HDU1027 Ignatius and the Princess II 【next_permutation】【DFS】

標籤：hdu1027

Ignatius and the Princess IITime Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others) Total Submission(s): 4571    Accepted Submission(s): 2733

Problem DescriptionNow 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?
 
InputThe 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.
 
OutputFor 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

6 411 8

 
Sample Output

1 2 3 5 6 41 2 3 4 5 6 7 9 8 11 10

 
AuthorIgnatius.L
題意：求數列1~n的第m個全排列。題解：用STL裡的next_permutation和DFS都可解，但時間複雜度就相去甚遠了。

STL:耗時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：耗時390ms

#include <stdio.h>#include <string.h>#define maxn 1002int 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;}

HDU1027 Ignatius and the Princess II 【next_permutation】【DFS】