【Codeforces】894E.Ralph and Mushrooms Tarjan缩点+DP

给定n个点m条边有向图及边权w，第i次经过一条边边权为w−1−2.−..−i，w≥0给定起点s问从起点出发最多能够得到权和，某条边可重复经过

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有向图能够重复经过的边当且仅当成环，所以tarjan缩点成DAG，缩点后每个点内的权值可以通过算出，假设最大的n使得w−n(n+1)2≥0，那么该点值为(n+1)w−n(n+1)(n+2)/6，通过对DAG进行dp算出最长路就是答案

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

typedef long long LL;
const int N=1000005;

int n,m,x,y,w,s;

int head[N],to[N],nxt[N],val[N],cnt;
void init(){memset(head,-1,sizeof(head)),cnt=0;}
void add(int u,int v,int w)
{
    to[cnt]=v;val[cnt]=w;nxt[cnt]=head[u];head[u]=cnt++;
}

int head2[N],to2[N],nxt2[N],cnt2;LL val2[N];
void init2(){memset(head2,-1,sizeof(head2)),cnt2=0;}
void add2(int u,int v,int w)
{
    to2[cnt2]=v;val2[cnt2]=w;nxt2[cnt2]=head2[u];head2[u]=cnt2++;
}

int dfs_ind = 1, dfn[N], low[N], sccno[N], scc_cnt=0;
LL w_[N];

stack<int> st;

void tarjan(int u)
{
    dfn[u]=low[u]=dfs_ind++;
    st.push(u);
    for(int i=head[u];~i;i=nxt[i])
    {
        int v=to[i];
        if(!dfn[v]){tarjan(v);low[u]=min(low[u],low[v]);}
        else if(!sccno[v]){low[u]=min(low[u],dfn[v]);}
    }
    if(low[u]==dfn[u])
    {
        scc_cnt++;
        while(1)
        {
            int x=st.top();
            st.pop();
            sccno[x]=scc_cnt;
            if(x==u)
                break;
        }
    }
}

LL cal(LL x)
{
    LL n=sqrt(2.0*x+0.25)-0.5;
    return (n+1)*x-(n+1)*(n+2)*n/6;
}

void DAG()
{
    memset(dfn,0,sizeof(dfn));
    memset(low,0,sizeof(low));
    memset(sccno,0,sizeof(sccno));
    memset(w_,0,sizeof(w_));

    init2();
    for(int i=1;i<=n;i++)
    {
        if(!dfn[i])
            tarjan(i);
    }
    for(int i=1;i<=n;i++)
    {
        for(int j=head[i];~j;j=nxt[j])
        {
            int v=to[j];
            if(sccno[i]!=sccno[v])
                add2(sccno[i],sccno[v],1LL*val[j]);
            else
                w_[sccno[i]]+=cal(val[j]);
        }
    }
}
LL dp[N];
void dfs(int u)
{
    if(~dp[u])
        return ;
    dp[u]=w_[u];
    for(int i=head2[u];~i;i=nxt2[i])
    {
        dfs(to2[i]);
        dp[u]=max(dp[u],w_[u]+val2[i]+dp[to2[i]]);
    }
}


int main()
{
    init();
    scanf("%d%d",&n,&m);
    for(int i=1;i<=m;i++)
        scanf("%d%d%d",&x,&y,&w),add(x,y,w);

    scanf("%d",&s);
    DAG();
    memset(dp,-1,sizeof(dp));
    dfs(sccno[s]);
    cout<<dp[sccno[s]]<<endl;

}