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QOJ
ID | 题目 | 提交者 | 结果 | 用时 | 内存 | 语言 | 文件大小 | 提交时间 | 测评时间 |
---|---|---|---|---|---|---|---|---|---|
#565917 | #8095. Lati@s | cocoa_chan | WA | 6ms | 10300kb | C++14 | 6.3kb | 2024-09-15 22:37:23 | 2024-09-15 22:37:23 |
Judging History
answer
#include<bits/stdc++.h>
using namespace std;
typedef unsigned long long int ll;
namespace nim {
using u16 = unsigned short;
using u32 = unsigned;
using u64 = unsigned long long;
// G16: primitive root in F_(2^16)
// G16\^3 = 2^15
constexpr u16 G16 = 10279U;
u16 expBuffer[4 * (1 << 16) + 4];
u16 *exp = expBuffer + (2 * (1 << 16) + 4), *exp3 = exp + 3, *exp6 = exp + 6;
int log[1 << 16];
u64 tabSq[4][1 << 16], tabSqrt[4][1 << 16], tabSolveQuad1[4][1 << 16];
// L: power of 2
// (a0 + 2^l a1) \* (b0 + 2^l b1)
// = (a0\*b0 \+ 2^(l-1)\*a1\*b1) + 2^l (a0\*b1 \+ a1\*b0 \+ a1\*b1)
template <int L> inline u64 mulSlow(u64 a, u64 b) {
static constexpr int l = L >> 1;
const u64 a0 = a & ((1ULL << l) - 1), a1 = a >> l;
const u64 b0 = b & ((1ULL << l) - 1), b1 = b >> l;
const u64 a0b0 = mulSlow<l>(a0, b0);
return (a0b0 ^ mulSlow<l>(1ULL << (l - 1), mulSlow<l>(a1, b1)))
| (a0b0 ^ mulSlow<l>(a0 ^ a1, b0 ^ b1)) << l;
}
template <> inline u64 mulSlow<1>(u64 a, u64 b) {
return a & b;
}
// 2^31 \* a
inline u32 mul31(u32 a) {
const u16 a0 = a, a1 = a >> 16;
const u16 a01 = a0 ^ a1;
return exp6[log[a1]] | (u32)exp3[log[a01]] << 16;
}
inline u16 mul(u16 a, u16 b) {
return exp[log[a] + log[b]];
}
inline u32 mul(u32 a, u32 b) {
const u16 a0 = a, a1 = a >> 16;
const u16 b0 = b, b1 = b >> 16;
const u16 a01 = a0 ^ a1;
const u16 b01 = b0 ^ b1;
const u16 a0b0 = mul(a0, b0);
return (a0b0 ^ exp3[log[a1] + log[b1]]) | (u32)(a0b0 ^ mul(a01, b01)) << 16;
}
inline u64 mul(u64 a, u64 b) {
const u32 a0 = a, a1 = a >> 32;
const u32 b0 = b, b1 = b >> 32;
const u32 a01 = a0 ^ a1;
const u32 b01 = b0 ^ b1;
const u32 a0b0 = mul(a0, b0);
return (a0b0 ^ mul31(mul(a1, b1))) | (u64)(a0b0 ^ mul(a01, b01)) << 32;
}
inline u16 sq(u16 a) {
return tabSq[0][a];
}
inline u32 sq(u32 a) {
const u16 a0 = a, a1 = a >> 16;
return tabSq[0][a0] ^ tabSq[1][a1];
}
inline u64 sq(u64 a) {
const u16 a0 = a, a1 = a >> 16, a2 = a >> 32, a3 = a >> 48;
return tabSq[0][a0] ^ tabSq[1][a1] ^ tabSq[2][a2] ^ tabSq[3][a3];
}
inline u16 sqrt(u16 a) {
return tabSqrt[0][a];
}
inline u32 sqrt(u32 a) {
const u16 a0 = a, a1 = a >> 16;
return tabSqrt[0][a0] ^ tabSqrt[1][a1];
}
inline u64 sqrt(u64 a) {
const u16 a0 = a, a1 = a >> 16, a2 = a >> 32, a3 = a >> 48;
return tabSqrt[0][a0] ^ tabSqrt[1][a1] ^ tabSqrt[2][a2] ^ tabSqrt[3][a3];
}
// (a0 + 2^l a1) \* (b0 + 2^l b1) = 1
// <=> [ a0 2^(l-1)\*a1 ] \* [ b0 ] = [ 1 ]
// [ a1 a0\+a1 ] [ b1 ] [ 0 ]
inline u16 inv(u16 a) {
assert(a);
return exp[((1 << 16) - 1) - log[a]];
}
inline u32 inv(u32 a) {
assert(a);
const u16 a0 = a, a1 = a >> 16;
const u16 a01 = a0 ^ a1;
const u16 d = inv((u16)(mul(a0, a01) ^ exp3[log[a1] + log[a1]]));
return mul(d, a01) | (u32)mul(d, a1) << 16;
}
inline u64 inv(u64 a) {
assert(a);
const u32 a0 = a, a1 = a >> 32;
const u32 a01 = a0 ^ a1;
const u32 d = inv(mul(a0, a01) ^ mul31(sq(a1)));
return mul(d, a01) | (u64)mul(d, a1) << 32;
}
// f(x) := x\^2 \+ x
// bsr(x\^2) = bsr(x)
// f: {even in [0, 2^L)} -> [0, 2^(L-1)): linear isom.
