Permutation Sequence

最新推荐文章于 2018-12-26 13:42:41 发布

pkufergus

最新推荐文章于 2018-12-26 13:42:41 发布

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分类专栏： leetcode 文章标签： leetcode

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本文介绍了一种算法，用于找出数字集合 [1,2,3,...,n] 中第 k 个字典序排列。该算法使用回溯法递归地构建目标排列，并通过计算在每个位置上的选择来确定第 k 个排列的具体形式。

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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 k^th permutation sequence.

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

class Solution {
public:
	
	void backtrace(string &ans, vector<int> &flag, vector<int> fac, string &str, int s, int k, int n){
		
		if(s == n){
			ans = str;
			return;
		}
		s++;
		
		int x;
		x = (k - 1) / fac[n - s];
		int t = 0;
		int i;
		for(i = 0; i < n; i++){
			if(!flag[i]){
				if(t >= x){
					flag[i] = 1;
					break;
				}
				t++;
			}
		}
		if(i == n){
			return;
		}
		str += ((i + 1) + '0');
		k = k - x * fac[n - s];
		backtrace(ans, flag, fac, str, s, k, n);
		
	}
    string getPermutation(int n, int k) {
        // Start typing your C/C++ solution below
        // DO NOT write int main() function
        string ans;
		vector<int> fac(n, 1);
		fac[0] = 1;
		for(int i = 1; i<n; i++){
			fac[i] = fac[i - 1] * i;
		}
		vector<int> flag(n+1, 0);
		int index = 0;
		string str="";
		backtrace(ans, flag, fac, str, 0, k, n);
		return ans;
    }
};