Roman numerals are represented by seven different symbols: I, V, X, L, C, D and M.
SymbolValue
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 before V (5) and X (10) to make 4 and 9.
X can be placed before L (50) and C (100) to make 40 and 90.
C can be placed before D (500) and M (1000) to make 400 and 900.
Given a roman numeral, convert it to an integer. Input is guaranteed to be within the range from 1 to 3999.
Example 1:
Input: "III"
Output: 3
Example 2:
Input: "IV"
Output: 4
Example 3:
Input: "IX"
Output: 9
Example 4:
Input: "LVIII"
Output: 58
Explanation: C = 100, L = 50, XXX = 30 and III = 3.
Example 5:
Input: "MCMXCIV"
Output: 1994
Explanation: M = 1000, CM = 900, XC = 90 and IV = 4.
Solution
accumulate the value of each letter.
If the value of current letter is greater than the previous one, deduct twice of the previous value.
e.g. IX, 1 + 10 – 2 * 1 = 9 instead of 1 + 10 = 11
Determine whether an integer is a palindrome. An integer is a palindrome when it reads the same backward as forward.
Example 1:
Input: 121
Output: true
Example 2:
Input: -121
Output: false
Explanation: From left to right, it reads -121. From right to left, it becomes 121-. Therefore it is not a palindrome.
Example 3:
Input: 10
Output: false
Explanation: Reads 01 from right to left. Therefore it is not a palindrome.
Follow up:
Could you solve it without converting the integer to a string?
Solution 1: Convert to string (cheating)
Time complexity: O(log10(x))
Space complexity: O(log10(x))
C++
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// Author: Huahua
classSolution{
public:
boolisPalindrome(intx){
strings=to_string(x);
returns==string(rbegin(s),rend(s));
}
};
Solution 2: Digit by Digit
Every time we compare the first and last digits of x, if they are not the same, return false. Otherwise, remove first and last digit and continue this process.
How can we achieve that via int math?
e.g. x = 9999, t = pow((10, int)log10(x)) = 1000
first digit: x / t, last digit: x % 10
then x = (x – x / t * t) / 10 removes first and last digits.
Given a 32-bit signed integer, reverse digits of an integer.
Example 1:
Input: 123
Output: 321
Example 2:
Input: -123
Output: -321
Example 3:
Input: 120
Output: 21
Note:
Assume we are dealing with an environment which could only store integers within the 32-bit signed integer range: [−231, 231 − 1]. For the purpose of this problem, assume that your function returns 0 when the reversed integer overflows.
Solution: Simulation
Reverse digit by digit. Be careful about the overflow and negative numbers (especially in Python)