牛客暑期多校训练营第一场 Infinite Tree

//#define LOCAL
#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define mem(a, b) memset(a,b,sizeof(a))
#define sz(a) (int)a.size()
#define INF 0x3f3f3f3f
#define DNF 0x7f
#define DBG printf("this is a input\n")
#define fi first
#define se second
#define mk(a, b) make_pair(a,b)
#define pb push_back
#define LF putchar('\n')
#define SP putchar(' ')
#define p_queue priority_queue
#define CLOSE ios::sync_with_stdio(0); cin.tie(0)

template<typename T>
void read(T &x) {x = 0;char ch = getchar();ll f = 1;while(!isdigit(ch)){if(ch == '-')f *= -1;ch = getchar();}while(isdigit(ch)){x = x * 10 + ch - 48; ch = getchar();}x *= f;}
template<typename T, typename... Args>
void read(T &first, Args& ... args) {read(first);read(args...);}
template<typename T>
void write(T arg) {T x = arg;if(x < 0) {putchar('-'); x =- x;}if(x > 9) {write(x / 10);}putchar(x % 10 + '0');}
template<typename T, typename ... Ts>
void write(T arg, Ts ... args) {write(arg);if(sizeof...(args) != 0) {putchar(' ');write(args ...);}}
using namespace std;

ll gcd(ll a, ll b) {
    return b == 0 ? a : gcd(b, a % b);
}

ll lcm(ll a, ll b) {
    return a / gcd(a, b) * b;
}
const int N = 200010;
int T;
int xs_head[N] , xs_cnt, n;
ll ww[N] , ff[N] , d[N], dp[N];
struct BIT
{
    int tree[N] ;
    void init()
    {
        mem(tree,0) ;
    }
    int lowbit(int k)
    {
        return k & -k;
    }
    void add(int x , int k)
    {
        while(x <= n)
        {
            tree[x] += k ;
            x += lowbit(x) ;
        }
    }
    int sum(int x)
    {
        int ans = 0 ;
        while(x != 0)
        {
            ans += tree[x] ;
            x -= lowbit(x) ;
        }
        return ans ;
    }
    int query(int l , int r)
    {
        return sum(r) - sum(l - 1) ;
    }
} bit ;
struct node1
{
    int next , t;
    int w;
}edge[N << 1], xs_edge[N << 1];
void xs_add (int f, int t ,int w)
{
    xs_edge[xs_cnt].t = t;
    xs_edge[xs_cnt].w = w;
    xs_edge[xs_cnt].next = xs_head[f];
    xs_head[f] = xs_cnt ++;
}
void init ()
{
    for (int i = 1 ; i <= 2*n ; i ++)
        xs_head[i] = -1;
    xs_cnt = 0;
}
int minv[N], dep[N] , lcadep[N], tot;
//求出每一个数的最小质因子
void pre_work()
{
    for (int i = 2 ; i <= N ; i ++)
    {
        for (int j = i ; j <= N ; j += i)
            if (!minv[j]) minv[j] = i;
    }
}
//预处理关键点LCA
void Deal_LCA()
{
    for (int i = 2 , j; i <= n ; i ++)
    {
        dep[i] = dep[i-1] + 1;
        for (j = i ; j != minv[j] ; j /= minv[j])
            dep[i] ++;
        lcadep[i] = bit.sum(n) - bit.sum(j - 1) + 1;
        for (j = i ; j != 1 ; j /= minv[j])
            bit.add(minv[j], 1);
    }
}
int st[N] , top;
//插入虚树节点
void insert (int x)
{
    while(top > 1 && dep[st[top - 1]] >= lcadep[x])
    {
        //cout << st[top-1] <<" "<< st[top]<< " " << abs(dep[st[top - 1]] - dep[st[top]]) << endl;
        xs_add(st[top - 1], st[top], abs(dep[st[top - 1]] - dep[st[top]]));
        top--;
    }
    if(dep[st[top]] != lcadep[x]) {
        dep[++ tot] = lcadep[x];
        ww[tot] = 0;
        //cout << tot <<" "<< st[top]<< " " << abs(dep[tot]-dep[st[top]]) << endl;
        xs_add(tot, st[top], abs(dep[tot]-dep[st[top]]));
        st[top] = tot;
    }
    st[++top] = x;
}
ll ans = 0;
//一次扫描
void dfs1 (int u , int fa)
{
    ff[u] = ww[u];
    dp[u] = d[u] * ww[u];
    for (int i = xs_head[u] ; i != -1 ; i = xs_edge[i].next)
    {
        int v = xs_edge[i].t, w = xs_edge[i].w;
        if (v != fa)
        {
            d[v] = d[u] + w;
            dfs1 (v, u);
            dp[u] += dp[v];
            ff[u] += ff[v];
        }
    }
}
//二次扫描
void dfs2 (int u , int fa)
{
    for (int i = xs_head[u] ; i != -1 ; i = xs_edge[i].next)
    {
        int v = xs_edge[i].t , w = xs_edge[i].w;
        if (v != fa)
        {
            dp[v] = dp[u] + 1ll * w * (ff[u] - ff[v]) - ff[v] * w;
            ff[u] -= ff[v];
            ff[v] += ff[u];
            ans = min (dp[v], ans);
            dfs2 (v , u);
            //由于之前的ff没有保留,所以需要回溯回去
            ff[v] -= ff[u];
            ff[u] += ff[v];
        }
    }
}
int main()
{
    pre_work ();
    while (scanf("%d",&n) != EOF)
    {
        tot = n;
        bit.init();
        init();
        for (int i = 1 ; i <= n ; i ++)
            read (ww[i]);
        dep[1] = 1;
        Deal_LCA();
        st[++ top] = 1;
        for (int i = 2 ; i <= n ; i ++)
            insert (i);
        while(-- top)
        {
            //cout << st[top] <<" "<< st[top + 1]<< " " << abs(dep[st[top]] - dep[st[top+1]]) <<endl;
            xs_add(st[top], st[top + 1], abs(dep[st[top]] - dep[st[top+1]]));
        }
        dfs1 (1, 1);
        ans = dp[1];
        dfs2 (1, 1);
        write(ans), LF;
    }
}
/*
2
6 5
0 1 0 1 0 1
1 3
3 5
1 2
2 4
4 5
 */