# Permutation Sequence Problem

## Description

LeetCode Problem 60.

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 for n = 3:

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

Given n and k, return the kth permutation sequence.

Example 1:

``````1
2
Input: n = 3, k = 3
Output: "213"
``````

Example 2:

``````1
2
Input: n = 4, k = 9
Output: "2314"
``````

Example 3:

``````1
2
Input: n = 3, k = 1
Output: "123"
``````

Constraints:

• 1 <= n <= 9
• 1 <= k <= n!

## Sample C++ Code

``````1
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string getPermutation(int n, int k) {
// pTable refers to permutation table and numSet refers to a set of numbers from 1 to 9.
int pTable[10] = {1};
for (int i = 1; i <= 9; i++){
pTable[i] = i * pTable[i - 1];
}
string result;
vector<char> numSet{'1', '2', '3', '4', '5', '6', '7', '8', '9'};
while (n > 0){
// 1 calculate which number we will use.
// 2 remove that number from numSet.
// 3 recalculate k.
// 4 n--.
int temp = (k - 1) / pTable[n - 1];
result += numSet[temp];
numSet.erase(numSet.begin() + temp);
k = k - temp * pTable[n - 1];
n--;
}
return result;
}
``````