Integer splitting is the process of splitting a positive integer into the sum of several positive integers. For example, the integer 5 divided by 2 and 3, 4 and 1 and so on. The partition of integers has many applications in mathematics, for example, in combinatorial mathematics, it is closely related to combinatorial identities and generating functions. In addition, in computer science, partition problem can be used to optimize the complexity of the algorithm, for example, in dynamic programming algorithm, it is often used to solve the minimum number of coins.

There are many divisible methods of integers, among which Euler number, ordinary divisible number and trivial divisible number are famous. Euler number refers to dividing an integer into several parts, plus 1, 2, ... respectively. Their nature is very complex and has profound mathematical connotation. Ordinary partition number is a common sequence in mathematics, which represents the scheme number of dividing an integer n into the sum of several positive integers, and has many research values like Euler number. Ordinary partition numbers are very easy to calculate, that is, dividing an integer into its own scheme numbers, such as 1 and 1, 2 and 2.

For some smaller integers, we can get their decomposition by exhaustive method, but it is very time-consuming to calculate their decomposition one by one for large integers. Therefore, there are many optimization algorithms in the partition problem, such as dynamic programming algorithm and generating function algorithm. The core idea of dynamic programming algorithm is to divide a big problem into several small problems, solve the small problems respectively, and then combine them to get the solution of the big problem. The generating function algorithm transforms the sequence into polynomial, so that the problem can be solved by algebraic operation. The use of these algorithms greatly improves the efficiency of solving the splitting problem and makes the splitting problem more widely used.