【leetcode】1017. Convert to Base -2

题目如下：

Given a number N, return a string consisting of "0"s and "1"s that represents its value in base -2 (negative two).

The returned string must have no leading zeroes, unless the string is "0".

 

Example 1:

Input: 2
Output: "110"
Explantion: (-2) ^ 2 + (-2) ^ 1 = 2

Example 2:

Input: 3
Output: "111"
Explantion: (-2) ^ 2 + (-2) ^ 1 + (-2) ^ 0 = 3

Example 3:

Input: 4
Output: "100"
Explantion: (-2) ^ 2 = 4

 

Note:

1. 0 <= N <= 10^9

解题思路：以12为例，转成二进制后是1100，假设最右边的下标为0，从右往左下标一次加1。很显然，下标是偶数位的情况，值是正数；而下标为奇数位的情况值是负数。为了要弥补负数带来的影响，需要加上等于这个负数*2的绝对值，而这个值恰好就是该负数的下一位。因此只要奇数位出现了1，那么相应就要在其后面的偶数位加上1，如果偶数位本来就是1，则需要考虑进位。

代码如下：

class Solution(object):
    def baseNeg2(self, N):
        """
        :type N: int
        :rtype: str
        """
        bs = bin(N)[2:][::-1]
        res =  [int(i) for i in list(bs)]

        def carrier(res,i):
            if i == len(res) - 1:
                res += [1]
                if len(res) % 2 == 0:
                    res += [1]
            else:
                res[i + 1] += 1
        for i in range(1,len(res)):
            if res[i] == 0:
                continue
            elif res[i] == 1 and i % 2 == 1:
                carrier(res,i)
            elif res[i] == 2:
                res[i] = 0
                carrier(res, i)
        return ''.join([str(i) for i in res[::-1]])