Integer partition/Cut (integer partion), and output results, Java, Python__python

Integer partitioning is a more typical recursive problem: dividing an integer n n n into a series of numbers that are not more than M m.
For example, if n=5 n = 5 n=5, m=4 m = 4 m=4, the partition can be: {4,1}, {3,1,1}, {3,2}, {2,1,1,1}, {2, 2, 1},{1,1,1,1,1}. A total of 6 combinations.

If as long as the total number of output division, online reference more, also easy to understand parity.
If you also require the specific results of the division of output, online data is relatively small, I myself from the foreign website search, found an answer, the same use of recursion thought, mainly:
A string argument is added to the function, and when n-n values drop to 0 o'clock, the line wraps .

Java code:

/** * @author Chen Zhen * @version creation Date: April 25, 2018 PM 4:51:23 * @value class Description: Integer partition, and output/public class Integerpartion {
        Query division number static int countpartion (int n, int m) {if (n ==1 | | | = = 1) return 1;
        else if (M > N) return countpartion (n, N);
        else if (M ==n) return 1 + countpartion (n, n-1);
        else if (M < n) return Countpartion (N-m, m) + countpartion (n, m-1);
    return 0; }//Output specific division static void Countoutput (int n, int m, String str) {if (n = = 0)//recursive jump out of condition 1 System
        . out.println (str);
            else {if (M > 1)///recursive jump out of Condition 2 countoutput (n, m-1, str);
        if (M <= N)///Because the m>n situation may occur when recursion Countoutput (N-m, M, M + "" + str);
        } public static void Main (string[] args) {int m = 5;
        int n = 6;
        System.out.println (Countpartion (M, n));
  Countoutput (M, N, "");  }
}
 

Python Code:

# output integer partition number
def f1 (n, m):
    if n==0 or M ==0: return
        0
    if n==1 or M ==1: return
        1
    if m = = N:        
        ret Urn 1 + F1 (n, n-1)
    elif m > N: Return
        F1 (n, N)
    elif m < n: return
        F1 (n-m, m) + F1 (n, m-1)

# Output Specific integer Division
def f2 (n, M, string):
    If n = 0:
        print (String)
    else:
        if m>1:
            f2 (N, m-1, string
        if M <= N:
            F2 (n-m, M, str (m) + ' +string) 

n = 5 m = 4
print (F1 (n, m))
F2 (n, M, ")

Output results:
6
1 1 1 1 1
1 1 1 2
1 2 2
1 1 3
2 3
1 4