(backtracking) and all non-augmented positive integer and decomposition algorithms for n

The recursive algorithm is used to output positive integers and all non-increasing positive integers of n. For example, when n=5, the non-additive formula is as follows:

5=5

5=4+1

5=3+2

5=3+1+1

5=2+2+1

5=2+1+1+1

5=1+1+1+1+1

The problem of finding a subset can be solved by backtracking method, which is a recursive algorithm with pruning judgment.

Keywords to solve the problem: no increase

The code is implemented as follows:

Array A is used to hold the decomposed sum, that is, a set of decomposition

Sum indicates the number that needs to be exploded

K indicates the K-sum to be decomposed

#include <iostream>#include<stdio.h>using namespacestd;#defineN 100voidSubsetofsumn (intA[],intSumintk) {     for(inti=sum;i>=1; i--){        if(i<=a[k-1]) {A[k]=i; if(i==sum) {printf ("%d=%d", a[0],a[1]);  for(intp=2;p <=k;p++) printf ("+%d", A[p]); printf ("\ n"); }            ElseSubsetofsumn (A,sum-i,k+1); }    }}intMain () {intN,a[n]; printf ("Please input an integer n (1<=n<=20):"); scanf ("%d",&N); a[0]=N; printf ("The result of nondescend integer factorization is:\n"); Subsetofsumn (A,n,1); return 0;}

(backtracking) and all non-augmented positive integer and decomposition algorithms for n