Programming question-Grouping Problem, output formula.

Programming questions:
Enter two integers N and P. (n <= P) in the command line. The program outputs a series of formulas that meet the following conditions:
Formula: A1 * B1 + A2 * B2 +... + an * bn
Requirements:
The formula must meet the following requirements:
A1 * B1 + A2 * B2 +... + an * bn = N
A1 + A2 +... + an = P
Where the number of columns: A1 A2... An is an integer number of> = 1.
B1 B2... BN is an integer Series> = 1, and satisfies: BN> Bn-1
Multiple formulas are in a parallel relationship and have no output sequence requirements.
This program is named grouping ). A batch of balls of multiple colors (unlimited quantity) need to be packed in N grids. each package contains only p-colored balls. the duplicates in these combinations.
For example, A1 appears B1 times + A2 appears B2 times.

For example:
Input
Grouping 7 5
4*1 + 1*3
3*1 + 2*2

Solution: (users who do not like the idea can directly look at the code)
Design a function to input n p ks. The function can be called recursively.
N is the remaining N value p is the remaining P value K is the smallest B value S is the input string.

When 7 or 5 is input, the function is called as follows:

F (7, 5, 1, null)
Function attempt:
5*1 P-5 = 0, 5*1 <7 F (7, 5, 2, null) Continue the next attempt.
4*1 P-4 = 1 call f (7-4*1, 5-4, 2, "4*1"), recursively return and continue the next attempt.
3*1 call f (4,2, 2, "3*1 ")
2*1 call f (5, 3, 2, "2*1 ")
1*1 call f (6, 4, 2, "1*1 ")
Return.

Call: F (7-4*1, 5-4, 2, "4*1") Resolution
F (3, 1, 2, "4*1 ")
Try
1*2 P-1 = 0, F (3, 1, 3, "4*1") ---> output 4*1 + 1*3

Call F (4,2, 2, "3*1 ")
Try
2*2 = 4 ---> output 3*1 + 2*2

 1 #include <stdio.h> 2 #include <string.h> 3 #include <stdlib.h> 4  5 void grouping(int N,int P,int K ,char* prestr) { 6 #define grouping_buf_size 128 7     // trying: N N-1 N-2 .... 8     char buf[grouping_buf_size]; 9     for(int i=P;i>0;i--) {10         if(prestr==NULL) {11             sprintf(buf,"%d*%d",i,K); 12         } 13         else {14             sprintf(buf,"%s + %d*%d",prestr,i,K); 15         }16         if(P-i==0) {17             if(N-i*K == 0) {18                 printf("%s\n",buf); 19             }20             else if(N-i*K > 0) {21                 grouping(N,P,K+1,prestr);22             }23             else if(N-i*K < 0) {24             }25         }26         else if(N-i*K>0){27 28             grouping(N-i*K,P-i,K+1,buf);29         }30 31     }32 33 #undef grouping_buf_size 34 }35 36 int main(int argc,char** argv) {37 int n=atoi(argv[1]);38 int p=atoi(argv[2]);39 grouping(n,p,1,NULL);40 41 return 1;42 }

Grouping code

Test:

$ Grouping 7 7
7*1
$ Grouping 7 6
5*1 + 1*2
$ Grouping 7 5
4*1 + 1*3
3*1 + 2*2
$ Grouping 7 4
3*1 + 1*4
2*1 + 1*2 + 1*3
1*1 + 3*2

 

Programming question-Grouping Problem, output formula.