hiho 54 連通性·三

問題

http://hihocoder.com/contest/hiho54/problem/1

解法

首先使用tarjan 求出強連通分量，將強連通分量看做一個節點，就消除了圖中的環， 然後使用拓撲排序尋找一條權值最大的路徑。

#include <bits/stdc++.h>
using namespace std;
enum{maxn = 20000+4};
vector<int> G[maxn];
vector<int> G2[maxn];
int n, m;
bool visit[maxn];
int val[maxn];
int sum[maxn];
int group[maxn];
int low[maxn];
int dfn[maxn];
int ss[maxn];
void tarjan(int u)
{
    static int count = 0;
    static int sCnt = -1;
    visit[u] = true;
    dfn[u] = low[u] = ++count;
    ss[++sCnt] = u;
    for (int i=0; i<G[u].size(); ++i)
    {
        int v = G[u][i];
        if (!visit[v])
        {
            tarjan(v);
            low[u] = min(low[u], low[v]);
        }else{
            bool flag = false;
            for (int j=0; j<=sCnt; ++j)
                if (ss[j] == v)
                {    flag = true; break;}
            if (flag)
            {
                low[u] = min(low[u], dfn[v]);
            }
        }
    }
    if (low[u] == dfn[u])
    {
        for (int v = ss[sCnt]; v != u; v= ss[--sCnt])
        {
            group[v] = u;
            val[u] += val[v];
        }
        group[u] = u;
        --sCnt;
    }
}
int inDegree[maxn];
void buildG2()
{
    memset(inDegree, 0, sizeof(inDegree));
    for (int u=1; u<=n; ++u)
    {
        if (visit[u])
        {
            for (int i=0; i<G[u].size(); ++i)
            {
                int v = G[u][i];
                if (group[u] == group[v])
                    continue;
                G2[group[u]].push_back(group[v]);
                ++inDegree[group[v]];
                //printf("add %d-> %d\n", group[u], group[v]);
            }
        }
        else
            val[u] = 0;
    }
}
int ret =0;
void solve()
{
    memset(sum, 0, sizeof(sum));
    queue<int> q;
    q.push(1);
    sum[1] = val[1];
    while(q.size())
    {
        int u = q.front();
        q.pop();
        ret = max(sum[u], ret);
        for (int i=0; i< G2[u].size(); ++i)
        {
            int v = G2[u][i];
            --inDegree[v];
            sum[v] = max(sum[v], sum[u]+val[v]);
            if (!inDegree[v])
                q.push(v);
        }
    }
}
int main()
{
   // freopen("in.txt", "r", stdin);
    scanf("%d %d", &n, &m);
    for (int i=1; i<=n; ++i)
        scanf("%d", val+i);
    for (int i=0; i<m; ++i)
    {
        int a, b;
        scanf("%d %d", &a, &b);
        G[a].push_back(b);
    }
    memset(visit, 0, sizeof(visit));
    tarjan(1);
    buildG2();
    solve();
    printf("%d\n", ret);
}