Ignatius and the Princess II
Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 4571 Accepted Submission(s): 2733
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?
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.
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
Author
Ignatius.L
题意：求数列1~n的第m个全排列。
题解：用STL里的next_permutation和DFS都可解，但时间复杂度就相去甚远了。
STL:耗时31ms
#include <cstdio>
#include <algorithm>
using namespace std; int arr[1002]; int main()
{
int n, m, i;
while(scanf("%d%d", &n, &m) != EOF){
for(i = 0; i < n; ++i)
arr[i] = i + 1;
while(--m) next_permutation(arr, arr + n);
for(i = 0; i < n; ++i)
if(i != n - 1) printf("%d ", arr[i]);
else printf("%d\n", arr[i]);
}
return 0;
}
DFS：耗时390ms
#include <stdio.h>
#include <string.h>
#define maxn 1002 int vis[maxn], n, m, arr[maxn], count, ok; void PRINT()
{
for(int i = 1; i <= n; ++i)
if(i != n) printf("%d ", arr[i]);
else printf("%d\n", arr[i]);
} void DFS(int k)
{
if(k > n) return;
for(int i = 1; i <= n; ++i){
if(!vis[i]){
vis[i] = 1; arr[k] = i;
if(k == n && m == ++count){
PRINT(); ok = 1; return;
}
DFS(k + 1); vis[i] = 0;
if(ok) return;
}
}
} int main()
{
while(scanf("%d%d", &n, &m) != EOF){
memset(vis, 0, sizeof(vis));
ok = count = 0; DFS(1);
}
return 0;
}