添加内容

website/content/ChapterFour/0036.Valid-Sudoku.md

@@ -0,0 +1,168 @@
+# [36. Valid Sudoku](https://leetcode.com/problems/valid-sudoku/)
+
+
+## 题目
+
+Determine if a 9x9 Sudoku board is valid. Only the filled cells need to be validated **according to the following rules**:
+
+1. Each row must contain the digits `1-9` without repetition.
+2. Each column must contain the digits `1-9` without repetition.
+3. Each of the 9 `3x3` sub-boxes of the grid must contain the digits `1-9` without repetition.
+
+![](https://upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Sudoku-by-L2G-20050714.svg/250px-Sudoku-by-L2G-20050714.svg.png)
+
+A partially filled sudoku which is valid.
+
+The Sudoku board could be partially filled, where empty cells are filled with the character `'.'`.
+
+**Example 1**:
+
+
+    Input:
+    [
+      ["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"]
+    ]
+    Output: true
+
+
+**Example 2**:
+
+
+    Input:
+    [
+      ["8","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"]
+    ]
+    Output: false
+    Explanation: Same as Example 1, except with the 5 in the top left corner being 
+        modified to 8. Since there are two 8's in the top left 3x3 sub-box, it is invalid.
+
+
+**Note**:
+
+- A Sudoku board (partially filled) could be valid but is not necessarily solvable.
+- Only the filled cells need to be validated according to the mentioned rules.
+- The given board contain only digits `1-9` and the character `'.'`.
+- The given board size is always `9x9`.
+
+## 题目大意
+
+判断一个 9x9 的数独是否有效。只需要根据以下规则，验证已经填入的数字是否有效即可。
+
+1. 数字 1-9 在每一行只能出现一次。
+2. 数字 1-9 在每一列只能出现一次。
+3. 数字 1-9 在每一个以粗实线分隔的 3x3 宫内只能出现一次。
+
+
+## 解题思路
+
+- 给出一个数独的棋盘，要求判断这个棋盘当前是否满足数独的要求：即行列是否都只包含 1-9，每个九宫格里面是否也只包含 1-9 。
+- 注意这题和第 37 题是不同的，这一题是判断当前棋盘状态是否满足数独的要求，而第 37 题是要求求解数独。本题中的棋盘有些是无解的，但是棋盘状态是满足题意的。
+
+## 代码
+
+```go
+
+package leetcode
+
+import "strconv"
+
+// 解法一 暴力遍历，时间复杂度 O(n^3)
+func isValidSudoku(board [][]byte) bool {
+	// 判断行 row
+	for i := 0; i < 9; i++ {
+		tmp := [10]int{}
+		for j := 0; j < 9; j++ {
+			cellVal := board[i][j : j+1]
+			if string(cellVal) != "." {
+				index, _ := strconv.Atoi(string(cellVal))
+				if index > 9 || index < 1 {
+					return false
+				}
+				if tmp[index] == 1 {
+					return false
+				}
+				tmp[index] = 1
+			}
+		}
+	}
+	// 判断列 column
+	for i := 0; i < 9; i++ {
+		tmp := [10]int{}
+		for j := 0; j < 9; j++ {
+			cellVal := board[j][i]
+			if string(cellVal) != "." {
+				index, _ := strconv.Atoi(string(cellVal))
+				if index > 9 || index < 1 {
+					return false
+				}
+				if tmp[index] == 1 {
+					return false
+				}
+				tmp[index] = 1
+			}
+		}
+	}
+	// 判断 9宫格 3X3 cell
+	for i := 0; i < 3; i++ {
+		for j := 0; j < 3; j++ {
+			tmp := [10]int{}
+			for ii := i * 3; ii < i*3+3; ii++ {
+				for jj := j * 3; jj < j*3+3; jj++ {
+					cellVal := board[ii][jj]
+					if string(cellVal) != "." {
+						index, _ := strconv.Atoi(string(cellVal))
+						if tmp[index] == 1 {
+							return false
+						}
+						tmp[index] = 1
+					}
+				}
+			}
+		}
+	}
+	return true
+}
+
+// 解法二 添加缓存，时间复杂度 O(n^2)
+func isValidSudoku1(board [][]byte) bool {
+	rowbuf, colbuf, boxbuf := make([][]bool, 9), make([][]bool, 9), make([][]bool, 9)
+	for i := 0; i < 9; i++ {
+		rowbuf[i] = make([]bool, 9)
+		colbuf[i] = make([]bool, 9)
+		boxbuf[i] = make([]bool, 9)
+	}
+	// 遍历一次，添加缓存
+	for r := 0; r < 9; r++ {
+		for c := 0; c < 9; c++ {
+			if board[r][c] != '.' {
+				num := board[r][c] - '0' - byte(1)
+				if rowbuf[r][num] || colbuf[c][num] || boxbuf[r/3*3+c/3][num] {
+					return false
+				}
+				rowbuf[r][num] = true
+				colbuf[c][num] = true
+				boxbuf[r/3*3+c/3][num] = true // r,c 转换到box方格中
+			}
+		}
+	}
+	return true
+}
+
+
+```