Find Kth Bit in Nth Binary String
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2022-05-18 20:30:21
...
Given two positive integers n
and k
, the binary string Sn
is formed as follows:
S1 = "0"
-
Si = Si-1 + "1" + reverse(invert(Si-1))
fori > 1
Where +
denotes the concatenation operation, reverse(x)
returns the reversed string x, and invert(x)
inverts all the bits in x (0 changes to 1 and 1 changes to 0).
For example, the first 4 strings in the above sequence are:
S1 = "0"
S2 = "011"
S3 = "0111001"
S4 = "011100110110001"
Return the kth
bit in Sn
. It is guaranteed that k
is valid for the given n
.
Example 1:
Input: n = 3, k = 1
Output: "0"
Explanation: S3 is "0111001". The first bit is "0".
Example 2:
Input: n = 4, k = 11
Output: "1"
Explanation: S4 is "011100110110001". The 11th bit is "1".
思路:这题就是递归,就是明白这一层的答案由上一层推倒得来,注意index的计算,是用数学公式推出来的,1234567, 顺数第三个是反着数第5个, 7 - 3 + 1;
class Solution {
public char findKthBit(int n, int k) {
if(n == 1) {
return '0';
}
int length = len(n - 1);
if(k <= length) {
return findKthBit(n - 1, k);
} else if( k == length + 1) {
return '1';
} else {
// k > len(n - 1) + 1;
return findKthBit(n - 1, length - (k - (length + 1)) + 1) == '0' ? '1' : '0';
}
}
private int len(int n) {
if(n == 1) {
return 1;
} else {
return 2*len(n - 1) + 1;
}
}
}
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