题目链接：https://ac.nowcoder.com/acm/contest/3003/J
根据条件构造下列矩阵
根据题意不难想到用线段树维护。
注意矩阵乘法的顺序，不遵循交换律，合并区间时右子树在前。
1 #include <bits/stdc++.h> 2 using namespace std; 3 typedef long long ll; 4 const int mod=1e9+7,maxn=2e5+10; 5 inline int lx(signed x){return x<<1;} 6 inline int rx(signed x){return x<<1|1;} 7 int kk[maxn],bb[maxn]; 8 struct mat{ 9 ll a11,a12,a21,a22; 10 mat(){} 11 mat(ll a,ll b,ll c,ll d){a11=a,a12=b,a21=c,a22=d;} 12 friend mat operator *(mat a,mat b){ 13 return mat( 14 (a.a11*b.a11+a.a12*b.a21)%mod, 15 (a.a11*b.a12+a.a12*b.a22)%mod, 16 (a.a21*b.a11+a.a22*b.a21)%mod, 17 (a.a21*b.a21+a.a22*b.a22)%mod 18 ); 19 } 20 }; 21 struct Node{ 22 int l,r; 23 mat val; 24 }tree[maxn<<2]; 25 inline void pushup(int root){tree[root].val=tree[rx(root)].val*tree[lx(root)].val;} 26 void build(int root,int l,int r){ 27 tree[root].l=l,tree[root].r=r; 28 if(l==r){ 29 tree[root].val=mat(kk[l],bb[l],0,1); 30 return; 31 } 32 int mid=(l+r)>>1; 33 build(lx(root),l,mid); 34 build(rx(root),mid+1,r); 35 pushup(root); 36 } 37 void update(int pos,mat ma,int root){ 38 if(tree[root].l==tree[root].r){ 39 tree[root].val=ma; 40 return; 41 } 42 int mid=(tree[root].l+tree[root].r)>>1; 43 if(pos<=mid) 44 update(pos,ma,lx(root)); 45 else 46 update(pos,ma,rx(root)); 47 pushup(root); 48 } 49 mat query(int l,int r,int root){ 50 assert(r>=l); 51 int mid=(tree[root].l+tree[root].r)>>1; 52 if(tree[root].l==l&&tree[root].r==r)return tree[root].val; 53 if(mid>=r)return query(l,r,lx(root)); 54 else if (mid<l)return query(l,r,rx(root)); 55 else return query(mid+1,r,rx(root))*query(l,mid,lx(root)); 56 } 57 int main(){ 58 int n,m; 59 scanf("%d %d",&n,&m); 60 for(int i=1;i<=n;i++) 61 scanf("%d",&kk[i]); 62 for(int i=1;i<=n;i++) 63 scanf("%d",&bb[i]); 64 build(1,1,n); 65 while(m--){ 66 int op; 67 cin>>op; 68 if(op==1){ 69 int i,k,b; 70 scanf("%d%d%d",&i,&k,&b); 71 update(i,mat(k,b,0,1),1); 72 }else{ 73 int l,r; 74 scanf("%d %d",&l,&r); 75 mat res=query(l,r,1); 76 printf("%lld ",(res.a11+res.a12)%mod); 77 } 78 } 79 return 0; 80 }
----------------------------------------------分割线---------------------------------------------------------------------------------------
另附官方题解
标程很短就不贴了，以我的脑子现场一时半会儿应该是推不出来的QAQ