Solution Explanation for IP to CIDR

This problem requires finding the minimal number of CIDR blocks to cover a given range of IP addresses. The key is to efficiently find the optimal prefix length for each CIDR block to minimize the total number of blocks.

Approach:

1. IP to Integer: Convert the input IP address string to its 32-bit integer representation. This simplifies calculations.

2. Iterative Block Creation: Iterate while the number of addresses (n) to cover is greater than 0. For each iteration:

   • Find the largest power of 2: Determine the largest power of 2 (powerOf2) that is less than or equal to n. This represents the maximum number of addresses a single CIDR block can cover without exceeding the given range.

   • Calculate Prefix Length: The prefix length (prefixLength) is 32 minus the logarithm base 2 of powerOf2. This is because a prefix length of k implies 32-k bits are variable (allowing 232-k addresses).

   • Create CIDR Block: Convert the current IP address integer back to its dotted-quad string representation. Append the prefix length to form the CIDR block string, and add it to the result list.

   • Update: Subtract powerOf2 from n (addresses covered) and add powerOf2 to the current IP address integer (move to the next IP address after the current block).

3. Return Result: The final result list contains the minimal set of CIDR blocks covering the IP address range.

Time Complexity Analysis:

The algorithm iterates at most log2(n) times because n is repeatedly halved (approximately) in each iteration. The conversion between integer and string representations of IP addresses takes constant time. Therefore, the overall time complexity is O(log n), where n is the number of IP addresses to cover.

Space Complexity Analysis:

The space complexity is determined by the size of the resulting CIDR block list. In the worst case, we might have O(log n) CIDR blocks, leading to a space complexity of O(log n).

Code Implementation (Python):

def ipToCIDR(ip, n):
    """
    Converts an IP address and a number of addresses to a list of CIDR blocks.
 
    Args:
        ip: The starting IP address (string).
        n: The number of IP addresses to cover.
 
    Returns:
        A list of CIDR blocks (strings).
    """
    num_ip = ip_to_int(ip)  # Convert IP to integer
    result = []
    while n > 0:
        powerOf2 = 1 << (ip_to_int(ip) & -ip_to_int(ip)).bit_length() -1
        powerOf2 = min(powerOf2, n)  # Adjust to not exceed n
        prefixLength = 32 - powerOf2.bit_length()
        result.append(int_to_ip(num_ip) + "/" + str(prefixLength))
        num_ip += powerOf2
        n -= powerOf2
    return result
 
def ip_to_int(ip):
  """Converts a dotted-quad IP string to its integer representation."""
  parts = map(int, ip.split('.'))
  return (parts[0] << 24) + (parts[1] << 16) + (parts[2] << 8) + parts[3]
 
def int_to_ip(num_ip):
  """Converts an integer IP representation to a dotted-quad string."""
  return f"{ (num_ip >> 24) & 0xFF }.{ (num_ip >> 16) & 0xFF }.{ (num_ip >> 8) & 0xFF }.{ num_ip & 0xFF }"
 
#Example
ip = "255.0.0.7"
n = 10
print(ipToCIDR(ip, n)) # Output: ['255.0.0.7/32', '255.0.0.8/29', '255.0.0.16/32']
 
ip = "117.145.102.62"
n = 8
print(ipToCIDR(ip,n)) # Output: ['117.145.102.62/31', '117.145.102.64/30', '117.145.102.68/31']

This Python code demonstrates the approach, including helper functions for IP address conversion. Similar approaches can be used in Java, C++, or Go, adapting the bit manipulation and string formatting as needed for each language. The core logic of finding the optimal prefix length and iteratively creating CIDR blocks remains the same.