目錄

• 題目描述
• 題目大意
• 解題方法
• 日期

題目描述

X is a good number if after rotating each digit individually by 180 degrees, we get a valid number that is different from X. A number is valid if each digit remains a digit after rotation. 0, 1, and 8 rotate to themselves; 2 and 5 rotate to each other; 6 and 9 rotate to each other, and the rest of the numbers do not rotate to any other number.

Now given a positive number N, how many numbers X from 1 to N are good?

Example:
Input: 10
Output: 4
Explanation: 
There are four good numbers in the range [1, 10] : 2, 5, 6, 9.
Note that 1 and 10 are not good numbers, since they remain unchanged after rotating.

Note:

1. N will be in range [1, 10000].

題目大意

在[1,N]雙閉區間中，有多少個數字，將其倒影之後和自身不同。

解題方法

重要的是理解題意，就好比下面的這個倒影，要求倒影和自身不同，但倒影也必須是數字：

可以總結出以下的要求：

1. 該數字中不含[3, 4, 7]，否則其倒影不是數字。
2. 該數字中必須包含[2, 5, 6, 9]中的至少一個，否則倒影和原數字相同

最後的結果是有多少個，遍歷之後很容易得到答案。

class Solution(object):
    def rotatedDigits(self, N):
        """
        :type N: int
        :rtype: int
        """
 

        valid = [2, 5, 6, 9]
        nonValid = [3, 4, 7]
        def isGood(num):
            for y in nonValid:
                if str(y) in str(num):
                    return False
            return any(str(x) in str(num) for x in valid)
        return sum(map(int, [isGood(n) for n in range(1, N + 1)]))

二刷，基於同樣的思想，寫了一個更簡潔的程式碼。

class Solution(object):
    def rotatedDigits(self, N):
        """
        :type N: int
        :rtype: int
        """
        dmap = {"0" : "0", "1" : "1", "8" : "8", "2" : "5", "5" : "2", "6" : "9", "9" : "6"}
        res = 0
        for num in range(1, N + 1):
            numlist = list(str(num))
            if any(x in numlist for x in ["3", "4", "7"]):
                continue
            numRotate = map(lambda x : dmap[x], numlist)
            if numRotate == numlist:
                continue
            res += 1
        return res

看了別人的提交，發現了一個更簡單的思路，就是我們不需要把翻轉後的數字構建出來，我們只需要找出特定的字元是否在字串中即可。比如，如果數字包含["3", "4", "7"]，那麼肯定不可以。如果數字包含["2", "5", "6", "9"]，那麼一定可以。如果這些數字都不包含，那麼就是翻轉之後是自身的數字，就不能計算到結果裡。

class Solution(object):
    def rotatedDigits(self, N):
        """
        :type N: int
        :rtype: int
        """
        dmap = {"0" : "0", "1" : "1", "8" : "8", "2" : "5", "5" : "2", "6" : "9", "9" : "6"}
        res = 0
        for num in range(1, N + 1):
            if any(x in str(num) for x in ["3", "4", "7"]):
                continue
            if any(x in str(num) for x in ["2", "5", "6", "9"]):
                res += 1
        return res

日期

2018 年 2 月 26 日
2018 年 11 月 11 日 —— 剁手節快樂