LeetCode_Permutation Sequence

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):

    "123"
    "132"
    "213"
    "231"
    "312"
    "321"

Given n and k, return the kth permutation sequence.

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

　　分析：数学的思路来做。

class Solution {
public:
    string getPermutation(int n, int k) {
        // Start typing your C/C++ solution below
        // DO NOT write int main() function
        int A[9] = {1,1, 2, 6, 24, 120, 720, 5040, 40320};
        string    res = "";
        vector<bool> flag(n+1, false);
        for(int i = n-1; i >= 0; --i)
        {
            int pos = k / A[i];
            if(k%A[i] ==0 && pos > 0) --pos;
            k = k - pos * A[i];
            for(int j = 1; j <= n; ++j)
            {
                if(flag[j] == false){
                    if(pos == 0)
                    {
                        char c = '0' + j;
                        res += c;
                        flag[j] = true;
                        break;
                    }else{
                        --pos;
                    }
                }
            }
        }

        return res;
    }
};