分类:Math
考察知识点:Math
最优解时间复杂度:**O(1) **
12. Integer to Roman
Roman numerals are represented by seven different symbols: I
, V
, X
, L
, C
, D
and M
.
Symbol Value
I 1
V 5
X 10
L 50
C 100
D 500
M 1000
For example, two is written as II
in Roman numeral, just two one's added together. Twelve is written as, XII
, which is simply X
+ II
. The number twenty seven is written as XXVII
, which is XX
+ V
+ II
.
Roman numerals are usually written largest to smallest from left to right. However, the numeral for four is not IIII
. Instead, the number four is written as IV
. Because the one is before the five we subtract it making four. The same principle applies to the number nine, which is written as IX
. There are six instances where subtraction is used:
-
I
can be placed beforeV
(5) andX
(10) to make 4 and 9. -
X
can be placed beforeL
(50) andC
(100) to make 40 and 90. -
C
can be placed beforeD
(500) andM
(1000) to make 400 and 900.
Given an integer, convert it to a roman numeral. Input is guaranteed to be within the range from 1 to 3999.
Example 1:
Input: 3
Output: "III"
Example 2:
Input: 4
Output: "IV"
Example 3:
Input: 9
Output: "IX"
Example 4:
Input: 58
Output: "LVIII"
Explanation: L = 50, V = 5, III = 3.
Example 5:
Input: 1994
Output: "MCMXCIV"
Explanation: M = 1000, CM = 900, XC = 90 and IV = 4.
代码:
枚举法:
class Solution:
def intToRoman(self, num):
"""
:type num: int
:rtype: str
"""
M=["","M","MM","MMM"]
C=["","C","CC","CCC","CD","D","DC","DCC","DCCC","CM"]
X=["","X","XX","XXX","XL","L","LX","LXX","LXXX","XC"]
I=["","I","II","III","IV","V","VI","VII","VIII","IX"]
return M[num//1000]+C[(num//100)%10]+X[(num//10)%10]+I[num%10]
非枚举法:
class Solution:
def intToRoman(self, num):
"""
:type num: int
:rtype: str
"""
num_dict=[(1000,'M'),(900,'CM'),(500,'D'),(400,'CD'),(100,'C'),(90,'XC'),
(50,'L'),(40,'XL'),(10,'X'),(9,'IX'),(5,'V'),(4,'IV'),(1,'I')]
roman_num=""
for n in num_dict:
if num//n[0]:
roman_num+=(n[1]*(num//n[0]))
num-=(num//n[0])*n[0]
return roman_num
讨论:
1.这个题主要考对罗马数字的理解,有哪些特殊情况,比如900,400这些,然后需要一一考虑进去
2.枚举法利用了空间复杂度,降低了时间复杂度,其实挺好的,但是有点麻烦。
3.但是说白了这道题好像确实没啥价值,而且也不容易考到