zoj 3772 Calculate the Function

http://acm.zju.edu.cn/onlinejudge/showProblem.do?problemId=5235

这道题需要构造矩阵：F(X)=F(X-1)+F(X-2)*A(X)转化为F(X)*A(X+2)+F(X+1)=F(X+2)，然后在构造矩阵

{1, A[x]}  {F(x+1)}  {F(X+2)}

{1,    0 }*{F(X)    }={F(X+1)}

然后用线段数维护乘号左边的乘积；

  1 #include <cstdio>
  2 #include <cstring>
  3 #include <algorithm>
  4 #define maxn 101000
  5 using namespace std;
  6 const int mod=1000000007;
  7 
  8 int t,a[maxn*10],n,m;
  9 int l,r;
 10 struct matrix
 11 {
 12     long long a[4][4];
 13 };
 14 
 15 struct node 
 16 {
 17     int l;
 18     int r;
 19     matrix c;
 20 } tree[maxn*4];
 21 
 22 matrix multi(matrix x,matrix y)
 23 {
 24     matrix temp;
 25     for(int i=1; i<=2; i++)
 26     {
 27         for(int j=1; j<=2; j++)
 28         {
 29             temp.a[i][j]=0;
 30             for(int k=1; k<=2; k++)
 31             {
 32                 temp.a[i][j]=(x.a[i][k]*y.a[k][j]+temp.a[i][j])%mod;
 33             }
 34         }
 35     }
 36     return temp;
 37 }
 38 
 39 matrix build(int i,int l,int r)
 40 {
 41     tree[i].l=l;
 42     tree[i].r=r;
 43     if(l==r)
 44     {
 45         tree[i].c.a[1][1]=1;
 46         tree[i].c.a[1][2]=a[l];
 47         tree[i].c.a[2][1]=1;
 48         tree[i].c.a[2][2]=0;
 49         return tree[i].c;
 50     }
 51     int mid=(l+r)>>1;
 52     build(i<<1,l,mid);
 53     build(i<<1|1,mid+1,r);
 54     tree[i].c=multi(tree[i<<1|1].c,tree[i<<1].c);
 55     return tree[i].c;
 56 }
 57 
 58 matrix search1(int i,int l,int r)
 59 {
 60     if(tree[i].l==l&&tree[i].r==r)
 61     {
 62         return tree[i].c;
 63     }
 64     int mid=(tree[i].l+tree[i].r)>>1;
 65     if(r<=mid)
 66     {
 67         return search1(i<<1,l,r);
 68     }
 69     else if(l>mid)
 70     {
 71         return search1(i<<1|1,l,r);
 72     }
 73     else
 74     {
 75         return multi(search1(i<<1|1,mid+1,r),search1(i<<1,l,mid));
 76     }
 77 }
 78 int main()
 79 {
 80     scanf("%d",&t);
 81     while(t--)
 82     {
 83         scanf("%d%d",&n,&m);
 84         for(int i=1; i<=n; i++)
 85         {
 86             scanf("%d",&a[i]);
 87         }
 88         build(1,1,n);
 89         while(m--)
 90         {
 91             scanf("%d%d",&l,&r);
 92             if(r-l>=2)
 93             {
 94                 matrix tm,ans;
 95                 tm.a[1][1]=a[l+1];
 96                 tm.a[2][1]=a[l];
 97                 ans=multi(search1(1,l+2,r),tm);
 98                 printf("%lld\n",ans.a[1][1]);
 99             }
100             else printf("%d\n",a[r]%mod);
101         }
102     }
103     return 0;
104 }
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posted @ 2014-08-07 10:44  null1019  阅读(139)  评论(0)  编辑  收藏  举报