生成组合序列算法

2024年6月8日 114次阅读

生成组合序列

1.递归算法

生成C(5,3)

#include <iostream>
#include <vector>

using namespace std;

vector<vector<int>> s;
vector<int> source;

void getCombination(int elementNeed, int startPos, const vector<int> &oneResult)
{
    if(elementNeed == 0)
    {
        s.push_back(oneResult);
        return;
    }
    while(startPos < source.size())
    {
        vector<int> tmp = oneResult;
        tmp.push_back(source[startPos]);
        getCombination(elementNeed - 1, startPos + 1, tmp);
        ++startPos;
    }
}

int main(int argc, const char * argv[])
{
    source = {1, 2, 3, 4, 5};
    vector<int> tmp;
    getCombination(3, 0, tmp);

    for(auto k : s)
    {
        for(auto i : k)
        {
            cout << i << ' ';
        }
        cout << endl;
    }

    return 0;
}

2.非递归版本

生成C(5,3)

#include <iostream>
#include <vector>


using namespace std;


vector<vector<int>> s;


void getCombination(const vector<int> &source, int elementNeed)
{
    if(elementNeed == 0)
    {
        return;
    }
    if(elementNeed > source.size())
    {
        return;
    }
    vector<int> pos;
    vector<int> tmp;
    for(int i = 0; i < elementNeed; ++i)
    {
        pos.push_back(i);
        tmp.push_back(source[i]);
    }
    while(pos[0] + elementNeed <= source.size())
    {
        for(int i = 0; i < pos.size(); ++i)
        {
            tmp[i] = source[pos[i]];
        }
        s.push_back(tmp);
        int k = pos.size() - 1;
        while(k>0 && pos[k] + elementNeed - k == source.size()) --k;
        ++pos[k];
        ++k;
        while(k < pos.size())
        {
            pos[k] = pos[k - 1] + 1;
            ++k;
        }
    }
}


int main(int argc, const char * argv[])
{
    vector<int> source = {1, 2, 3, 4, 5};
    getCombination(source, 3);


    for(auto k : s)
    {
        for(auto i : k)
        {
            cout << i << ' ';
        }
        cout << endl;
    }


    return 0;
}

3.优化的非递归版本

生成C(5,3)，优化减少了赋值的次数

#include <iostream>
#include <vector>

using namespace std;

vector<vector<int>> s;

void getCombination(const vector<int> &source, int elementNeed)
{
    if(elementNeed == 0)
    {
        return;
    }
    if(elementNeed > source.size())
    {
        return;
    }
    vector<int> pos;
    vector<int> tmp;
    for(int i = 0; i<elementNeed; ++i)
    {
        pos.push_back(i);
        tmp.push_back(source[i]);
    }
    while(pos[0] + elementNeed <= source.size())
    {
        s.push_back(tmp);
        int k = pos.size() - 1;
        while(k>0 && pos[k] + elementNeed - k == source.size())
        {
            --k;
        }
        ++pos[k];
        tmp[k] = source[pos[k]];
        ++k;
        while(k < pos.size())
        {
            pos[k] = pos[k - 1] + 1;
            if(pos[k] < source.size())
            {
                tmp[k] = source[pos[k]];
            }
            ++k;
        }
    }
}

int main(int argc, const char * argv[])
{
    vector<int> source = {1, 2, 3, 4, 5};
    getCombination(source, 3);

    for(auto k : s)
    {
        for(auto i : k)
        {
            cout << i << ' ';
        }
        cout << endl;
    }

    return 0;
}
点赞