Ip To Cidr - Leetcode Solution

The 'IP to CIDR' problem on LeetCode asks us to take an IP address as well as a number, and then to output a list of CIDR blocks with the given number of IP addresses as requested.

A CIDR block is a range of IP addresses that are all covered by the same subnet mask. For example, the IP address 192.168.1.1 might be covered by the CIDR block 192.168.1.0/24, which means that the first 24 bits of the IP address are fixed and the remaining 8 bits can take on any value between 0 and 255.

To solve this problem, we can follow the following approach:

1. Convert the IP address to a 32-bit binary string: We can start by taking the given IP address and splitting it into four decimal numbers. Then, we can convert each of these decimal numbers to an 8-bit binary number and concatenate them together to form a 32-bit binary string.

For example, if the input IP address is "255.0.0.7", we can convert it to the binary string "11111111000000000000000000000111".

2. Compute the number of addresses requested: We are given a number 'n' that represents the number of IP addresses that we need to cover. To find the size of the CIDR block that we need, we can keep halving the number of addresses requested until we reach a power of 2. This is because a CIDR block always has a size that is a power of 2.

For example, if n=10, we can keep halving it until we reach a power of 2: 10 -> 5 -> 2 -> 1. Therefore, we need a CIDR block of size 2^3=8.

3. Calculate the prefix length of the CIDR block: The prefix length of a CIDR block represents the number of leading bits in the subnet mask. To calculate this, we can count the number of consecutive 1's starting from the most significant bit of the binary IP address until we reach a count that is greater than or equal to the log base 2 of the number of requested addresses.

For example, if the binary IP address is "11111111000000000000000000000111", and we need to cover 8 addresses, we can count the number of leading 1's: 11111111. Since this is 8 bits long and 2^3=8, the prefix length of the CIDR block is 8.

4. Generate the CIDR blocks: Once we have the binary IP address and the prefix length, we can use these to generate the CIDR blocks. We can start by taking the prefix and using it to generate a subnet mask (by setting the first 'prefix' bits to 1 and the remaining bits to 0). Then, we can use this subnet mask to split the IP address into multiple blocks, each of size equal to the number of requested addresses.

For example, if the binary IP address is "11111111000000000000000000000111" and we need to cover 8 addresses, we can calculate the subnet mask as "11111111000000000000000000000000". Then, we can split the IP address into 8 blocks, each with a size of 1 address:

• 11111111000000000000000000000000 (subnet mask)
• 11111111000000000000000000000000 (first block: 255.0.0.0/32)
• 11111111000000000000000000000100 (second block: 255.0.0.4/30)
• 11111111000000000000000000001000 (third block: 255.0.0.8/29)
• 11111111000000000000000000001100 (fourth block: 255.0.0.12/30)
• 11111111000000000000000000010000 (fifth block: 255.0.0.16/29)
• 11111111000000000000000000010100 (sixth block: 255.0.0.20/30)
• 11111111000000000000000000011000 (seventh block: 255.0.0.24/29)
• 11111111000000000000000000011100 (eighth block: 255.0.0.28/30)

We can generate the blocks in this way by iterating over the binary IP address and subnet mask, and dividing the address into blocks according to the size requested.

Now we can combine all these steps to get the solution for the problem. Here is the complete Python code:

def ipToCIDR(ip: str, n: int) -> List[str]:
    # Convert the IP address to binary
    ip_num = 0
    for x in ip.split('.'):
        ip_num = ip_num * 256 + int(x)
    ip_bin = "{0:b}".format(ip_num)

    # Calculate CIDR blocks
    blocks = []
    while n > 0:
        # Find the largest power of 2 that is <= n
        mask = 1
        while mask < n:
            mask *= 2
        mask -= 1

        # Calculate the prefix length
        prefix_len = 0
        while mask > 0:
            mask //= 2
            prefix_len += 1

        # Add the CIDR block to the list
        blocks.append(ip_num_to_ip_str(ip_num) + '/' + str(32 - prefix_len))

        # Update the IP address and the number of addresses remaining
        ip_num += mask + 1
        n -= mask + 1

    return blocks

def ip_num_to_ip_str(ip_num: int) -> str:
    return '.'.join(str((ip_num >> (8 * i)) % 256) for i in range(4)[::-1])

The 'ipToCIDR' function takes two inputs: a string representing the IP address and an integer representing the number of addresses required. The function uses the approach outlined above to generate the CIDR blocks, and returns a list of strings representing the CIDR blocks.

The 'ip_num_to_ip_str' function is a helper function that takes a 32-bit integer representing an IP address in binary format and converts it to a string representation in decimal format.

The time complexity of this function is O(n), where n is the number of requested addresses. This is because we may need to generate up to n CIDR blocks. The space complexity is also O(n), since we need to store the CIDR blocks in a list.

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