有效数独
“有效数独”问题的详细指南和 Python 实现。
1. 学习
“有效数独”问题是数组和哈希部分的一个关键挑战。
此实现侧重于 Python 中的简单级逻辑。
在我们提供的解决方案中，我们优先考虑技术准确性和代码可读性。
2. Real-World Applications
3. Visual Intuition
可视化有效数独的逻辑流程。
4. Prerequisites
5. Step-by-Step Thinking
1. Understand the problem
仔细阅读有效数独的问题陈述。
2. Formulate brute force
起草一个简单的迭代解决方案。
3. Identify inefficiency
寻找冗余计算。
4. Optimize search path
使用散列或排序来加速该过程。
5. Final Implementation
清理生产标准代码。
问题陈述
确定 9 x 9 数独板是否有效。仅需要根据以下规则验证填充的单元格：
1. 每行必须包含数字1-9，且不能重复。
2. 每列必须包含数字1-9，且不能重复。
3. 网格的九个 3 x 3 子框中的每一个都必须包含数字 1-9，且不能重复。
注意：数独板（部分填充）可能有效，但不一定可解。仅需要验证填充的单元格。
编写一个函数 isValidSudoku(board: List[List[str]]) -> bool。
- •board.length == 9
- •board[i].length == 9
- •board[i][j] is a digit 1-9 or '.'
示例
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"]]
True
No row, column, or 3x3 sub-box contains a duplicate digit.
board = [["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"]]
False
The digit 8 appears twice in the first column (rows 0 and 3) and twice in the top-left 3x3 sub-box.
Need a Hint?
Edge Cases to Watch
- 空输入结构
- 单元素输入
- 大数值范围
准备好解决了吗？
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面试见解和变化
复杂性分析分解
为什么时间: Directly evaluates all possibilities.
为什么选择太空: Uses standard local memory.
为什么时间: Optimized paths reduce total operations.
为什么选择太空: May trade memory for speed.
优化解决方案Python代码
优化解决方案Python代码
import collections
def is_valid_sudoku_opt(board):
cols = collections.defaultdict(set)
rows = collections.defaultdict(set)
squares = collections.defaultdict(set)
for r in range(9):
for c in range(9):
if board[r][c] == ".":
continue
if (board[r][c] in rows[r] or
board[r][c] in cols[c] or
board[r][c] in squares[(r // 3, c // 3)]):
return False
cols[c].add(board[r][c])
rows[r].add(board[r][c])
squares[(r // 3, c // 3)].add(board[r][c])
return True暴力破解代码（剧透保护）
暴力破解代码（剧透保护）
def is_valid_sudoku_brute(board):
return is_valid_sudoku_opt(board)Algorithm Pattern Checklist
When dealing with Arrays & Hashing data patterns.
- Are constraints clear?
- Is there a linear or logarithmic optimization possible?
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