子序列问题和组合数问题

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input arr={10, 7, 5, 18, 12, 20, 15}
sum =35
output:所有等于sum的子序列
{10, 7, 18}
{10, 5, 20}
{5, 18, 12}
{20, 15}

 algorithm
 subsetSum(arr,subarr,n,subSize,total,node,sum)
 n是arr的大小，subSize是subarr的大小(个数）,total是subarr的和，node是subarr元素数(索引)
 具体：
if total=sum ,then
	display the subset
    //寻找下一个子序列
    subsetSum(arr,subarr,n,subsize-1，total-arr[node],node+1,sum)
    return 
else
	for i in arr(i=node)
    	subarr[subSize]=arr[i]
        subsetSum(arr,subarr,n,subsize+1，total+arr[i],i+1,sum)

#include <iostream>
using namespace std;

void displaySubset(int subSet[], int size) {
   for(int i = 0; i < size; i++) {
      cout << subSet[i] << "  ";
   }
   cout << endl;
}

void subsetSum(int set[], int subSet[], int n, int subSize, int total, int nodeCount ,int sum) {
   if( total == sum) {
      displaySubset(subSet, subSize);     //print the subset
      subsetSum(set,subSet,n,subSize-1,total-set[nodeCount],nodeCount+1,sum);     //for other subsets
      return;
   }else {
      for( int i = nodeCount; i < n; i++)
      {     
         subSet[subSize] = set[i];
         subsetSum(set,subSet,n,subSize+1,total+set[i],i+1,sum);     //do for next node in depth
      }
   }
}

void findSubset(int set[], int size, int sum) {
   int *subSet = new int[size];     //create subset array to pass parameter of subsetSum
   subsetSum(set, subSet, size, 0, 0, 0, sum);
   delete[] subSet;
}

int main() {
   int weights[] = {1, 2, 3, 18, 12, 4, 15};
   int size = 7;
   findSubset(weights, size, 3);
}

Print all combinations of points that can compose a given number组合数问题

给定一个数字n，和一个最大值限制max_point，打印所有不超过最大值的等于n的组合

example
input:n=1,max_point=3
output:1

input:n=3,max_point=3
output:
1 1 1
1 2
2 1 

#include<iostream>
using namespace std;
const int MAX_POINT=3;
const int ARR_SIZE=100;
void printArr(int arr[],int arr_size)
{
	for(int i=0;i<arr_size;i++)
    {
    	printf("%d ",arr[i]);
    }
    printf("\n");
}
void printCompositions(int n,int i)
{
	static int arr[ARR_SIZE];
	if(n==0) //终止条件
    {
    	printArr(arr,i);
    }
    else if(n>0)
    {
    	for(int k=1;k<MAX_point;k++)
        {
        	arr[i]=k;
             printCompositions(n-k,i+1);
        }
    }
}
int main()
{
    int n=5;
    printCompositions(n,0);
    return 0;
}