The main idea of the topic ： Seek to use $C$ Two colors for the cube 8 The essence of vertex coloring is different . The essence of the two methods is different, that is, they can't make the two cubes have the same dyeing situation by rotating the cube .

A brief explanation of the problem ： First of all, we can get some results 24 It's a combined rotation . according to Polya Theorem and Lagrange theorem in group theory , Then think about it for yourself , You can get ：$Ans=\frac{x^8+Ax^4+Bx^2+Cx}{24}$, Do you know 3 An unknown number , And then the sample happens to have 3 Group data , So you can solve the equation and get $A=17,B=6,C=0$. Notice that the third data is modulus $10^{15}$ Subordinate , But obviously $112^4$ The fourth power of is not more than $10^{15}$, So it can also be used . In the end, high precision is enough .

#include <cstdio>
#include <cstring>
#include <algorithm>
using namespace std;
#define K 10
#define D 15 const int T[] = {, , , , };
int Case, n; struct Big
{
int len, num[];
Big () {len = ; memset(num, , sizeof(num));}
void init(int k)
{
len = ;
memset(num, , sizeof(num));
for (; k; k /= K)
num[++ len] = k % K;
len = max(len, );
}
{
len = max(len, a.len);
for (int i = ; i <= len; i ++)
num[i] += a.num[i];
for (int i = ; i < len; i ++)
if (num[i] >= K)
{
num[i + ] ++;
num[i] -= K;
}
if (num[len] >= K)
{
num[len + ] = ;
num[len ++] -= K;
}
}
void Times(Big a)
{
Big b;
b.len = len + a.len - ;
for (int i = ; i <= len; i ++)
for (int j = ; j <= a.len; j ++)
b.num[i + j - ] += num[i] * a.num[j];
for (int i = ; i < b.len; i ++)
if (b.num[i] >= K)
{
b.num[i + ] += b.num[i] / K;
b.num[i] %= K;
}
while (b.num[b.len] >= K)
{
b.num[b.len + ] += b.num[b.len] / K;
b.num[b.len ++] %= K;
}
len = b.len;
for (int i = ; i <= len; i ++)
num[i] = b.num[i];
}
void Multi(int k)
{
for (int i = ; i <= len; i ++)
num[i] *= k;
for (int i = ; i < len; i ++)
if (num[i] >= K)
{
num[i + ] += num[i] / K;
num[i] %= K;
}
while (num[len] >= K)
{
num[len + ] += num[len] / K;
num[len ++] %= K;
}
}
void Divide(int k)
{
for (int i = len; i >= ; i --)
{
if (i > ) num[i - ] += (num[i] % k) * K;
num[i] /= k;
}
for (; !num[len] && len > ; len --) ;
}
void out()
{
for (int i = min(D, len); i; i --)
printf("%d", num[i]);
puts("");
}
}A[], Ans; int main()
{
scanf("%d", &Case);
for (int Test = ; Test <= Case; Test ++)
{
scanf("%d", &n);
A[].init(n), Ans.init();
for (int i = ; i <= ; i ++)
{
A[i] = A[i - ];
A[i].Times(A[i - ]);
A[i].Multi(T[i]);
A[i].Divide(T[i]);
}
Ans.Divide();
printf("Case %d: ", Test);
Ans.out();
}
return ;
}

HDOJ 3547

#include <cstdio>
typedef long long LL;
#define Mod 10000000000000000LL const int Base[] = {, , , };
const LL Ans[] = {0LL, 23LL, 296LL, 2675058176LL}; struct Frac
{
LL fz, fm;
Frac (LL _fz = 0LL, LL _fm = 0LL) {fz = _fz, fm = _fm;}
LL Abs(LL x)
{
return x > ? x : -x;
}
LL gcd(LL x, LL y)
{
return !y ? x : gcd(y, x % y);
}
void Simplify()
{
LL d = gcd(Abs(fz), Abs(fm));
fz /= d, fm /= d;
if (fm < ) fm = -fm, fz = -fz;
}
Frac operator + (const Frac a)
{
Frac b;
b.fz = fz * a.fm + fm * a.fz;
b.fm = fm * a.fm;
b.Simplify();
return b;
}
Frac operator - (const Frac a)
{
Frac b;
b.fz = fz * a.fm - fm * a.fz;
b.fm = fm * a.fm;
b.Simplify();
return b;
}
Frac operator * (const Frac a)
{
Frac b;
b.fz = fz * a.fz;
b.fm = fm * a.fm;
b.Simplify();
return b;
}
Frac operator / (const Frac a)
{
Frac b;
b.fz = fz * a.fm;
b.fm = fm * a.fz;
b.Simplify();
return b;
}
void out()
{
printf("%lld/%lld\n", fz, fm);
}
}X[][], Y[]; inline void Gauss()
{
for (int i = ; i < ; i ++)
for (int j = i + ; j <= ; j ++)
{
Frac t = X[j][i] / X[i][i];
for (int k = i; k <= ; k ++)
X[j][k] = X[j][k] - X[i][k] * t;
Y[j] = Y[j] - Y[i] * t;
}
for (int i = ; i; i --)
{
Frac sum;
sum.fz = 0LL, sum.fm = 1LL;
for (int j = i + ; j <= ; j ++)
sum = sum + X[i][j] * Y[j];
Y[i] = (Y[i] - sum) / X[i][i];
}
} int main()
{
for (int i = ; i <= ; i ++)
{
for (int j = ; j; j --)
{
if (j == ) X[i][j].fz = Base[i];
else X[i][j].fz = X[i][j + ].fz * X[i][j + ].fz;
X[i][j].fm = 1LL;
}
Y[i].fz = Ans[i], Y[i].fm = 1LL;
}
Gauss();
for (int i = ; i <= ; i ++)
Y[i].out();
return ;
}

HDOJ 3547 (Gauss)

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