Combinations

Combinations

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Given two integers n and k, return all possible combinations of k numbers out of 1 ... n.

For example,
If n = 4 and k = 2, a solution is:

[  [2,4],  [3,4],  [2,3],  [1,2],  [1,3],  [1,4],]

解法1，2： DFS遍历所有组合，注意判断当前cur的长度以及当前可以值的状态是否可以继续
解法3，4：用next（prev） permutation来实现获取所有组合
解法5： 类似非递归的DFS（或者可以想象成为整数逐步加1进位，遍历所有可能数值）来编译状态
解法6：长度从1到k，每次把所有长度为i- 1的已有组合遍历一次，取所有可能的组合形成长度为i的所有组合（题目要求从小到大，这也为我们这样实现提供的依据）

class Solution {public:    vector<vector<int> > combine(int n, int k) {        // IMPORTANT: Please reset any member data you declared, as        // the same Solution instance will be reused for each test case.        vector<vector<int>> ret;        if (k < 1 || k > n) return ret;                // 1        /*        vector<int> cur;        genCombination1(ret, cur, n, k, 1);        */                // 2        /*        vector<int> cur;        genCombination2(ret, cur, n, k, 1);        */                // 3        /*        vector<int> flag(n, 0);        for (int i = 0; i < k; ++i) {            flag[i] = 1;        }                do {            ret.push_back(vector<int>());            auto it = back_inserter(ret.back());            for (int i = 0; i < n; ++i) {                if (flag[i] == 1) it = i + 1;            }        //} while (prev_permutation(flag.begin(), flag.end()));        } while (m_prev_permutation(flag));        */                // 4        /*        vector<int> flag(n, 0);        for (int i = n - k; i < n; ++i) {            flag[i] = 1;        }                do {            ret.push_back(vector<int>());            auto it = back_inserter(ret.back());            for (int i = 0; i < n; ++i) {                if (flag[i] == 1) it = i + 1;            }        //} while (next_permutation(flag.begin(), flag.end()));        } while (m_next_permutation(flag));        */                // 5        /*        vector<int> lo(k, 0), hi(k, 0);        for (int i = 1; i <= k; ++i) {            lo[i - 1] = i;            hi[i - 1] = n - k + i;        }                while (true) {            ret.push_back(lo);            int cpos = k - 1;            while (cpos >= 0) {                if (lo[cpos] < hi[cpos]) {                    ++lo[cpos];                    for (int i = cpos + 1; i < k; ++i) {                        lo[i] = lo[i - 1] + 1;                    }                    break;                }                                --cpos;            }                        if (cpos < 0) break;        }        */                // 6        for (int i = 1; i <= n - k + 1; ++i) {            ret.push_back(vector<int>(1, i));        }                for (int i = 2; i <= k; ++i) {            int cnt = ret.size();            for (int j = 0; j < cnt; ++j) {                int cval = ret[j].back();                int lastval = n - k + i;                for (int t = cval + 1; t < lastval; ++t) {                    ret.push_back(ret[j]);                    ret.back().push_back(t);                }                                ret[j].push_back(lastval);            }        }                return ret;    }    private:    void genCombination1(vector<vector<int>> &ret, vector<int> &cur, int n, int k, int cval) {        if (n - cval + 1 < k - cur.size()) return;        if (cur.size() == k) {            ret.push_back(cur);            return;        }                cur.push_back(cval);        genCombination1(ret, cur, n, k, cval + 1);        cur.pop_back();        genCombination1(ret, cur, n, k, cval + 1);    }        void genCombination2(vector<vector<int>> &ret, vector<int> &cur, int n, int k, int cval) {        int cnt = cur.size();        if (cnt == k) {            ret.push_back(cur);            return;        }                        for (int i = cval; i <= n - k + cnt + 1; ++i) {            cur.push_back(i);            genCombination2(ret, cur, n, k, i + 1);            cur.pop_back();        }    }        bool m_prev_permutation(vector<int> &f) {        for (int i = f.size() - 1; i > 0; --i) {            if (f[i] >= f[i - 1]) continue;            int spos = i;            for (int j = spos + 1; j < f.size(); ++j) {                if (f[j] >= f[spos] && f[j] < f[i - 1])                    spos = j;            }                        swap(f[spos], f[i - 1]);            reverse(f.begin() + i, f.end());            return true;        }                return false;    }        bool m_next_permutation(vector<int> &f) {        for (int i = f.size() - 1; i > 0; --i) {            if (f[i] <= f[i - 1]) continue;            int spos = i;            for (int j = spos + 1; j < f.size(); ++j) {                if (f[j] > f[i - 1] && f[j] <= f[spos])                    spos = j;            }                        swap(f[spos], f[i - 1]);            reverse(f.begin() + i, f.end());            return true;        }                return false;    }};