6060
6161<!-- 这里可写通用的实现逻辑 -->
6262
63+ ** 方法一：分类讨论**
64+
65+ 我们先统计当前棋盘上 ` 'X' ` 和 ` 'O' ` 的数量，记为 $x$ 和 $o$。接下来，我们分情况讨论：
66+
67+ - 如果 $x \neq o$ 且 $x - 1 \neq o$，则当前棋盘不可能是有效棋盘，返回 ` false ` 。
68+ - 如果当前棋盘上玩家 1 获胜，但 $x-1 \neq o$，则当前棋盘不可能是有效棋盘，返回 ` false ` 。
69+ - 如果当前棋盘上玩家 2 获胜，但 $x \neq o$，则当前棋盘不可能是有效棋盘，返回 ` false ` 。
70+ - 其他情况下，当前棋盘是有效棋盘，返回 ` true ` 。
71+
72+ 时间复杂度 $O(C)$，空间复杂度 $O(1)$。其中 $C$ 是棋盘上的格子数。本题中 $C = 9$。
73+
6374<!-- tabs:start -->
6475
6576### ** Python3**
6980``` python
7081class Solution :
7182 def validTicTacToe (self board : List[str ]) -> bool :
72- def win (p ):
83+ def win (x ):
7384 for i in range (3 ):
74- if board[i][0 ] == board[i][ 1 ] == board[i][ 2 ] == p :
85+ if all ( board[i][j ] == x for j in range ( 3 )) :
7586 return True
76- if board[0 ][i] == board[ 1 ][i] == board[ 2 ][i] == p :
87+ if all ( board[j ][i] == x for j in range ( 3 )) :
7788 return True
78- if board[0 ][ 0 ] == board[ 1 ][ 1 ] == board[ 2 ][ 2 ] == p :
89+ if all ( board[i][i ] == x for i in range ( 3 )) :
7990 return True
80- return board[0 ][2 ] == board[1 ][1 ] == board[2 ][0 ] == p
81-
82- x, o = 0 , 0
83- for i in range (3 ):
84- for j in range (3 ):
85- if board[i][j] == ' X'
86- x += 1
87- elif board[i][j] == ' O'
88- o += 1
91+ return all (board[i][2 - i] == x for i in range (3 ))
8992
93+ x = sum (board[i][j] == ' X' for i in range (3 ) for j in range (3 ))
94+ o = sum (board[i][j] == ' O' for i in range (3 ) for j in range (3 ))
9095 if x != o and x - 1 != o:
9196 return False
92-
9397 if win(' X' and x - 1 != o:
9498 return False
95-
9699 return not (win(' O' and x != o)
97100```
98101
@@ -102,121 +105,153 @@ class Solution:
102105
103106``` java
104107class Solution {
108+ private String [] board;
109+
105110 public boolean validTicTacToe (String [] board ) {
106- int x = 0 , o = 0 ;
107- for (int i = 0 ; i < 3 ; i++ ) {
108- for (int j = 0 ; j < 3 ; j++ ) {
109- if (board[i]. charAt(j) == ' X'
110- x++ ;
111- } else if (board[i]. charAt(j) == ' O'
112- o++ ;
113- }
114- }
115- }
111+ this . board = board;
112+ int x = count(' X' = count(' O'
116113 if (x != o && x - 1 != o) {
117114 return false ;
118115 }
119- if (win(board, ' X' && x - 1 != o) {
116+ if (win(' X' && x - 1 != o) {
120117 return false ;
121118 }
122- return ! (win(board, ' O' && x != o);
119+ return ! (win(' O' && x != o);
123120 }
124121
125- private boolean win (String [] b , char p ) {
126- for (int i = 0 ; i < 3 ; i ++ ) {
127- if (b [i]. charAt(0 ) == p && b [i]. charAt(1 ) == p && b [i]. charAt(2 ) == p ) {
122+ private boolean win (char x ) {
123+ for (int i = 0 ; i < 3 ; ++ i ) {
124+ if (board [i]. charAt(0 ) == x && board [i]. charAt(1 ) == x && board [i]. charAt(2 ) == x ) {
128125 return true ;
129126 }
130- if (b [0 ]. charAt(i) == p && b [1 ]. charAt(i) == p && b [2 ]. charAt(i) == p ) {
127+ if (board [0 ]. charAt(i) == x && board [1 ]. charAt(i) == x && board [2 ]. charAt(i) == x ) {
131128 return true ;
132129 }
133130 }
134- if (b [0 ]. charAt(0 ) == p && b [1 ]. charAt(1 ) == p && b [2 ]. charAt(2 ) == p ) {
131+ if (board [0 ]. charAt(0 ) == x && board [1 ]. charAt(1 ) == x && board [2 ]. charAt(2 ) == x ) {
135132 return true ;
136133 }
137- return b[0 ]. charAt(2 ) == p && b[1 ]. charAt(1 ) == p && b[2 ]. charAt(0 ) == p;
134+ return board[0 ]. charAt(2 ) == x && board[1 ]. charAt(1 ) == x && board[2 ]. charAt(0 ) == x;
135+ }
136+
137+ private int count (char x ) {
138+ int cnt = 0 ;
139+ for (var row : board) {
140+ for (var c : row. toCharArray()) {
141+ if (c == x) {
142+ ++ cnt;
143+ }
144+ }
145+ }
146+ return cnt;
138147 }
139148}
140149```
141150
151+ ### ** C++**
152+
153+ ``` cpp
154+ class Solution {
155+ public:
156+ bool validTicTacToe(vector<string >& board) {
157+ auto count = [ &] (char x) {
158+ int ans = 0;
159+ for (auto& row : board) for (auto& c : row) ans += c == x;
160+ return ans;
161+ };
162+ auto win = [ &] (char x) {
163+ for (int i = 0; i < 3; ++i) {
