POJ - 3233 矩阵套矩阵

题意:给你矩阵\(A\),求\(S=\sum_{i=1}^{k}A^i\)

构造矩阵

\[\begin{bmatrix}
A & E \\ 0 & E\\
\end{bmatrix}
\]

很酷炫的矩阵套矩阵,学习了

PS.更通用的解法是二分求等比

#include<iostream>

#include<algorithm>

#include<cstdio>

#include<cstring>

#include<cstdlib>

#include<cmath>

#include<string>

#include<vector>

#include<stack>

#include<queue>

#include<set>

#include<map>

#define rep(i,j,k) for(register int i=j;i<=k;i++)

#define rrep(i,j,k) for(register int i=j;i>=k;i--)

#define erep(i,u) for(register int i=head[u];~i;i=nxt[i])

#define iin(a) scanf("%d",&a)

#define lin(a) scanf("%lld",&a)

#define din(a) scanf("%lf",&a)

#define s0(a) scanf("%s",a)

#define s1(a) scanf("%s",a+1)

#define print(a) printf("%lld",(ll)a)

#define enter putchar('\n')

#define blank putchar(' ')

#define println(a) printf("%lld\n",(ll)a)

#define IOS ios::sync_with_stdio(0)

using namespace std;

const int maxn = 1e6+11;

const int oo = 0x3f3f3f3f;

const double eps = 1e-7;

typedef long long ll;

ll read(){

    ll x=0,f=1;register char ch=getchar();

    while(ch<'0'||ch>'9'){if(ch=='-')f=-1;ch=getchar();}

    while(ch>='0'&&ch<='9'){x=x*10+ch-'0';ch=getchar();}

    return x*f;

}

ll MOD;

inline ll mod(ll a){return a%MOD;}

struct Matrix{

    ll mt[77][77],r,c;

    void init(int rr,int cc,bool flag=0){

        r=rr;c=cc;

        memset(mt,0,sizeof mt);

        if(flag) rep(i,1,r) mt[i][i]=1;

    }

    Matrix operator * (const Matrix &rhs)const{

        Matrix ans; ans.init(r,rhs.c);

        rep(i,1,r){

            rep(j,1,rhs.c){

                int t=max(r,rhs.c);

                rep(k,1,t){

                    ans.mt[i][j]+=mod(mt[i][k]*rhs.mt[k][j]);

                    ans.mt[i][j]=mod(ans.mt[i][j]);

                }

            }

        }

        return ans;

    }

};

Matrix fpw(Matrix A,ll n){

    Matrix ans;ans.init(A.r,A.c,1);

    while(n){

        if(n&1) ans=ans*A;

        n>>=1;

        A=A*A;

    }

    return ans;

}

int main(){

	ll n,k,m;

	while(cin>>n>>k>>m){

		MOD=m;

		Matrix A; A.init(n,n);

		rep(i,1,n)rep(j,1,n) A.mt[i][j]=read();

		Matrix UNIT; UNIT.init(n,n,1);

		Matrix B; B.init(n<<1,n<<1);

		rep(i,1,n)rep(j,1,n) B.mt[i][j]=A.mt[i][j];

		rep(i,1,n)rep(j,n+1,n<<1) B.mt[i][j]=UNIT.mt[i][j-n];

		rep(i,n+1,n<<1)rep(j,n+1,n<<1) B.mt[i][j]=UNIT.mt[i-n][j-n];

		Matrix res=fpw(B,k+1);

		rep(i,1,n) rep(j,1,n){

			print(mod(res.mt[i][j+n]-(i==j)+m));

			if(j<n) blank;

			else enter;

		}

	}

	return 0;

}

巴特西

POJ - 3233 矩阵套矩阵

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