首页 > 代码库 > hdu 5015 233 Matrix(最快的搞法)
hdu 5015 233 Matrix(最快的搞法)
233 Matrix
Time Limit: 10000/5000 MS (Java/Others) Memory Limit: 65536/65536 K (Java/Others)Total Submission(s): 191 Accepted Submission(s): 125
Problem Description
In our daily life we often use 233 to express our feelings. Actually, we may say 2333, 23333, or 233333 ... in the same meaning. And here is the question: Suppose we have a matrix called 233 matrix. In the first line, it would be 233, 2333, 23333... (it means a0,1 = 233,a0,2 = 2333,a0,3 = 23333...) Besides, in 233 matrix, we got ai,j = ai-1,j +ai,j-1( i,j ≠ 0). Now you have known a1,0,a2,0,...,an,0, could you tell me an,m in the 233 matrix?
Input
There are multiple test cases. Please process till EOF.
For each case, the first line contains two postive integers n,m(n ≤ 10,m ≤ 109). The second line contains n integers, a1,0,a2,0,...,an,0(0 ≤ ai,0 < 231).
For each case, the first line contains two postive integers n,m(n ≤ 10,m ≤ 109). The second line contains n integers, a1,0,a2,0,...,an,0(0 ≤ ai,0 < 231).
Output
For each case, output an,m mod 10000007.
Sample Input
1 1 1 2 2 0 0 3 7 23 47 16
Sample Output
234 2799 72937Hint
Source
2014 ACM/ICPC Asia Regional Xi‘an Online
Recommend
hujie | We have carefully selected several similar problems for you: 5017 5016 5014 5013 5012
解释在代码里:
#include<cstdio> #define MOD 10000007 using namespace std; typedef long long LL; #define rep(i,a,b) for(int i=a;i<b;i++) LL inv[11]; ///逆元 LL inv_fac[11]; ///阶乘逆元 LL n,m,a[11],tmp; /** 经过模拟之后发现ans=c(m,0)*a[n-1]+c(m+1,1)*a[n-2]+...c(m+n,n)*a[0]+c(n,0)*(23333...)+ c(n+1,1)*(2333...)+c(n+m-2,m-1)*233; 变形如下: ans=c(m,0)*a[n-1]+c(m+1,1)*a[n-2]+...c(m+n,n)*a[0]+c(n,n)*(23333...)+ c(n+1,n)*(2333...)+c(n+m-2,n)*233; ans=c(m,0)*a[n-1]+c(m+1,1)*a[n-2]+...c(m+n,n)*a[0]+{c(n,n)+ c(n+1,n)+c(n+m-2,n)}*233+2100*{10^(m-2)*c(n,n)+10^(m-3)*c(n+1,n)+10^0*c(n+m-4,n)}; ans=c(m,0)*a[n-1]+c(m+1,1)*a[n-2]+...c(m+n,n)*a[0]+c(n+m-1,n)*233 +2100*{10^(m-2)*c(n,n)+10^(m-3)*c(n+1,n)+10^0*c(n+m-4,n)}; 设f(n)={10^(m-2)*c(n,n)+10^(m-3)*c(n+1,n)+10^0*c(n+m-4,n)},则有f(n)=((10*f(n-1)-c(n+m-2,n))/9)%MOD; 即f(n)=(10*f(n-1)-c(n+m-2,n)*inv[9]%MOD; **/ void Init()///初始化数组 { int i; inv[0]=inv[1]=1; inv_fac[0]=inv_fac[1]=1; for(i=2;i<15;i++){ inv[i]=(inv[MOD%i]*(MOD-MOD/i))%MOD;///递推求逆元 inv_fac[i]=(inv_fac[i-1]*inv[i])%MOD;///递推求阶乘的逆元 } } LL C(LL N,LL k)///计算组合数 { if(k==0)return 1; LL i,ans=inv_fac[k]; for(i=0;i<k;i++) ans=ans*(N-i)%MOD; return ans; } LL quick_mod(LL x,LL N)///快速幂取模 { LL temp=x%MOD,result=1; while(N) { if(N&1) result=result*temp%MOD; temp=temp*temp%MOD; N>>=1; } return result; } LL f(LL N) { if(N==0) return (tmp-1+MOD)*inv[9]%MOD;///用到了等比数列求和sum[n]=a1(1-q^n)/(1-q); return (10*f(N-1)-C(N+m-2,N))*inv[9]%MOD; } void solve() { if(n==0&&m==0) { puts("0"); return; } tmp=quick_mod(10,m-1); LL ans=(C(n+m-1,n)*233+f(n)*2100)%MOD;///第一行的和乘组合数 int i; for(i=1;i<=n;i++) ans=(ans+C(n+m-1-i,n-i)*a[i-1])%MOD;///加上第一列的和乘组合数 printf("%I64d\n",ans); } int main() { Init(); while(~scanf("%I64d%I64d",&n,&m)) { rep(i,0,n){ scanf("%I64d",&a[i]); a[i]%=MOD; } solve(); } return 0; }
hdu 5015 233 Matrix(最快的搞法)
声明:以上内容来自用户投稿及互联网公开渠道收集整理发布,本网站不拥有所有权,未作人工编辑处理,也不承担相关法律责任,若内容有误或涉及侵权可进行投诉: 投诉/举报 工作人员会在5个工作日内联系你,一经查实,本站将立刻删除涉嫌侵权内容。