A valid IP address consists of four numeric segments separated by single dots. Each segment must be an integer between 0 and 255 (inclusive), and leading zeros are not allowed unless the segment is exactly ‘0.”
For instance, “10.0.1.25” and “172.16.0.5” are valid IP addresses, while “01.200.100.3,” “256.100.50.25,” and “172.16.0.500” are invalid.
Given a string s made up of digits only, return all possible valid IP addresses that can be created by inserting exactly three dots into the string. You cannot rearrange or delete any digits. The resulting list of valid IP addresses can be returned in any order.
Constraints:
The naive approach would be to check all possible positions of the dots. Because an IP address requires inserting three dots, and if the input string contains 12 digits, then there are 11 possible positions between the digits where a dot can be placed. So, we initially have 11 choices for the first dot, then 10 choices for the second dot, and 9 choices for the third dot. This results in at most 11×10×9=990 combinations to validate in the worst case.
We can introduce three nested loops to try all possible positions for placing the dots: the outer loop iterates through every valid position for the first dot (up to position 11), the middle loop tries all possible positions for the second dot that come after the first, and the inner loop attempts every possible position for the third dot following the second. After placing the dots, each resulting substring between the dots must be validated as a valid number, meaning it should be between 0 and 255 (inclusive) and must not have leading zeros.
Overall, this approach has a time complexity of O(n3) due to the three nested loops required to place the dots. The space complexity is O(1), since we are not using any additional data structures beyond a constant amount of space.
Each numeric segment in the IP address is known as an octet, and each octet can have 1 to 3 digits.
Example IP Address: 192.168.0.1