// f(x0 + 2^l x1) = (f(x0) \+ 2^(l-1)\*x1\^2) + 2^l f(x1)
template <int L> inline u64 solveQuad1Slow(u64 a) {
static constexpr int l = L >> 1;
assert(!(a >> (L - 1)));
const u64 a0 = a & ((1ULL << l) - 1), a1 = a >> l;
const u64 x1 = solveQuad1Slow<l>(a1);
const u64 b0 = a0 ^ mul(1ULL << (l - 1), sq(x1));
const u64 s = b0 >> (l - 1);
return solveQuad1Slow<l>(b0 ^ s << (l - 1)) | (x1 ^ s) << l;
}
template <> inline u64 solveQuad1Slow<1>(u64 a) {
assert(!a);
return 0;
}
// x\^2 \+ x \+ a = 0
// solutions: x, x \+ 1
inline u64 solveQuad1(u64 a) {
assert(!(a >> 63));
const u16 a0 = a, a1 = a >> 16, a2 = a >> 32, a3 = a >> 48;
return tabSolveQuad1[0][a0] ^ tabSolveQuad1[1][a1] ^ tabSolveQuad1[2][a2] ^ tabSolveQuad1[3][a3];
}
// x\^2 \+ a\*x \+ b = 0
// solutions: x, x \+ a
inline bool isSolvableQuad(u64 a, u64 b) {
return !(mul(inv(sq(a)), b) >> 63);
}
inline u64 solveQuad(u64 a, u64 b) {
return a ? mul(a, solveQuad1(mul(inv(sq(a)), b))) : sqrt(b);
}
struct Preparator {
Preparator() {
exp[0] = 1;
for (int i = 1; i < (1 << 16) - 1; ++i) exp[i] = mulSlow<16>(exp[i - 1], G16);
for (int i = (1 << 16) - 1; i < 2 * (1 << 16); ++i) exp[i] = exp[i - ((1 << 16) - 1)];
for (int i = 0; i < (1 << 16) - 1; ++i) log[exp[i]] = i;
log[0] = -(1 << 16) - 2;
for (int e = 0; e < 64; ++e) {
const u64 x = mul(1ULL << e, 1ULL << e);
for (int i = 0; i < 1 << (e & 15); ++i) tabSq[e >> 4][i | 1 << (e & 15)] = tabSq[e >> 4][i] ^ x;
}
for (int e = 0; e < 64; ++e) {
u64 x = 1ULL << e;
for (int j = 0; j < 63; ++j) x = sq(x);
for (int i = 0; i < 1 << (e & 15); ++i) tabSqrt[e >> 4][i | 1 << (e & 15)] = tabSqrt[e >> 4][i] ^ x;
}
for (int e = 0; e < 63; ++e) {
const u64 x = solveQuad1Slow<64>(1ULL << e);
for (int i = 0; i < 1 << (e & 15); ++i) tabSolveQuad1[e >> 4][i | 1 << (e & 15)] = tabSolveQuad1[e >> 4][i] ^ x;
}
}
} preparator;
} // namespace nim
ll n,m,i,j,k,l,r,x,y,z,w,s,t;
vector<vector<nim::u64>> a;
ll determinant()
{
ll i,j,k,x;
for(i=1;i<=n;i++)
{
x=-1;
for(j=i;j<=n;j++)
{
if(a[j][i]!=0)
{
x=j;
break;
}
}
if(x==-1)
return 0;
// printf("(%lld,%lld)\n",x,a[x][i]);
for(j=1;j<=n;j++)
{
swap(a[i][j],a[x][j]);
}
// printf("(%lld:%lld)\n",i,a[i][i]);
for(j=1;j<=n;j++)
{
if(j==i)
continue;
nim::u64 z=nim::mul(nim::inv(a[i][i]),a[j][i]);
for(k=1;k<=n;k++)
{
a[j][k]=a[j][k]^nim::mul(z,a[i][k]);
}
}
}
return 1;
}
int main()
{
scanf("%ulld",&n);
a.resize(n+1);
for(i=1;i<=n;i++)
a[i].resize(n+1);
for(i=1;i<=n;i++)
{
for(j=1;j<=n;j++)
{
scanf("%ulld",&x);
a[i][j]=x;
}
}
//printf("?");
if(determinant()!=0)
{
printf("First");
}
else
printf("Second");
}
详细
Test #1:
score: 100
Accepted
time: 5ms
memory: 10264kb
input:
3 0 1 2 1 2 3 1 2 1
output:
First
result:
ok Correct!
Test #2:
score: 0
Accepted
time: 3ms
memory: 10268kb
input:
2 1 2 2 3
output:
Second
result:
ok Correct!
Test #3:
score: 0
Accepted
time: 6ms
memory: 10224kb
input:
1 1
output:
First
result:
ok Correct!
Test #4:
score: 0
Accepted
time: 5ms
memory: 10268kb
input:
1 0
output:
Second
result:
ok Correct!
Test #5:
score: 0
Accepted
time: 2ms
memory: 10300kb
input:
1 10989383527054532353
output:
First
result:
ok Correct!
Test #6:
score: 0
Accepted
time: 5ms
memory: 10268kb
input:
2 1005615900205140029 1751816340545810590 9799519860537995223 8238669462598964242
output:
First
result:
ok Correct!
Test #7:
score: -100
Wrong Answer
time: 6ms
memory: 10208kb
input:
2 14541323676997420853 9863599201339623558 7531150024641852914 12902197593218027764
output:
First
result:
wrong answer Wrong answer!