[LeetCode] 60. Permutation Sequence 序列排序

The set [1,2,3,…,n] contains a total of n! unique permutations.

By listing and labeling all of the permutations in order,
We get the following sequence (ie, for n = 3):

1. "123"
2. "132"
3. "213"
4. "231"
5. "312"
6. "321"

Given n and k, return the kth permutation sequence.

Note: Given n will be between 1 and 9 inclusive.

求由n个数字组成的有序的排列中的第k个排列，因为只需返回第k个，所以不用将所有的排列组合都求出来，只求出第k个排列组合即可，重点在于找出排序和k的规律。

参考：喜刷刷

Python：

class Solution(object):
    def getPermutation(self, n, k):
        """
        :type n: int
        :type k: int
        :rtype: str
        """
        seq, k, fact = "", k - 1, math.factorial(n - 1)
        perm = [i for i in xrange(1, n + 1)]
        for i in reversed(xrange(n)):
            curr = perm[k / fact]
            seq += str(curr)
            perm.remove(curr)
            if i > 0:
                k %= fact
                fact /= i
        return seq　

C++：

class Solution {
public:
    string getPermutation(int n, int k) {
        string ret;
        vector<int> factorial(n,1);
        vector<char> num(n,1);
        
        for(int i=1; i<n; i++) 
            factorial[i] = factorial[i-1]*i;
        
        for(int i=0; i<n; i++)
            num[i] = (i+1)+'0';
        
        k--;
        for(int i=n; i>=1; i--) {
            int j = k/factorial[i-1];
            k %= factorial[i-1];
            ret.push_back(num[j]);
            num.erase(num.begin()+j);
        }
        
        return ret;
    }
}; 

C++：

class Solution {
public:
    string getPermutation(int n, int k) {
        string res;
        string num = "123456789";
        vector<int> f(n, 1);
        for (int i = 1; i < n; ++i) f[i] = f[i - 1] * i;
        --k;
        for (int i = n; i >= 1; --i) {
            int j = k / f[i - 1];
            k %= f[i - 1];
            res.push_back(num[j]);
            num.erase(j, 1);
        }
        return res;
    }
};

　　

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