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QOJ
ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#322872 | #6549. Two Missing Numbers | hotboy2703 | 0 | 67ms | 4716kb | C++14 | 3.7kb | 2024-02-07 21:41:28 | 2024-02-07 21:41:28 |
Judging History
answer
#include<bits/stdc++.h>
using namespace std;
using ll = long long;
using ull = unsigned long long;
#define pll pair <ll,ll>
#define fi first
#define se second
#define sz(a) (ll((a).size()))
#define MASK(i) (1LL<<(i))
#define BIT(mask,i) (((mask) >> (i))&1LL)
namespace nimber{
//inspired by adamant && https://natsugiri.hatenablog.com/entry/2020/03/29/073605
bool log_computed = 0;
const ull small = MASK(16);
ull pw[small],lg[small];
ull mul(ull a,ull b,ull half = 32){
if (a <= 1 || b <= 1)return a*b;
if (log_computed && a < small && b < small){
ull t = lg[a] + lg[b];
if (t >= small-1){
t-=small-1;
}
return pw[t];
}
ull mask = MASK(half)-1;
//P = MASK(half);
ull a0 = a & mask,a1 = a >> half;
ull b0 = b & mask,b1 = b >> half;
//a * b = (a1 * P + a0) * (b1 * P + b0) = a0 * b0 + P * (a1 * b0 + a0 * b1) + P * P * (a1 * b1)
ull A = mul(a0,b0,half/2);
ull C = mul(a1,b1,half/2);
ull B = mul(a0^a1,b0^b1,half/2) ^ A ^ C; // a1*b0+a0*b1 = (a0+a1) * (b0+b1) - A - C
B = (B<<half);
C = (C<<half) ^ mul(C,MASK(half-1),half/2);
return A^B^C;
}
bool init(){
const ull base = 696;//some base does not work(cycle issue) but 696 does work heeheeheehaw
pw[0] = 1;
lg[1] = 0;
for (ull i = 1;i < small-1;i ++){
pw[i] = mul(pw[i-1],base);
lg[pw[i]] = i;
}
log_computed = 1;
return 1;
}
bool pre_computed = init();
struct nim{
ull v;
nim(ull x=0):v(x){}
nim operator * (nim u){return mul(v,u.v);}
nim operator + (nim u){return v^u.v;}
nim pw(ull y){
nim res = 1;
for (nim x = *this;y;y>>=1,x=x*x){
if (y&1)res = res*x;
}
return res;
}
nim inv(){return pw(-2ULL);}
nim sqrt(){return pw(MASK(63));}
};
//find nimber x satisfies: x*x + x + c = 0;
ull little_quadratic(ull c,ll half = 4){
//x*x+x=c
if (half == 0){
return 0;
}
//x1 * P + x0 = x
//(x1^2+x1) * P + (x0 ^ 2 + x0 + P/2 * x1 * x1) = c1 * P + c0
ull mask = MASK(half) - 1;
ull c0 = c & mask,c1 = c >> half;
ull x1 = little_quadratic(c1,half/2);
if ((mul(mul(x1,x1,half/2),MASK(half-1),half/2) ^ c0) >= ull(MASK(half-1)))x1 ^= 1;
ull x0 = little_quadratic(mul(mul(x1,x1,half/2),MASK(half-1),half/2) ^ c0,half/2);
ull res = (x1<<half)^x0;
// cout<<c<<' '<<half <<' '<<x0<<' '<<x1<<' '<<res<<'\n';
return res;
}
nim little_quadratic(nim c){
return little_quadratic(c.v);
}
//find nimber z satisfies: z*z + bz + d = 0;
nim full_quadratic(nim b,nim d){
if (b.v==0)return d.sqrt();
else{
//z = bx, b^2*x^2+b^2*x+d=0 <=> x^2 + x + c = 0 (c = d/b^2)
// cout<<d.v<<' '<<b.v<<' '<<(b*b).inv().v<<' '<<(d*((b*b).inv())).v<<'\n';
return little_quadratic(d*((b*b).inv()))*b;
}
}
}
int main(){
ios_base::sync_with_stdio(0);cin.tie(nullptr);cout.tie(nullptr);
using namespace nimber;
ll q,n;
cin>>q>>n;
nim a1,a3;
if (q==2)cin>>a1.v>>a3.v;
for (ll i = 1;i <= n;i ++){
nim x;
cin>>x.v;
a1 = a1+x;
a3 = a3+x*x*x;
// cout<<(x*x*x).v<<'\n';
}
if (q==1){
cout<<a1.v<<' '<<a3.v<<'\n';
}
else{
nim ab = a3*a1.inv()+a1*a1;
nim a = full_quadratic(a1,ab);
nim b = a1 + a;
cout<<a.v<<' '<<b.v<<'\n';
}
return 0;
}
Details
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Test #1:
score: 100
Accepted
time: 63ms
memory: 4696kb
First Run Input
1 5 5 1 4 4 5
First Run Output
1 1
Second Run Input
2 3 1 1 9 9 3
Second Run Output
3 1
result:
ok correct
Test #2:
score: 100
Accepted
time: 67ms
memory: 4692kb
First Run Input
1 1 0
First Run Output
0 0
Second Run Input
2 1 0 0 1
Second Run Output
0 1
result:
ok correct
Test #3:
score: 0
Wrong Answer
time: 67ms
memory: 4716kb
First Run Input
1 1 10625130587464985929
First Run Output
10625130587464985929 1640162740173739743
Second Run Input
2 1 10625130587464985929 1640162740173739743 1167154569617655189
Second Run Output
3563327085256105960 12841416232829974324
result:
wrong answer incorrect, read 3563327085256105960 12841416232829974324 but expected 1167154569617655189 10625130587464985929