【LeetCode】60. Permutation Sequence

题目描述

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.

解题思路

排列本身是有规律的，所以直接根据数学规律算出结果就好了。

AC代码

class Solution {
public:
string getPermutation(int n, int k) {
string ans;
//记录数字1到n
vector<char> nums;
//记录1到n的阶乘，因为全排序的个数是n的阶乘
vector<int> fac;
fac.push_back(0);
int mul = 1;
for (int i = 1; i <= n; ++i) {
nums.push_back(i + '0');
mul *= i;
fac.push_back(mul);
}

k -= 1;
int curIdx = 0;
for (int i = 0; i < n - 1; ++i) {
curIdx = k / fac[n - i - 1];
ans.push_back(nums[curIdx]);
//当前数字已经加入排序中，移除
nums.erase(nums.begin() + curIdx);
k %= fac[n - i - 1];
}
ans.push_back(nums[0]);
return ans;
}
};