组合问题和全排列

1.组合问题

问题描述：从n个元素中选出k个元素，列出所有可能的情况

template<typename T>
void combineCore(vector<T> data, int n, int k, int start, vector<T> & v, vector<vector<T>> & res)
{
	if (k < 0) return;
	else if (k == 0)
		res.push_back(v);
	else {
		for (int i = start; i < n; i++) {
			v.push_back(data[i]);
			combineCore(data, n, k-1, i+1, v, res);
			v.pop_back();
		}
	}
}

template<typename T>
vector<vector<T>> combine(vector<T> data, int n, int k)
{
	vector<vector<T>> res;
	vector<T> v;
	combineCore(data, n, k, 0, v, res);
	return res;

}

2.全排列

(1) 问题描述：求n个元素的所有可能的组合

template <typename T>
void PermutationCore(vector<T> & v,  int start,  vector<vector<T>> & res)
{
	if (start == v.size()) {
		res.push_back(v);
		return;
	}
	else {
		for (int i = start; i < v.size(); i++) {
			if (v[i] != v[start])
				swap(v[i], v[start]);
			 PermutationCore(v, start+1, res);
			if (v[i] != v[start])
				swap(v[i], v[start]);
		}
	}

}

template <typename T>
vector<vector<T>> Permutation(vector<T> v)
{
	vector<vector<T>> res;
	 PermutationCore(v, 0, res);
	return res;
}

(2) 问题描述：从n个元素选出k个元素,求这k个元素的全排列

template <typename T>
void PermutationCore(vector<T> & v, int k, int start,  vector<vector<T>> & res)
{
	if (start == k) {
		vector<T> temp(v.begin(), v.begin()+k);
		res.push_back(temp);
		return;
	}
	else {
		for (int i = start; i < v.size(); i++) {
			if (v[i] != v[start])
				swap(v[i], v[start]);
			 PermutationCore(v, k, start+1, res);
			if (v[i] != v[start])
				swap(v[i], v[start]);
		}
	}

}

template <typename T>
vector<vector<T>> Permutation(vector<T> v, int k)
{
	vector<vector<T>> res;
	 PermutationCore(v, k,  0, res);
	return res;
}

注意：(1),(2)没有考虑到元素中有重复元素出现的情况，因此返回值当中可能有重复的组合

(3) 使用next_permutation()算法

next_permutation()算法将区间内容转换为下一种排列方式，头文件为<algorithm>

template <class BidirectionalIterator>
  bool next_permutation (BidirectionalIterator first,
                         BidirectionalIterator last);

template <class BidirectionalIterator, class Compare>
  bool next_permutation (BidirectionalIterator first,
                         BidirectionalIterator last, Compare comp);

#include <iostream>
#include <string>
#include <algorithm>
using namespace std;

int main(void)
{
	string str = "abcd";
	cout << str << endl;
	while (next_permutation(str.begin(), str.end()))
		cout << str << endl;
	return 0;
}