CCPC[长春] 6.Harmonic Value Description 规律+贪心
2016-10-04 17:27
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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
.
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
经过总结规律,4个数的harmonic value为3 4....
5个的为 4 5 ....
6个的为5 6....
7个的为6 7 .....
8个的为7 8 ....
........
n个的为n-1 n ....
所以第k小的数的harmonic value为n-2+k
然后再利用贪心算法,把后面的数的位置放到适当位置,
使其harmonic value的值为n-2+k
具体分析看代码:
#include <iostream> #include <cstdio> #include <cstdlib> #include <cmath> #include <algorithm> #include <climits> #include <cstring> #include <string> #include <set> #include <map> #include <queue> #include <stack> #include <vector> #include <list> #define rep(i,m,n) for(i=m;i<=n;i++) #define rsp(it,s) for(set<int>::iterator it=s.begin();it!=s.end();it++) const int inf_int = 2e9; const long long inf_ll = 2e18; #define inf_add 0x3f3f3f3f #define mod 1000000007 #define vi vector<int> #define pb push_back #define mp make_pair #define fi first #define se second #define PI acos(-1.0) #define pii pair<int,int> #define Lson L, mid, rt<<1 #define Rson mid+1, R, rt<<1|1 const int maxn=5e2+10; using namespace std; typedef long long ll; typedef unsigned long long ull; inline int read(){int ra,fh;char rx;rx=getchar(),ra=0,fh=1; while((rx<'0'||rx>'9')&&rx!='-')rx=getchar();if(rx=='-') fh=-1,rx=getchar();while(rx>='0'&&rx<='9')ra*=10,ra+=rx-48, rx=getchar();return ra*fh;} //#pragma comment(linker, "/STACK:102400000,102400000") ll gcd(ll p,ll q){return q==0?p:gcd(q,p%q);} ll qpow(ll p,ll q){ll f=1;while(q){if(q&1)f=f*p;p=p*p;q>>=1;}return f;} int dir[4][2]={{1,0},{-1,0},{0,1},{0,-1}}; int T,n; int a[10005]; int m,m1; int main() { scanf("%d",&T); for(int k=1;k<=T;k++) { memset(a,0,sizeof(a)); scanf("%d %d",&n,&m); for(int i=1;i<=n;i++) a[i]=i; m--; if(m%2==1) { for(int j=(m+1)*2;j>m+2;j--)//前移一个数 a[j]=a[j-1]; a[m+2]=(m+1)*2; } else { for(int j=m*2;j>m+1;j--)//前移一个数 a[j]=a[j-1]; a[m+1]=m*2; if(n%2==0)//交换 { int t; t = a ; a =a[n-1]; a[n-1]=t; } else { int t; t = a[n-3]; a[n-3]=a[n-2]; a[n-2]=t; } } printf("Case #%d:",k); for(int i=1;i<=n;i++) printf(" %d",a[i]); printf("\n"); } return 0; }
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