Permutation & Combination

最新推荐文章于 2022-09-21 13:48:54 发布

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最新推荐文章于 2022-09-21 13:48:54 发布

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分类专栏： Data structures and algorithms

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1.Permutation:

1.1 Recursion

Perm(vec, beg, end)

1.When beg = end, print;

2.Otherwise swap the first element denoted by beg with following elements, then do Perm(vec, beg + 1, end):

for(i = beg; i <= end; ++i)

swap(beg, i);

Perm(vec, beg+1, end);

swap(beg,i);

    vector<vector<int>> permutation(vector<int> &nums)
    {
        sort(nums.begin(), nums.end());
        vector<vector<int>> ret;
        permutation(nums, 0, ret);
        return ret;
    }


    void permutation(vector<int> nums, int beg, vector<vector<int>> &ret)
    {
        if(beg == nums.size()-1)
        {
            ret.push_back(nums);
            return;
        }
        for(int i = beg; i < nums.size(); ++i)
        {
            vector<int> tmp = nums;
            if(i == beg || nums[i] != nums[i-1])    //handle duplicates
            {
                swap(nums[beg], nums[i]);
                permutation(nums, beg + 1, ret);
                nums = tmp;
            }
        }
    }

1.2 Non-recursion

    vector<vector<int>> permuteUnique(vector<int>& nums) 
    {
        sort(nums.begin(), nums.end());
        vector<vector<int>> ret;
        ret.push_back(nums);
        int k = -1, l = -1;
        while(true)
        {
            k = -1, l = -1;
            for(int i = 0; i < nums.size()-1; ++i)
                if(nums[i] < nums[i + 1])
                    k = i;
            if(k == -1) break;
            for(int i = k + 1; i < nums.size(); ++i)
                if(nums[i] > nums[k])
                    l = i;
            swap(nums[k], nums[l]);
            reverse(nums.begin() + k + 1, nums.end());
            ret.push_back(nums);
        }
        return ret;
    }

2.Combination

The result is stored in vector<vector<int>> &v. The helper function take vec as the first parameter which stores the integers that will be used to perform the combination. k is the number of integers that will be used.

class Solution <span style="font-family: Arial, Helvetica, sans-serif;">{</span>

public:
void Comb(int k, vector<vector<int>> &v)
{
<span style="white-space:pre">	</span>vector<int> vec, tmp;
<span style="white-space:pre">	</span>for(int i = 0; i < 9; ++i)
<span style="white-space:pre">		</span>vec.push_back(i+1);
<span style="white-space:pre">	</span>Comb(vec, 0, tmp, k, v);
}

void Comb(vector<int> &vec, int beg, vector<int> &tmp, int k, vector<vector<int>> &v)
{
<span style="white-space:pre">	</span>if(k == 0 )
<span style="white-space:pre">	</span>{
<span style="white-space:pre">		</span>v.push_back(tmp);
<span style="white-space:pre">		</span>return;
<span style="white-space:pre">	</span>}

<span style="white-space:pre">	</span>for(int i = beg; i <= vec.size() - k; ++i)
<span style="white-space:pre">	</span>{
<span style="white-space:pre">		</span>tmp.push_back(vec[i]);
<span style="white-space:pre">		</span>Comb(vec, i+1, tmp,  k-1, v);
<span style="white-space:pre">		</span>tmp.pop_back();
<span style="white-space:pre">	</span>}
};