c++ 数组的排列子集和组合子集 排列数和组合数计算

c++ 的数组排列子集和组合子集

class Combinatorial{
    //组合
public:
    vector<int> nums;//进行抽样的数组
    vector<vector<int>> result;//保存最后的排列结果
    vector<int> res;//数组中选取组合子集,t会保存到result中

    vector<vector<int>> Combinatorial_Set(vector<int>data,int select_Num){
        if(select_Num>data.size()) cout<<"error!"<<endl;

        nums=data;
        recursion(0,select_Num);
        return result;
    }
    //计算组合数
    int Combinatorial_count(int a, int m){
        int res=1;
        for(int i=0;i<a;i++){
            res*=(m-i);
        }
        for(int i=1;i<=a;i++){
            res/=i;
        }
        return res;
    }

private:
    //递归函数
    void recursion(int index,int select_Num){
        if(res.size() == select_Num){    //长度为指定长度时，保存到ans后，返回，结束这一次递归
            result.push_back(res);
            for(auto v:res) cout<<v;cout<<endl;
            return;
        }

        for(int i=index;i<nums.size();i++){
            res.push_back(nums[i]);
            recursion(i+1,select_Num);
            res.pop_back();    //回溯
        }
    }

};

class Permutation{
    //排列
public:
    vector<int> nums;//进行抽样的数组
    vector<vector<int>> result;//保存最后的排列结果
    vector<int> used_Flag;
    vector<int> res;//数组中选取排列子集

    vector<vector<int>> Permutation_Set(vector<int>data,int select_Num){
        if(select_Num>data.size()) cout<<"error!"<<endl;

        used_Flag=vector<int>(data.size(),0);
        nums=data;

        recursion(0,select_Num);
        cout<<result.size()<<endl;
        return result;
    }

    //计算排列数
    int Permutation_count(int a, int m){
        int res=1;
        for(int i=0;i<a;i++){
            res*=(m-i);
        }
        return res;
    }

private:
    //递归函数
    void recursion(int cur_Position,int select_Num){
        if(cur_Position==select_Num){
            result.push_back(res);
            for(auto v:res) cout<<v;
            cout<<endl;
            return;
        }

        for(int i=0;i<nums.size();i++){
            //如果当前元素没有被选择
            if(used_Flag[i]==0){
                res.push_back(nums[i]);
                used_Flag[i]=1;
                recursion(cur_Position+1,select_Num);//选择下一位
                used_Flag[i]=0;
                res.pop_back();
            }
        }
    }
};

int main(){
    vector<int> nums={1,2,3,4,5};

    Combinatorial combinatorial;
    combinatorial.Combinatorial_Set(nums,2);

    Permutation permutation;
    permutation.Permutation_Set(nums,2);
    cout<<permutation.Permutation_count(2,5)<<endl;
    return 0;
}