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一，字符串相乘

1，程序简介

• 给定两个以字符串形式表示的非负整数 num1 和 num2，返回 num1 和 num2 的乘积，它们的乘积也表示为字符串形式。

示例 1:

• 输入: num1 = “2”, num2 = “3”
• 输出: “6”

示例 2:

• 输入: num1 = “123”, num2 = “456”
• 输出: “56088”

说明：

• num1 和 num2 的长度小于110。
• num1 和 num2 只包含数字 0-9。
• num1 和 num2 均不以零开头，除非是数字 0 本身。
• 不能使用任何标准库的大数类型（比如 BigInteger）或直接将输入转换为整数来处理。

2，程序代码

# -*- coding: utf-8 -*-
"""
Created on Wed Jan 19 21:30:10 2022
Function: 字符串相乘
@author: 小梁aixj
"""
class Solution(object):def multiply(self, num1, num2):if num1 == '0' or num2 == '0':return '0'res = ''ls1, ls2, = len(num1), len(num2)ls = ls1 + ls2arr = [0] * lsfor i in reversed(range(ls1)):for j in reversed(range(ls2)):arr[i + j + 1] += int(num1[i]) * int(num2[j])for i in reversed(range(1, ls)):arr[i - 1] += arr[i] / 10arr[i] %= 10pos = 0if arr[pos] == 0:pos += 1while pos < ls:res = res + str(arr[pos])pos += 1return res
if __name__ == '__main__':s = Solution()print (s.multiply("2", "3"))

3，运行结果

二，有效的数独

1，程序简介

• 请你判断一个 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。（请参考示例图）

• 数独部分空格内已填入了数字，空白格用 ‘.’ 表示。

注意：

• 一个有效的数独（部分已被填充）不一定是可解的。
• 只需要根据以上规则，验证已经填入的数字是否有效即可。

示例 1：

• 输入：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”]]
• 输出：true

示例 2：

• 输入：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”]]
• 输出：false
• 解释：除了第一行的第一个数字从 5 改为 8 以外，空格内其他数字均与 示例1 相同。 但由于位于左上角的 3x3 宫内有两个 8 存在, 因此这个数独是无效的。

提示：

• board.length == 9
• board[i].length == 9
• board[i][j] 是一位数字或者 ‘.’

2，程序代码

# -*- coding: utf-8 -*-
"""
Created on Wed Jan 19 21:30:52 2022
Function: 有效的数独
@author: 小梁aixj
"""
from typing import List
class Solution:def isValidSudoku(self, board):""":type board: List[List[str]]:rtype: bool"""raw = [{},{},{},{},{},{},{},{},{}]col = [{},{},{},{},{},{},{},{},{}]cell = [{},{},{},{},{},{},{},{},{}]for i in range(9):for j in range(9):                                 num = (3*(i//3) + j//3)temp = board[i][j]if temp != ".":if temp not in raw[i] and temp not in col[j] and temp not in cell[num]:raw [i][temp] = 1col [j][temp] = 1cell [num][temp] =1else:return False    return True
# %%
s = Solution()
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"]]
print(s.isValidSudoku(board))

3，运行结果