s0037

include/s0037_sudoku_solver.hpp

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+#ifndef S0037_SUDOKU_SOLVER_HPP
+#define S0037_SUDOKU_SOLVER_HPP
+
+#include <vector>
+#include <unordered_map>
+#include <cmath>
+#include <algorithm>
+
+using namespace std;
+
+class Solution {
+ public:
+  void solveSudoku(vector<vector<char>>& board);
+};
+
+#endif

src/s0037_sudoku_solver.cpp

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+#include "s0037_sudoku_solver.hpp"
+
+#include <unordered_map>
+#include <vector>
+
+// 返回结果为当前传递进去的数独是否存在解
+bool recusiveSolveSudoku(vector<vector<char>> &board,
+                         vector<unordered_map<char, bool>> &rows,
+                         vector<unordered_map<char, bool>> &cols,
+                         vector<unordered_map<char, bool>> &grids, int row,
+                         int col) {
+  int size = board.size();
+  // 边界校验
+  if (col == size) {
+    // 进入下一行
+    col = 0;
+    row++;
+    // 填充完成，返回 True
+    if (row == size) {
+      return true;
+    }
+  }
+  // 如果不为空则跳过，填充下一个
+  if (board[row][col] != '.') {
+    return recusiveSolveSudoku(board, rows, cols, grids, row, col + 1);
+  } else {  // 否则开始填充
+    // 尝试填充 1 ~ 9
+    for (char num{'1'}; num <= '9'; ++num) {
+      int gridIndex = static_cast<int>(floor(row / 3)) +
+                      3 * static_cast<int>(floor(col / 3));
+      // 如果这个数字还没有出现过
+      if (!(rows[row].count(num) == 1 || cols[col].count(num) == 1 ||
+            grids[gridIndex].count(num) == 1)) {
+        // 先把这个数字填进去
+        rows[row][num] = true;
+        cols[col][num] = true;
+        grids[gridIndex][num] = true;
+        board[row][col] = num;
+        // 然后试试看填进去后下一个能不能解
+        // 如果下一个能解的话，现在这个肯定能解
+        if (recusiveSolveSudoku(board, rows, cols, grids, row, col + 1)) {
+          return true;
+        }
+        // 如果不能解，那么说明这个数字填错了，把它重新设为空，然后尝试下一个数字
+        board[row][col] = '.';
+        rows[row].erase(num);
+        cols[col].erase(num);
+        grids[gridIndex].erase(num);
+      }
+    }
+  }
+  return false;
+}
+
+void Solution::solveSudoku(vector<vector<char>> &board) {
+  // 每个行/列/单元格中某个数字是否出现过
+  vector<unordered_map<char, bool>> rows;
+  vector<unordered_map<char, bool>> cols;
+  vector<unordered_map<char, bool>> grids;
+  // 初始化
+  int size = board.size();
+  for (int i{0}; i < size; ++i) {
+    rows.push_back(unordered_map<char, bool>{});
+    cols.push_back(unordered_map<char, bool>{});
+    grids.push_back(unordered_map<char, bool>{});
+  }
+  for (int row{0}; row < size; ++row) {
+    for (int col{0}; col < size; ++col) {
+      if (board[row][col] != '.') {
+        rows[row][board[row][col]] = true;
+        cols[col][board[row][col]] = true;
+        int gridIndex = static_cast<int>(floor(row / 3)) +
+                        3 * static_cast<int>(floor(col / 3));
+        grids[gridIndex][board[row][col]] = true;
+      }
+    }
+  }
+  // 从 (0, 0) 开始递归求解
+  recusiveSolveSudoku(board, rows, cols, grids, 0, 0);
+}

tests/s0037_sudoku_solver.cpp

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+#include "s0037_sudoku_solver.hpp"
+
+#include <gtest/gtest.h>
+
+TEST(Problem37, Case1) {
+  vector<vector<char>> board{{'5', '3', '.', '.', '7', '.', '.', '.', '.'},
+                             {'6', '.', '.', '1', '9', '5', '.', '.', '.'},
+                             {'.', '9', '8', '.', '.', '.', '.', '6', '.'},
+                             {'8', '.', '.', '.', '6', '.', '.', '.', '3'},
+                             {'4', '.', '.', '8', '.', '3', '.', '.', '1'},
+                             {'7', '.', '.', '.', '2', '.', '.', '.', '6'},
+                             {'.', '6', '.', '.', '.', '.', '2', '8', '.'},
+                             {'.', '.', '.', '4', '1', '9', '.', '.', '5'},
+                             {'.', '.', '.', '.', '8', '.', '.', '7', '9'}};
+  vector<vector<char>> expected{{'5', '3', '4', '6', '7', '8', '9', '1', '2'},
+                                {'6', '7', '2', '1', '9', '5', '3', '4', '8'},
+                                {'1', '9', '8', '3', '4', '2', '5', '6', '7'},
+                                {'8', '5', '9', '7', '6', '1', '4', '2', '3'},
+                                {'4', '2', '6', '8', '5', '3', '7', '9', '1'},
+                                {'7', '1', '3', '9', '2', '4', '8', '5', '6'},
+                                {'9', '6', '1', '5', '3', '7', '2', '8', '4'},
+                                {'2', '8', '7', '4', '1', '9', '6', '3', '5'},
+                                {'3', '4', '5', '2', '8', '6', '1', '7', '9'}};
+  Solution solution;
+  solution.solveSudoku(board);
+  EXPECT_EQ(board, expected);
+}