CS Academy Gcd on a Circle(dp + 線段樹)
阿新 • • 發佈:2018-12-10
給你一個長為 n 的環,你可以把它斷成任意 k 段 (1
#include<bits/stdc++.h>
using namespace std;
#define maxn 100020
#define rep(i,l,r) for(register int i = l ; i <= r ; i++)
#define repd(i,r,l) for(register int i = r ; i >= l ; i--)
#define rvc(i,S) for(register int i = 0 ; i < (int)S.size() ; i++)
#define rvcd(i,S) for(register int i = ((int)S.size()) - 1 ; i >= 0 ; i--)
#define pb push_back
#define prev prev_
#define stack stack_
#define inf 0x3f3f3f3f
#define ls(x) (x << 1)
#define rs(x) ((x << 1) | 1)
typedef long long ll;
const int mod = 1e9 + 7;
int f[maxn],ans,sum[maxn];
int a[maxn],v[maxn << 2],n,pre[maxn],a2[maxn];
vector <int> vec;
int gcd(int a,int b){
if ( !b ) return a;
return gcd(b,a % b);
}
inline void update(int x){
v[x] = gcd(v[ls(x)],v[rs(x)]);
}
void build(int x,int l,int r){
if ( l == r ){ v[x] = a[l]; return; }
int mid = (l + r) >> 1 ;
build(ls(x),l,mid) , build(rs(x),mid + 1,r);
update(x);
}
int query(int x,int l,int r,int L,int R){
if ( L <= l && R >= r ) return v[x];
register int mid = (l + r) >> 1,res = 0;
if ( L <= mid ) res = query(ls(x),l,mid,L,R);
if ( R > mid ) res = gcd(res,query(rs(x),mid + 1,r,L,R));
return res;
}
void init(){
build(1,1,n);
pre[1] = 1;
rep(i,2,n){
pre[i] = pre[i - 1];
while ( query(1,1,n,pre[i],i) == 1 ) pre[i]++;
if ( pre[i] == 1 ) vec.pb((int)i) , a2[i] = query(1,1,n,2,i);
}
if ( pre[n] == 1 ) ans = mod - (n - 1);
// rep(i,1,n) cout<<pre[i]<<" ";
// cout<<endl;
}
inline void getans(int n){
rep(i,1,n){
if ( pre[i] == 1 ) f[i] = sum[i - 1] + 1;
else f[i] = sum[i - 1] - sum[pre[i] - 2];
f[i] = (f[i] + mod) % mod;
sum[i] = (sum[i - 1] + f[i]) % mod;
}
ans = (ans + f[n]) % mod;
// cout<<f[n]<<endl;
}
void solve(){
int last = a[1];
getans(n);
repd(k,n,2){
a[1] = gcd(a[1],a[k]);
if ( a[1] != last ){
if ( a[1] == 1 ) break;
last = a[1];
if ( vec.size() ){
int x = vec.back();
while ( vec.size() && gcd(a2[x],a[1]) == 1 ){
pre[x] = 2; vec.pop_back();
x = vec.back();
}
}
getans(k - 1);
}
else ans = (ans + f[k - 1]) % mod;
}
cout<<ans<<endl;
}
int main(){
freopen("input.txt","r",stdin);
scanf("%d",&n);
rep(i,1,n) scanf("%d",&a[i]);
init();
solve();
}