按位求和问题

 1 #include<bits/stdc++.h>
 2 using namespace std;
 3 typedef long long ll;
 4 
 5 ll getsum1(ll n,int k){
 6     ll b=1;
 7     for(int i=0;i<n;i++)b*=k;
 8     return b*n*(k-1)/2;
 9 }
10 
11 ll getsum(ll pre,ll n,int k){
12     ll b=getsum1(n,k);
13     ll c=pre;
14     for(int i=0;i<n;i++)
15         c*=k;
16     return b+c;
17 }
18 
19 ll solve(ll pre,ll n,int k){
20     //n<k
21     if(n<k){
22         ll ret=0;
23         for(int i=0;i<=n;i++)ret+=pre+i;
24         return ret;
25     }
26     ll tn=n,t=1,tot=0;
27     while(tn>=k){
28         tot++;
29         t*=k;
30         tn/=k;
31     }
32     ll ret=0;
33     for(int i=0;i<tn;i++)
34         ret+=getsum(pre+i,tot,k);
35     ret+=solve(pre+tn,n-t*tn,k);
36     return ret;
37 }
38 
39 ll judge(ll n,int k){
40     ll ret=0;
41     for(int i=1;i<=n;i++){
42         ll tn=i;
43         while(tn>0){
44             ret+=tn%k;
45             tn/=k;
46         }
47     }
48     return ret;
49 }
50 
51 int main(){
52     cout<<judge(1000,7)<<endl;
53     cout<<solve(0,1000,7)<<endl;
54  return 0;
55 }