Update 0037.解数独.md

0037.解数独 java bitmap解法

Author: carlvine500

problems/0037.解数独.md

@@ -224,7 +224,7 @@ public:
 
 
 ### Java
-
+解法一:
 ```java
 class Solution {
     public void solveSudoku(char[][] board) {
@@ -291,7 +291,73 @@ class Solution {
     }
 }
 ```
+解法二(bitmap标记)
+```
+class Solution{
+    int[] rowBit = new int[9];
+    int[] colBit = new int[9];
+    int[] square9Bit = new int[9];
+
+    public void solveSudoku(char[][] board) {
+        // 1 10 11
+        for (int y = 0; y < board.length; y++) {
+            for (int x = 0; x < board[y].length; x++) {
+                int numBit = 1 << (board[y][x] - '1');
+                rowBit[y] ^= numBit;
+                colBit[x] ^= numBit;
+                square9Bit[(y / 3) * 3 + x / 3] ^= numBit;
+            }
+        }
+        backtrack(board, 0);
+    }
+
+    public boolean backtrack(char[][] board, int n) {
+        if (n >= 81) {
+            return true;
+        }
+
+        // 快速算出行列编号 n/9 n%9
+        int row = n / 9;
+        int col = n % 9;
+
+        if (board[row][col] != '.') {
+            return backtrack(board, n + 1);
+        }
+
+        for (char c = '1'; c <= '9'; c++) {
+            int numBit = 1 << (c - '1');
+            if (!isValid(numBit, row, col)) continue;
+            {
+                board[row][col] = c;    // 当前的数字放入到数组之中，
+                rowBit[row] ^= numBit; // 第一行rowBit[0],第一个元素eg: 1 , 0^1=1,第一个元素:4, 100^1=101,...
+                colBit[col] ^= numBit;
+                square9Bit[(row / 3) * 3 + col / 3] ^= numBit;
+            }
+            if (backtrack(board, n + 1)) return true;
+            {
+                board[row][col] = '.';    // 不满足条件，回退成'.'
+                rowBit[row] &= ~numBit; // 第一行rowBit[0],第一个元素eg: 1 , 101&=~1==>101&111111110==>100
+                colBit[col] &= ~numBit;
+                square9Bit[(row / 3) * 3 + col / 3] &= ~numBit;
+            }
+        }
+        return false;
+    }
+
 
+    boolean isValid(int numBit, int row, int col) {
+        // 左右
+        if ((rowBit[row] & numBit) > 0) return false;
+        // 上下
+        if ((colBit[col] & numBit) > 0) return false;
+        // 9宫格: 快速算出第n个九宫格,编号[0,8] , 编号=(row / 3) * 3 + col / 3
+        if ((square9Bit[(row / 3) * 3 + col / 3] & numBit) > 0) return false;
+        return true;
+    }
+
+}
+
+```
 ### Python
 
 ```python