Efficient allocation of numbers in a non-contiguous list using gap values

A system comprising:

• one or more processors;
• and
• a memory storing instructions that, when executed by the one or more processors, cause the system to perform operations comprising:
• receiving, from a requesting system via a network, a request for one or more numbers, wherein the request includes an original range of possible numbers;
• loading an original list of previously allocated numbers into an indexed data structure stored in a data store;
• generating gap values for the original list of previously allocated numbers in the indexed data structure, each gap value representing a mathematical difference between one of the original list of previously allocated numbers and an index value in the indexed data structure corresponding to the one of the original list of previously allocated numbers;
• performing an available number search process on the original list of previously allocated numbers in the indexed data structure to identify one or more currently available numbers within the original range of possible numbers and using the original list of previously allocated numbers as an initial current number list, wherein each iteration of the available number search process includes, for a current number list:
• determining whether there are one or more available numbers between a lowest number in the current number list and a highest number in the current number list based on a comparison of the gap value associated with the highest number in the current number list to the gap value associated with the lowest number in the current number list;
• and
• in accordance with a determination that there are one or more available numbers between the lowest number in the current number list and the highest number in the current number list:
• identifying one or more of the available numbers between the lowest number in the current number list and the highest number in the current number list;
• and
• transmitting, via the network, one or more of the identified available numbers to the requesting system.

A non-transitory computer-readable storage medium storing instructions that, when executed by one or more processors of a machine, cause the machine to perform operations comprising:

• receiving, from a requesting system via a network, a request for one or more numbers, wherein the request includes an original range of possible numbers;
• loading an original list of previously allocated numbers into an indexed data structure stored in a data store;
• generating gap values for the original list of previously allocated numbers in the indexed data structure, each gap value representing a mathematical difference between one of the original list of previously allocated numbers and an index value in the indexed data structure corresponding to the one of the original list of previously allocated numbers;
• performing an available number search process on the original list of previously allocated numbers in the indexed data structure to identify one or more currently available numbers within the original range of possible numbers and using the original list of previously allocated numbers as an initial current number list, wherein each iteration of the available number search process includes, for a current number list:
• determining whether there are one or more available numbers between a lowest number in the current number list and a highest number in the current number list based on a comparison of the gap value associated with the highest number in the current number list to the gap value associated with the lowest number in the current number list;
• and
• in accordance with a determination that there are one or more available numbers between the lowest number in the current number list and the highest number in the current number list:
• identifying one or more of the available numbers between the lowest number in the current number list and the highest number in the current number list;
• and
• transmitting, via the network, one or more of the identified available numbers to the requesting system.