164+ if (board[ i] [ 0 ] == x && board[ i] [ 1 ] == x && board[ i] [ 2 ] == x) return true;
165+ if (board[ 0] [ i ] == x && board[ 1] [ i ] == x && board[ 2] [ i ] == x) return true;
166+ }
167+ if (board[ 0] [ 0 ] == x && board[ 1] [ 1 ] == x && board[ 2] [ 2 ] == x) return true;
168+ return board[ 0] [ 2 ] == x && board[ 1] [ 1 ] == x && board[ 2] [ 0 ] == x;
169+ };
170+ int x = count('X'), o = count('O');
171+ if (x != o && x - 1 != o) return false;
172+ if (win('X') && x - 1 != o) return false;
173+ return !(win('O') && x != o);
174+ }
175+ };
176+ ```
177+
142178### **Go**
143179
144180```go
145181func validTicTacToe(board []string) bool {
146- x , o := 0 , 0
147- for i := 0 ; i < 3 ; i++ {
148- for j := 0 ; j < 3 ; j++ {
149- if board[i][j] == ' X'
182+ var x, o int
183+ for _, row := range board {
184+ for _, c := range row {
185+ if c == 'X' {
150186 x++
151- } else if board[i][j] == ' O'
187+ } else if c == 'O' {
152188 o++
153189 }
154190 }
155191 }
156- if x != o && x-1 != o {
157- return false
158- }
159- if win (board, ' X' 1 != o {
160- return false
161- }
162- return !(win (board, ' O'
163- }
164-
165- func win (b []string , p byte ) bool {
166- for i := 0 ; i < 3 ; i++ {
167- if b[i][0 ] == p && b[i][1 ] == p && b[i][2 ] == p {
168- return true
192+ win := func(x byte) bool {
193+ for i := 0; i < 3; i++ {
194+ if board[i][0] == x && board[i][1] == x && board[i][2] == x {
195+ return true
196+ }
197+ if board[0][i] == x && board[1][i] == x && board[2][i] == x {
198+ return true
199+ }
169200 }
170- if b [0 ][i ] == p && b [1 ][i ] == p && b [2 ][i ] == p {
201+ if board [0][0 ] == x && board [1][1 ] == x && board [2][2 ] == x {
171202 return true
172203 }
204+ return board[0][2] == x && board[1][1] == x && board[2][0] == x
173205 }
174- if b[0 ][0 ] == p && b[1 ][1 ] == p && b[2 ][2 ] == p {
175- return true
206+ if x != o && x-1 != o {
207+ return false
208+ }
209+ if win('X') && x-1 != o {
210+ return false
176211 }
177- return b[ 0 ][ 2 ] == p && b[ 1 ][ 1 ] == p && b[ 2 ][ 0 ] == p
212+ return !(win('O') && x != o)
178213}
179214```
180215
181- ### ** C++**
182-
183- ``` cpp
184- class Solution {
185- public:
186- bool validTicTacToe(vector<string >& board) {
187- int x = 0, o = 0;
188- for (int i = 0; i < 3; ++i) {
189- for (int j = 0; j < 3; ++j) {
190- if (board[ i] [ j ] == 'X') {
191- ++x;
192- } else if (board[ i] [ j ] == 'O') {
193- ++o;
194- }
216+ ### ** JavaScript**
217+
218+ ``` js
219+ /**
220+ * @param {string[]} board
221+ * @return {boolean}
222+ */
223+ var validTicTacToe = function (board ) {
224+ function count (x ) {
225+ let cnt = 0 ;
226+ for (const row of board) {
227+ for (const c of row) {
228+ cnt += c == x;
195229 }
196230 }
197- if (x != o && x - 1 != o) {
198- return false;
199- }
200- if (win(board, 'X') && x - 1 != o) {
201- return false;
202- }
203- return !(win(board, 'O') && x != o);
231+ return cnt;
204232 }
205-
206- bool win(vector<string>& b, char p) {
207- for (int i = 0; i < 3; ++i) {
208- if (b[i][0] == p && b[i][1] == p && b[i][2] == p) {
233+ function win (x ) {
234+ for (let i = 0 ; i < 3 ; ++ i) {
235+ if (board[i][0 ] == x && board[i][1 ] == x && board[i][2 ] == x) {
209236 return true ;
210237 }
211- if (b [0 ][i] == p && b [1 ][i] == p && b [2 ][i] == p ) {
238+ if (board [0 ][i] == x && board [1 ][i] == x && board [2 ][i] == x ) {
212239 return true ;
213240 }
214241 }
215- if (b [0][0] == p && b [1][1] == p && b [2][2] == p ) {
242+ if (board [0 ][0 ] == x && board [1 ][1 ] == x && board [2 ][2 ] == x ) {
216243 return true ;
217244 }
218- return b[0][2] == p && b[1][1] == p && b[2][0] == p;
245+ return board[0 ][2 ] == x && board[1 ][1 ] == x && board[2 ][0 ] == x;
246+ }
247+ const [x , o ] = [count (' X' count (' O'
248+ if (x != o && x - 1 != o) {
249+ return false ;
250+ }
251+ if (win (' X' && x - 1 != o) {
252+ return false ;
219253 }
254+ return ! (win (' O' && x != o);
220255};
221256```
222257
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