好題！ 題目 題解非常詳細這裡寫連結內容

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();
}