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.

class Solution {
public:
string getPermutation(int n, int k)
{
vector<int> nums(n);
int pCount = 1;
for(int i = 0 ; i < n; ++i) {
nums[i] = i + 1;
pCount *= (i + 1);
}

k--;
string res = "";
for(int i = 0 ; i < n; i++) {
pCount = pCount/(n-i);
int selected = k / pCount;
res += ('0' + nums[selected]);

for(int j = selected; j < n-i-1; j++)
nums[j] = nums[j+1];
k = k % pCount;
}
return res;
}
};