HDU 5916 Harmonic Value Description 【构造】(2016中国大学生程序设计竞赛(长春))

2022-04-14 13:33:04

Harmonic Value Description

Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/65536 K (Java/Others)
Total Submission(s): 0 Accepted Submission(s): 0
Special Judge

Problem Description

The harmonic value of the permutation p1,p2,⋯pn is
∑i=1n−1gcd(pi.pi+1)

Mr. Frog is wondering about the permutation whose harmonic value is the strictly k-th smallest among all the permutations of [n].

Input

The first line contains only one integer T (1≤T≤100), which indicates the number of test cases.
For each test case, there is only one line describing the given integers n and k (1≤2k≤n≤10000).

Output

For each test case, output one line “Case #x: p1 p2 ⋯ pn”, where x is the case number (starting from 1) and p1 p2 ⋯ pn is the answer.

Sample Input

2
4 1
4 2

Sample Output

Case #1: 4 1 3 2
Case #2: 2 4 1 3

Statistic | Submit | Clarifications | Back

题目链接：

　　http://acm.hdu.edu.cn/showproblem.php?pid=5916

题目大意：

　　给你N和K（1<=K<2K<=2N），求一个1~2N的排列，使得∑gcd(A_i,A_i+1)恰为第K小（等视为相同小）。

题目思路：

　　【构造】

　　这题一看2K<=2N，可能就是构造题。如果1,2,3...2N排列的话∑gcd(A_i,A_i+1)为第1小。

　　若要∑gcd(A_i,A_i+1)=K，只需要将2K和K提出来，将2K放在开头，K放在第二个，接下来只要满足相邻两个数仍然相差1即可。

　　只要将K-1~1接在K后面，把K+1~2N接在1后面，去掉2K即可。（2K-1，2K+1为奇数，gcd=1）

 //

 //by coolxxx

 //#include<bits/stdc++.h>

 #include<iostream>

 #include<algorithm>

 #include<string>

 #include<iomanip>

 #include<map>

 #include<stack>

 #include<queue>

 #include<set>

 #include<bitset>

 #include<memory.h>

 #include<time.h>

 #include<stdio.h>

 #include<stdlib.h>

 #include<string.h>

 //#include<stdbool.h>

 #include<math.h>

 #define min(a,b) ((a)<(b)?(a):(b))

 #define max(a,b) ((a)>(b)?(a):(b))

 #define abs(a) ((a)>0?(a):(-(a)))

 #define lowbit(a) (a&(-a))

 #define sqr(a) ((a)*(a))

 #define swap(a,b) ((a)^=(b),(b)^=(a),(a)^=(b))

 #define mem(a,b) memset(a,b,sizeof(a))

 #define eps (1e-10)

 #define J 10000

 #define mod 1000000007

 #define MAX 0x7f7f7f7f

 #define PI 3.14159265358979323

 #pragma comment(linker,"/STACK:1024000000,1024000000")

 #define N 104

 using namespace std;

 typedef long long LL;

 double anss;

 LL aans,sum;

 int cas,cass;

 int n,m,lll,ans;

 int main()

 {

     #ifndef ONLINE_JUDGEW

 //    freopen("1.txt","r",stdin);

 //    freopen("2.txt","w",stdout);

     #endif

     int i,j,k;

 //    init();

 //    for(scanf("%d",&cass);cass;cass--)

     for(scanf("%d",&cas),cass=;cass<=cas;cass++)

 //    while(~scanf("%s",s))

 //    while(~scanf("%d",&n))

     {

         scanf("%d%d",&n,&m);

         printf("Case #%d: ",cass);

         printf("%d %d",m+m,m);

         for(i=m-;i;i--)printf(" %d",i);

         for(i=m+;i<=n;i++)

             if(i!=m+m)printf(" %d",i);

         puts("");

     }

     return ;

 }

 /*

 //

 //

 */

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Harmonic Value Description

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