[Explanations] [magical] Oscar race simulation on campus POIN doubts

Digression:

sol: Routine

I:? ? ? What is immortal ideas? ,

---

Has given a \ (n \) tree nodes, you can choose some point, these points can not be adjacent

The total value of what you get is the product of the weights of these nodes

Seeking the most value \ (mod 998244353 \)

---

sol

Consider a magical thing: log

Obviously we have:

If
\ [ab = c \]
so
\ [log_x (a) + log_x
(b) = log (c) \] Therefore, the maximum weight problem into independent set of the tree

Classic question, can a tree DP

---

code

#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <cmath>
using namespace std;

const int N=200010;
const int M=N;
const int mod=998244353;

inline void read(int &x) {
    x=0;
    int f=1;
    char ch=getchar();
    while(ch<'0'||ch>'9') {
        if (ch=='-') {
            f=-1;
        }
        ch=getchar();
    }
    while(ch>='0'&&ch<='9') {
        x=x*10+ch-'0';
        ch=getchar();
    }
    x*=f;
}

struct note {
    int t;
    int next;
};

int cnt;
int head[N];
note e[M<<1];
int n;

inline void add(int x,int y) {
    e[++cnt].t=y;
    e[cnt].next=head[x];
    head[x]=cnt;
}

double f[N][2];
double val[N];
int v[N];

void dfs(int p,int fa) {
    f[p][0]=0;
    f[p][1]=val[p];
    for(int i=head[p];i+1;i=e[i].next) {
        int t=e[i].t;
        if (t==fa) {
            continue;
        }
        dfs(t,p);
        f[p][1]+=f[t][0];
        f[p][0]+=max(f[t][1],f[t][0]);
    }
}

int ans=1;

void dfs2(int p,int fa,bool d) {
    if (d) {
        ans=(1ll*v[p]*ans)%mod;
    }
    for(int i=head[p];i+1;i=e[i].next) {
        int t=e[i].t;
        if (t==fa) {
            continue;
        }
        if (d) {
            dfs2(t,p,0);
        } else {
            if (f[t][1]>f[t][0]) {
                dfs2(t,p,1);
            } else {
                dfs2(t,p,0);
            }
        }
    }
}

int main() {
    read(n);
    memset(head,-1,sizeof(head));
    for(int i=1;i<=n;i++) {
        read(v[i]);
        val[i]=log10(v[i]);
    }
    for(int i=1;i<n;i++) {
        int x,y;
        read(x),read(y);
        add(x,y);
        add(y,x);
    }
    dfs(1,-1);
    if (f[1][0]<f[1][1]) {
        dfs2(1,-1,1);
    } else {
        dfs2(1,-1,0);
    }
    printf("%d\n",ans);
    return 0;
}