HDU 5916 Harmonic Value Description 【构造】(2016中国大学生程序设计竞赛(长春))
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Harmonic Value Description
Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/65536 K (Java/Others)
Total Submission(s): 3 Accepted Submission(s): 3
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].
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 ).
For each test case, there is only one line describing the given integers n and k (
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
24 14 2
Sample Output
Case #1: 4 1 3 2Case #2: 2 4 1 3
Source
2016中国大学生程序设计竞赛(长春)-重现赛
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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(Ai,Ai+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(Ai,Ai+1)为第1小。
若要∑gcd(Ai,Ai+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 104using 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);#endifint i,j,k;//init();//for(scanf("%d",&cass);cass;cass--)for(scanf("%d",&cas),cass=1;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-1;i;i--)printf(" %d",i);for(i=m+1;i<=n;i++)if(i!=m+m)printf(" %d",i);puts("");}return 0;}/*////*/
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