Leetcode 60.Permutation Sequence (permutation sequence) thinking and method of solving problems

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):

2. "123"
4. "132"
6. "213"
8. "231"
10. "312"
12. "321"

Given n and K, return the kth permutation sequence.

Note: Given N would be between 1 and 9 inclusive.

Idea: This problem is still relatively difficult, violence is to find dead, time-out did not gave. But the method of mathematical induction is not everyone can think, read a lot of information, also just understand some ideas.

Law: Known n values, learned permutations and combinations know a common n! Species arrangement.
The first sequence with each number starts with (N-1)! sequence, so n numbers so there's a n! A sequence.
And so on, the second digit starts with every number (N-2)! A sequence.

The specific code is as follows:

public class Solution {    String str = "";    Public String getpermutation (int n, int k) {    int[] num = new Int[n];        int[] data = new int[n];//the dataset of the factorial,        int i = 0;        for (; i < n; i++) {        num[i] = i+1;        if (i = = 0)        data[i] = 1;        else{        Data[i] = data[i-1]*i;        }        }        k--;        while (---->-1) {//loop get the numbers        int k1 = k/data[i];        int p = k1+ (n-1-i);//Digital position        swap (n-1-i,p,num);        if (k = k%data[i]) = = 0)//k==0 end break        ;        }        for (int x:num)//Get str        str + = x;        return str;    }    Insert the data, followed by the public    Void swap (int i,int j,int[] num)    {    int m = num[j];        for (int k=j;k>i;k--)        num[k]=num[k-1];        num[i]=m;}    }

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Leetcode 60.Permutation Sequence (permutation sequence) thinking and method of solving problems