02_Bellman-Ford.cpp

  //SPFA锛堥槦鍒椾紭鍖朆ellmanFord锛?鏈€鍧忔椂闂村鏉傚害n*m锛屼竴鑸儏鍐垫瘮杩欎釜濂界殑澶?
const int MAXN = "Edit";
const int INF = 0x3f3f3f3f;
struct Edge
{
    int from, to, dist;
    Edge() {}
    Edge(int u, int v, int w) : from(u), to(v), dist(w) {}
};
struct BellmanFord
{
    int n, m;            // 鐐规暟鍜岃竟鏁?
    vector<Edge> edges;  // 杈瑰垪琛?
    vector<int> G[MAXN]; // 姣忎釜鑺傜偣鍑哄彂鐨勮竟缂栧彿锛堜粠0寮€濮嬬紪鍙凤級
    bool inq[MAXN];      // 鏄惁鍦ㄩ槦鍒椾腑
    int d[MAXN];         // s鍒板悇涓偣鐨勮窛绂?
    int p[MAXN];         // p[i]琛ㄧず鏈€鐭矾寰勬爲涓埌杈緄鐐圭殑杈圭殑缂栧彿
    int cnt[MAXN];       // 杩涢槦娆℃暟

    void init(int n)
    {
        this->n = n, m = 0;
        edges.clear();
        for (int i = 0; i <= n; i++) G[i].clear();
    }

    void AddEdge(int from, int to, int dist)
    {
        edges.emplace_back(from, to, dist);
        m = edges.size();
        G[from].push_back(m - 1);
    }

    bool bellmanford(int s)
    {
        queue<int> Q;
        memset(inq, 0, sizeof(inq));
        memset(cnt, 0, sizeof(cnt));
        for (int i = 0; i <= n; i++) d[i] = INF;
        d[s] = 0;
        inq[s] = true;
        Q.push(s);
        while (!Q.empty())
        {
            int u = Q.front(); Q.pop();
            inq[u] = false;
            for (auto& id : G[u])
            {
                Edge& e = edges[id];
                if (d[u] < INF && d[e.to] > d[u] + e.dist)
                {
                    d[e.to] = d[u] + e.dist;
                    p[e.to] = id;
                    if (!inq[e.to])
                    {
                        Q.push(e.to);
                        inq[e.to] = true;
                        if (++cnt[e.to] > n) return false;//鏈夎礋鐜?
                    }
                }
            }
        }
        return true;//鏃犺礋鐜?
    }

};

//鏃堕棿澶嶆潅搴*m
const int MAXN = "Edit";
const int INF = 0x3f3f3f3f;
struct Edge
{
    int from, to, dist;       //璧风偣,缁堢偣,璺濈
    Edge(int u, int v, int w):from(u), to(v), dist(w) {}
};
struct BellmanFord
{
    int n, m;            // 鐐规暟鍜岃竟鏁?
    vector<Edge> edges;  // 杈瑰垪琛?
    vector<int> G[MAXN]; // 姣忎釜鑺傜偣鍑哄彂鐨勮竟缂栧彿锛堜粠0寮€濮嬬紪鍙凤級
    bool inq[MAXN];      // 鏄惁鍦ㄩ槦鍒椾腑
    int d[MAXN];         // s鍒板悇涓偣鐨勮窛绂?
    int p[MAXN];         // p[i]琛ㄧず鏈€鐭矾寰勬爲涓埌杈緄鐐圭殑杈圭殑缂栧彿
 
    void init(int n)
    {
        this->n = n, m = 0;
        edges.clear();
        for (int i = 0; i <= n; i++) G[i].clear();
    }

    void AddEdge(int from, int to, int dist)
    {
        edges.emplace_back(from, to, dist);
        m = edges.size();
        G[from].push_back(m - 1);
    }

    bool bellmanford(int s)//bellmanford
    {
        for (int i = 0; i <= n; i++) d[i] = INF;
        d[s] = 0;
        for (int k = 0; k < n - 1; k++)//杩唬n-1娆?
        {
            bool flag = false;
            for (int i = 0; i < m; i++)//妫€鏌ユ瘡鏉¤竟
            {
                Edge& e = edges[i];
                if (d[e.from] < INF && d[e.to] > d[e.from] + e.dist)
                {
                    flag = true;
                    d[e.to] = d[e.from] + e.dist;
                    p[e.to] = i;
                }
            }
            if (!flag) break;//鍙鏌愪竴娆℃病relax锛岃鏄庢渶鐭矾寰勫凡缁忔煡鎵惧畬姣曪紝鎴栬€呴儴鍒嗙偣涓嶅彲杈撅紝鍙互璺冲嚭
        }
        for (int i = 0; i < m; i++)
        {
            Edge& e = edges[i];
            if (d[e.from] < INF && d[e.to] > d[e.from] + e.dist) return false;//鏈夎礋鐜?
        }
        return true;//娌℃湁璐熺幆
    }

}gao;



//dfs鐗堟湰鐨凷PFA,濂藉儚鍙互鏇村揩涓€浜涳紵
const int MAXN = "Edit";
const int INF = 0x3f3f3f3f;
struct Edge
{
    int from, to, dist;       //璧风偣,缁堢偣,璺濈
    Edge(int u, int v, int w):from(u), to(v), dist(w) {}
};
struct BellmanFord
{
    int n, m;            // 鐐规暟鍜岃竟鏁?
    vector<Edge> edges;  // 杈瑰垪琛?
    vector<int> G[MAXN]; // 姣忎釜鑺傜偣鍑哄彂鐨勮竟缂栧彿锛堜粠0寮€濮嬬紪鍙凤級
    bool vis[MAXN];      // 鏄惁鍦ㄩ槦鍒椾腑
    int d[MAXN];         // s鍒板悇涓偣鐨勮窛绂?
    int p[MAXN];         // p[i]琛ㄧず鏈€鐭矾寰勬爲涓埌杈緄鐐圭殑杈圭殑缂栧彿
    bool flag;

    void init(int n)
    {
        flag = false;
        this->n = n, m = 0;
        edges.clear();
        for (int i = 0; i <= n; i++) G[i].clear();
    }

    void AddEdge(int from, int to, int dist)
    {
        edges.emplace_back(from, to, dist);
        m = edges.size();
        G[from].push_back(m - 1);
    }

    void dfs(int u)//spfa
    {
        vis[u] = true;
        for (int i = 0; i < G[u].size(); i++)
        {
            Edge& e = edges[G[u][i]];
            if (d[e.to] > d[u] + e.dist)
            {
                if (vis[e.to]) { flag = true; break ; }
                d[e.to] = d[u] + e.dist;
                p[e.to] = G[u][i];
                dfs(e.to);
            }
        }
        vis[u] = false;
    }

    bool bellmanford(int s)
    {
        memset(d, INF, sizeof(d));
        memset(vis, 0, sizeof(vis));
        d[s] = 0;
        dfs(s);
        if (flag) return false;//鏈夎礋鐜?
        return true;//鏃犺礋鐜?
    }
 
}gao;

参考刘汝佳蓝书