Missing Number Problem Statement

You are provided with an array named BINARYNUMS consisting of N unique strings. Each string represents an integer in binary, covering every integer from 0 to N except for one. Your task is to identify this missing integer and return its binary representation as a string without any leading zeros.

Input:

The first line indicates an integer T, the number of test cases. Each test case consists of: First line: An integer N indicating the number of binary strings in BINARYNUMS. Second line: N space-separated binary strings representing BINARYNUMS.

Output:

For each test case, output a single string, representing the binary form of the missing integer without leading zeros. Each test case result should be on a different line.

Example:

Input: N = 5, BINARYNUMS = ["0", "01", "010", "100", "101"] Output: "11" Explanation: The missing number is 3 and its binary representation is "11".

Constraints:

1

Question

Missing Number Problem Statement

You are provided with an array named BINARYNUMS consisting of N unique strings. Each string represents an integer in binary, covering every integer from 0 to N except for one. Your task is to identify this missing integer and return its binary representation as a string without any leading zeros.

Input:

The first line indicates an integer T, the number of test cases. Each test case consists of: First line: An integer N indicating the number of binary strings in BINARYNUMS. Second line: N space-separated binary strings representing BINARYNUMS.

Output:

For each test case, output a single string, representing the binary form of the missing integer without leading zeros. Each test case result should be on a different line.

Example:

Input: N = 5, BINARYNUMS = ["0", "01", "010", "100", "101"] Output: "11" Explanation: The missing number is 3 and its binary representation is "11".

Constraints:

1 <= T <= 50
1 <= N <= 10^4
Time limit: 1 second.

Note:

Ensure your implementation returns the output without printing to the console, as output handling is already managed.

Accepted Answer

Identify the missing integer in an array of binary strings and return its binary representation without leading zeros.

Iterate through the binary strings to convert them to integers and find the missing number using the formula for sum of integers from 0 to N.
Calculate the sum of all integers from 0 to N using the formula (N*(N+1))/2 and subtract the sum of the integers in the array to find the missing number.
Convert the missing integer to binary representation and return it as a string without leading zeros.

Accepted Answer

Without Convert into integers

The number of bits required to represent an integer ‘N’ will be floor(logN) + 1 (log on base 2).

You can observe that number of integers between 0 to N (inclusive) that have the 0th-bit set will be floor((N + 1)/2).

The number of integers between 0 to N (inclusive) that have the 1st-bit set will be 2 * floor((N + 1)/4) + max(0, (N + 1) % 4 - 2)

The number of integers between 0 to N (inclusive) that have the 2nd-bit set will be 4 * floor((N + 1) / 8) + max(0, (N + 1) % 8 - 4)

In general, we can say that number of integers between 0 to N (inclusive that have ith bit-set will be 2 ^ i * floor((N + 1) / 2 ^ (i + 1)) + max(0, (N + 1) % 2 ^ (i + 1) - 2 ^ i).

Algorithm

Initialize an integer variable totalBits:= floor(logN) + 1.
Create an empty string ‘missingNum’
Run a loop where ‘i’ ranges from 0 to totalBits - 1, and for each ‘i’ do the following -:
- Initialize an integer variable countReq: = 2 ^ i * floor((N + 1) / 2 ^ (i + 1)) + max(0, (N + 1) % 2 ^ (i + 1) - 2 ^ i).
- Initialize another integer variable count:= 0.
- Run a loop where ‘j’ ranges from 0 to N - 1 and for each ‘j’ do the following -:
  - Let len = binaryNums[j].length
  - If len > i and binaryNums[j][len - i - 1] = ‘1’, then increment count by 1.
- If count != countReq, then append ‘1’ in ‘missingNum’ otherwise append ‘0’ in ‘missingNum’.
Reverse ‘missingNum’ and remove all leading ‘0’s.
Return ‘missingNum’.

Space Complexity: O(1)Explanation:

O(1).

We are using constant extra space here.

Time Complexity: O(nlogn)Explanation:

O(N * log(N)), where ‘N’ is the size of the given list binaryNums.

The total number of bits in all the ‘N’ string will be N log(N). In this approach, we are iterating over every bit. Thus overall time complexity will be O(N log(N))

Python (3.5)