HDU 6628 permutation 1 (暴力)

2019 杭电多校 5 1005

题目链接：HDU 6628

比赛链接：2019 Multi-University Training Contest 5

Problem Description

A sequence of length \(n\) is called a permutation if and only if it's composed of the first \(n\) positive integers and each number appears exactly once.

Here we define the "difference sequence" of a permutation \(p_1, p_2,...,p_n\) as \(p_2−p_1,p_3−p_2,...,p_n−p_{n−1}\). In other words, the length of the difference sequence is \(n−1\) and the \(i\)-th term is \(p_{i+1}−p_i\)

Now, you are given two integers \(N,K\). Please find the permutation with length \(N\) such that the difference sequence of which is the \(K\)-th lexicographically smallest among all difference sequences of all permutations of length \(N\).

Input

The first line contains one integer \(T\) indicating that there are \(T\) tests.

Each test consists of two integers \(N,K\) in a single line.

\(*\ 1≤T≤40\)

\(*\ 2≤N≤20\)

\(*\ 1\le K\le min(10^4, N!)\)

Output

For each test, please output \(N\) integers in a single line. Those \(N\) integers represent a permutation of \(1\) to \(N\), and its difference sequence is the \(K\)-th lexicographically smallest.

Sample Input

7
3 1
3 2
3 3
3 4
3 5
3 6
20 10000

Sample Output

3 1 2
3 2 1
2 1 3
2 3 1
1 2 3
1 3 2
20 1 2 3 4 5 6 7 8 9 10 11 13 19 18 14 16 15 17 12

Solution

题意：

定义排列 \(p_1, p_2, ... , p_n\) 的 "difference sequence" 为 \(p_2-p_1, p_3-p_2,...,p_n-p_{n-1}\)。现在给定 \(N\) 和 \(K\)，求长度为 \(N\) 的所有排列中 "difference sequence" 的字典序第 \(K\) 小的排列。

题解：

暴力 STL 全排列

题目给定 \(K\) 的范围不超过 \(10^4\)，而 \(8! = 40320 > K\)，因此可以预处理 \(N <= 8\) 的情况，当 \(N > 8\) 时暴力求 \(a[1] = n\) 的全排列。

Code

#include <bits/stdc++.h>
using namespace std;

const int maxn = 1e5 + 10;

struct P {
    int num[10];
    string str;
} ans[10][maxn];

int cmp(P p1, P p2) {
    return p1.str < p2.str;
}

int main() {
    int a[10] = {0, 1, 2, 3, 4, 5, 6, 7, 8};
    for(int i = 2; i <= 8; ++i) {
        int cnt = 1;
        do {
            // for(int j = 0; j < i; ++j) {
            //     cout << a[j] << " ";
            // }
            // cout << endl;
            for(int j = 1; j <= i; ++j) {
                ans[i][cnt].num[j] = a[j];
                if(j < i) ans[i][cnt].str += a[j + 1] - a[j] + 'A';
            }
            ++cnt;
        } while(next_permutation(a + 1, a + 1 + i));
        sort(ans[i] + 1, ans[i] + cnt, cmp);
        // for(int j = 1; j < cnt; ++j) { for(int k = 1; k <= i; ++k) cout << ans[i][j].num[k] << ""; cout << endl;}
    }
    int T;
    cin >> T;
    while(T--) {
        int n, k;
        scanf("%d%d", &n, &k);
        if(n <= 8) {
            for(int j = 1; j <= n; ++j) {
                printf("%d", ans[n][k].num[j]);
                printf("%s", j == n? "\n": " ");
            }
        } else {
            int a[30];
            a[1] = n;
            for(int i = 2; i <= n; ++i) {
                a[i] = i - 1;
            }
            for(int i = 0; i < k - 1; ++i) {
                next_permutation(a + 1, a + 1 + n);
            }
            for(int i = 1; i <= n; ++i) {
                printf("%d", a[i]);
                printf("%s", i == n? "\n": " ");
            }
        }
    }
    return 0;
}