36 Valid Sudoku

Author: int32bit

README.md

@@ -28,6 +28,7 @@
 + [33 Search in Rotated Sorted Array(二分搜索)](algorithms/SearchinRotatedSortedArray)
 + [34 Search for a Range(二分)](algorithms/SearchforaRange)
 + [35 Search Insert Position(二分查找)](algorithms/SearchInsertPosition)
++ [36 Valid Sudoku(数独、hash表)](algorithms/ValidSudoku)
 + [38 Count and Say(字符串和数字转化详解)](algorithms/CountandSay)
 + [43 Multiply Strings(大数乘法)](algorithms/MultiplyStrings)
 + [46 Permutations(全排列)](algorithms/Permutations)

algorithms/ValidSudoku/README.md

@@ -0,0 +1,92 @@
+## Valid Sudoku
+
+Determine if a Sudoku is valid, according to: [Sudoku Puzzles - The Rules](http://sudoku.com.au/TheRules.aspx).
+
+The Sudoku board could be partially filled, where empty cells are filled with the character '.'.
+
+
+A partially filled sudoku which is valid.
+
+Note:
+*A valid Sudoku board (partially filled) is not necessarily solvable. Only the filled cells need to be validated.
+
+Subscribe to see which companies asked this question*
+
+## Solution
+
+此题是纯粹的模拟题，只需要根据数独的规则分别判断每一行、每一列、每一个九宫格是否出现重复数字即可。判断数字是否重复使用hash表即可。
+
+### 判断每一行
+
+```cpp
+bool check_row(const vector<vector<char>> &a, int row) {
+	vector<bool> used(9, false);
+	for (char i : a[row]) {
+		if ('.' == i)
+			continue;
+		int pos = i - '0' - 1;
+		if (used[pos])
+			return false;
+		else
+			used[pos] = true;
+	}
+	return true;
+}
+```
+
+### 判断每一列
+
+```cpp
+bool check_col(const vector<vector<char>> &a, int col) {
+	vector<bool> used(9, false);
+	for (int i = 0; i < 9; ++i) {
+		if (a[i][col] == '.')
+			continue;
+		int pos = a[i][col] - '0' - 1;
+		if (used[pos])
+			return false;
+		else
+			used[pos] = true;
+	}
+	return true;
+}
+```
+
+### 判断每一个九宫格
+
+需要注意确定每一个九宫格对应行首和列首，假设九宫格从0开始编号，则第n个九宫格的行位置为`n / 3 * 3`, 列位置为`n % 3 * 3`
+
+```cpp
+bool check_box(const vector<vector<char>> &a, int box) {
+	int row_begin = box / 3 * 3;
+	int col_begin = box % 3 * 3;
+	vector<bool> used(9, false);
+	for (int i = row_begin; i < row_begin + 3; ++i) {
+		for (int j = col_begin; j < col_begin + 3; ++j) {
+			if (a[i][j] == '.')
+				continue;
+			int pos = a[i][j] - '0' - 1;
+			if (used[pos])
+				return false;
+			else
+				used[pos] = true;
+		}
+	}
+	return true;
+}
+```
+
+实习代码为：
+
+```cpp
+bool isValidSudoku(vector<vector<char>>& board) {
+	for (int i = 0; i < 9; ++i) {
+		if (!(check_row(board, i)
+		    && (check_col(board, i))
+		    && (check_box(board, i)))
+		)
+			return false;
+	}
+	return true;
+}
+```

algorithms/ValidSudoku/in.txt

@@ -0,0 +1,9 @@
+.87654321
+2........
+2........
+4........
+5........
+6........
+7........
+8........
+9........

algorithms/ValidSudoku/solve.cpp

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+#include <vector>
+#include <iostream>
+#include <cassert>
+using namespace std;
+class Solution {
+	public:
+		bool isValidSudoku(vector<vector<char>>& board) {
+			for (int i = 0; i < 9; ++i) {
+				if (!(check_row(board, i)
+				    && (check_col(board, i))
+				    && (check_box(board, i)))
+				)
+					return false;
+			}
+			return true;
+		}
+	private:
+		bool check_row(const vector<vector<char>> &a, int row) {
+			vector<bool> used(9, false);
+			for (char i : a[row]) {
+				if ('.' == i)
+					continue;
+				int pos = i - '0' - 1;
+				if (used[pos])
+					return false;
+				else
+					used[pos] = true;
+			}
+			return true;
+		}
+		bool check_col(const vector<vector<char>> &a, int col) {
+			vector<bool> used(9, false);
+			for (int i = 0; i < 9; ++i) {
+				if (a[i][col] == '.')
+					continue;
+				int pos = a[i][col] - '0' - 1;
+				if (used[pos])
+					return false;
+				else
+					used[pos] = true;
+			}
+			return true;
+		}
+		bool check_box(const vector<vector<char>> &a, int box) {
+			int row_begin = box / 3 * 3;
+			int col_begin = box % 3 * 3;
+			vector<bool> used(9, false);
+			for (int i = row_begin; i < row_begin + 3; ++i) {
+				for (int j = col_begin; j < col_begin + 3; ++j) {
+					if (a[i][j] == '.')
+						continue;
+					int pos = a[i][j] - '0' - 1;
+					if (used[pos])
+						return false;
+					else
+						used[pos] = true;
+				}
+			}
+			return true;
+		}
+};
+static void input(vector<vector<char>> &board, string s) {
+	vector<char> t;
+	assert(s.size() == 9);
+	for (auto c : s) {
+		t.push_back(c);
+	}
+	board.push_back(t);
+}
+int main(int arch, char **argv)
+{
+	Solution solution;
+	vector<vector<char>> board;
+	for (int i = 0; i < 9; ++i) {
+		string a;
+		cin >> a;
+		input(board, a);
+	}
+	cout << solution.isValidSudoku(board) << endl;
+	return 0;
+}