标签：line element printf har ram mat for define esc
A frightful matrix is a square matrix of order n where the first row and the first column are explicitly specified, while the other elements are calculated using a frightful formula which is, actually, a simple recursive rule.
Given two integer sequences l and t,both of size n,as well as integer parameters a,b and c,the frightful matrix F is defined as follows:
* The first column of the matrix is the sequence l:
$$F[k, 1] = lk$$
* The first row of the matrix is the sequence t:
$$F[1, k] = tk$$
* Other elements are calculated using a recursive formula:
$$F[i,j]=a*F[i,j-1]+b*F[i-1,j]+c$$
Given a frightful matrix, ?nd the value of the element $F[n,n]$ modulo $10^6 +3$.
如果$c=0$可以直接计算每一个格子对答案的贡献
$l_i$对答案的贡献为$a^{n-1}b^{n-i} \binom{2n-i-2}{n-2}$，其他的同理
考虑$c$
使用待定系数法，设$F_{i,j}+k=a(F_{i,j-1}+k)+b(F_{i-1,j}+k)$
解得$k=\frac 1{a+b-1}$，当$a+b \neq 1$
在上式中计算贡献，最后把$k$减掉即可
数据水，没有$a+b=1$的情况
#include<iostream> #include<cstdio> using namespace std; long long n,a,b,c,l[200005],t[200005],fac[400005]={1},inv[400005],k,ans,A[200005]={1},B[200005]={1}; const long long mod=1e6+3; inline int read() { int f=1,w=0; char ch=0; while(ch<‘0‘||ch>‘9‘){if(ch==‘-‘) f=-1;ch=getchar();} while(ch>=‘0‘&&ch<=‘9‘) w=(w<<1)+(w<<3)+ch-‘0‘,ch=getchar(); return f*w; } long long ksm(long long a,long long p) { long long ret=1; while(p) { if(p&1) (ret*=a)%=mod; (a*=a)%=mod,p>>=1; } return ret; } long long C(int x,int y) { return fac[x]*inv[y]%mod*inv[x-y]%mod; } int main() { n=read(),a=read(),b=read(),c=read(),k=c*ksm(a+b-1,mod-2)%mod; for(int i=1;i<=400000;i++) fac[i]=fac[i-1]*i%mod; for(int i=1;i<=200000;i++)A[i]=A[i-1]*a%mod,B[i]=B[i-1]*b%mod; inv[400000]=ksm(fac[400000],mod-2); for(int i=399999;~i;i--) inv[i]=inv[i+1]*(i+1)%mod; for(int i=1;i<=n;i++) l[i]=read(); for(int i=1;i<=n;i++) t[i]=read(); for(int i=2;i<=n;i++) (ans+=((l[i]+k)*A[n-1]%mod*B[n-i]%mod*C(n+n-i-2,n-2)%mod+(t[i]+k)*A[n-i]%mod*B[n-1]%mod*C(n+n-i-2,n-2)%mod)%mod)%=mod; printf("%lld\n",(ans-k+mod)%mod); return 0; }
LG P4351 [CERC2015]Frightful Formula
标签：line element printf har ram mat for define esc
原文地址：https://www.cnblogs.com/JDFZ-ZZ/p/14095587.html
