【leetcode】1023. Binary String With Substrings Representing 1 To N

题目如下：

Given a binary string S (a string consisting only of '0' and '1's) and a positive integer N, return true if and only if for every integer X from 1 to N, the binary representation of X is a substring of S.

 

Example 1:

Input: S = "0110", N = 3
Output: true

Example 2:

Input: S = "0110", N = 4
Output: false

 

Note:

1. 1 <= S.length <= 1000
2. 1 <= N <= 10^9

解题思路：最初我的想法是判断1~N是否存在于S中，但是这样效率太低。思路转换一下，判断S中能否组成从1~N中所有的数即可，

代码如下：

class Solution(object):
    def queryString(self, S, N):
        """
        :type S: str
        :type N: int
        :rtype: bool
        """
        dic = {}
        for i in range(len(S)-1,-1,-1):
            power = 0
            amount = 0
            for j in range(i,-1,-1):
                if S[j] == '0':
                    power += 1
                    continue
                tmp = amount + pow(2, power)
                if tmp > N:
                    break
                dic[tmp] = 1
                power += 1
                amount = tmp
        return len(dic) == N