
for(int i = 1; i < n+1; i++){
if(valid(line, i, queen)){
queen[line] = i;
dfs(queen ,line+1, n);
queen[line] = 0;
}
}
}
public boolean valid(int row, int col, int []queen) {
for (int i = 1; i < row; i++) {
if (queen[i] != 0 && (queen[i] == col
|| Math.abs(i - row) == Math.abs(queen[i] - col)))
return false;
}
return true;
}
}Java BFS AC
public class Solution {
public ArrayList<String[]> solveNQueens(int n) {
ArrayList<String[]> list = new ArrayList<String[]>();
if(n <= 0){
return list;
}
for(int i = 1; i < n+1; i++){
Queue<Node> queue = new LinkedList<Node>();
String[][] queenArr = new String[n+1][n+1];
queenArr[1][i] = "Q";
int location[] = new int[n+1];
location[1] = i;
queue.offer(new Node(location,queenArr,1));
bfs(list,queue,n);
}
return list;
}
public void bfs(ArrayList<String[]> list,Queue<Node> queue, int n){
while(!queue.isEmpty()){
Node node = queue.peek();
queue.poll();
String [][]tempArr = node.queenArr;
int location[] = node.location;
int line = node.line;
if(line == n){
String array[] = new String[n];
for(int i = 1; i < n+1 ; i++){
StringBuffer sb = new StringBuffer();
for(int j = 1; j < n+1; j++){
if(tempArr[i][j] == null){
tempArr[i][j] = ".";
}
sb.append(tempArr[i][j]);
}
array[i-1] = sb.toString();
}
list.add(array);
continue;
}
for(int i = 1; i < n+1; i++){
String array[][] = new String[n+1][n+1];
int queen[] = new int[n+1];
if(valid(line+1,i,location,n)){
for (int j = 1; j < n+1; j++) {
queen[j] = location[j];
}
queen[line+1] = i;
for (int j = 1; j < n+1; j++) {
for (int k = 1; k < n+1; k++) {
array[j][k] = tempArr[j][k];
}
}
array[line+1][i] = "Q";
queue.offer(new Node(queen,array,line+1));
}
}
}
}
public boolean valid(int row, int col, int queen[], int n ) {
for (int i = 1; i < row; i++) {
if (queen[i] != 0 && (queen[i] == col
|| Math.abs(i - row) == Math.abs(queen[i] - col))){
return false;
}
}
return true;
}
public class Node{
int location[];
String[][] queenArr;
int line;
Node(int location[], String [][]queenArr, int line){
this.location = location;
this.queenArr = queenArr;
this.line = line;
}
}
} 九度题目1140：八皇后 Java AC
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.StreamTokenizer;
import java.util.ArrayList;
import java.util.Collections;
public class Main{
/*
* 1140
*/
public static void main(String[] args) throws Exception {
int n = 8;
// count = 0;
solveNQueens(n);
StreamTokenizer st = new StreamTokenizer
(new BufferedReader(new InputStreamReader(System.in)));
while (st.nextToken() != StreamTokenizer.TT_EOF) {
int allNum = (int) st.nval;
while (allNum > 0) {
st.nextToken() ;
int seq = (int) st.nval;
// Collections.sort(arrList);
// System.out.println(count);
System.out.println(list.get(seq-1));
allNum -- ;
}
}
}
public static void solveNQueens(int n) {
list = new ArrayList<String>();
if(n <= 0){
return;
}
int []queen = new int[n + 1];
for(int i = 1; i < n+1 ; i++){
queen[1] = i;
dfs(queen,2,n);
}
Collections.sort(list);
}
public static ArrayList<String> list;
public static void dfs(int queen[], int line, int n) {
if(line == n+1){
StringBuffer sb = new StringBuffer();
for(int i = 1; i < n+1; i++){
sb.append(queen[i]);
}
list.add(sb.toString());
return;
}
for(int i = 1; i < n+1; i++){
if(valid(line, i, queen)){
int array[] = new int[n+1];
for(int j = 1; j < n+1; j++){
array[j] = queen[j];
}
array[line] = i;
dfs(array ,line+1, n);
}
}
}
public static boolean valid(int row, int col, int []queen) {
for (int i = 1; i < row; i++) {
if (queen[i] != 0 && (queen[i] == col
|| Math.abs(i - row) == Math.abs(queen[i] - col)))
return false;
}
return true;
}
}
/**************************************************************
Problem: 1140
User: wangzhenqing
Language: Java
Result: Accepted
Time:130 ms
Memory:21604 kb
****************************************************************/