杭电1027_Ignatius and the Princess II ——java

Problem Description

Now our hero finds the door to the BEelzebub feng5166. He opens the door and finds feng5166 is about to kill our pretty Princess. But now the BEelzebub has to beat our hero first. feng5166 says, "I have three question for you, if you can work them out, I will release the Princess, or you will be my dinner, too." Ignatius says confidently, "OK, at last, I will save the Princess."

"Now I will show you the first problem." feng5166 says, "Given a sequence of number 1 to N, we define that 1,2,3...N-1,N is the smallest sequence among all the sequence which can be composed with number 1 to N(each number can be and should be use only once in this problem). So it's easy to see the second smallest sequence is 1,2,3...N,N-1. Now I will give you two numbers, N and M. You should tell me the Mth smallest sequence which is composed with number 1 to N. It's easy, isn't is? Hahahahaha......"
Can you help Ignatius to solve this problem?

 

Input

The input contains several test cases. Each test case consists of two numbers, N and M(1<=N<=1000, 1<=M<=10000). You may assume that there is always a sequence satisfied the BEelzebub's demand. The input is terminated by the end of file.

 

Output

For each test case, you only have to output the sequence satisfied the BEelzebub's demand. When output a sequence, you should print a space between two numbers, but do not output any spaces after the last number.

 

Sample Input

6 4

11 8

 

Sample Output

1 2 3 5 6 4

1 2 3 4 5 6 7 9 8 11 10

题目的意思是数，N,M，1到N的第M个排列。

排列的算法：

对任意排列：A[0] A[1] A[2] ... A[i]... A[n]

假设 A[i - 1] < A[i]，且有A[i] >= A[i+1] >= A[i + 2] >= ... >= A[n - 1]

从A[i]到A[n - 1]中选取一个最小的数A[k]，A[k]满足条件：A[k] > A[i - 1]

则A[0] A[1] A[2] ... A[i]... A[n]的下一个排列为

A[0] A[1] A[2] ... A[k] A[n - 1] A[n - 2] ... A[k + 1] A[i - 1] A[k - 1] ... A[i]。

代码如下：

import java.util.*;

public class Main {

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        while (sc.hasNextInt()) {
            int n = sc.nextInt();//1 - n
            int m = sc.nextInt(); //全排列的第m次
            int[] a = new int[n+1];
            for(int i = 1;i<=n;i++){
                a[i] = i;
            }
            for(int i = 0;i < m-1;i++){
                fnc(a);

            }
            for(int j = 1;j<= n;j++){
                if(j != n)
                    System.out.print(a[j]+" ");
                else
                    System.out.println(a[j]);
            }

        }

    }
    public static void fnc(int[] a){
        for(int i = a.length - 1;i >= 2;i--){
            int right = a[i];
            int left = a[i-1];
            if(right > left){
                for(int j = a.length - 1; j >= i;j--){
                    if(a[j] > a[i-1]){
                        int temp = a[j];
                        a[j] = a[i-1];
                        a[i-1] = temp;
                        Arrays.sort(a,i,a.length);
                        return;
                    }
                }
            }
        }
    }
}