LogSeq/pages/基础图论算法.md

• 链星

  inline void add_edge(int u, int v, int w) {
    edge[cnt].next = head[u]; edge[cnt].v = v; edge[cnt].w = w; head[u] = cnt++;
  }
  

• Dijkstra最短路
  • 要求：边权非负（不仅仅是没有负环）
  • 随手敲一个

    priority_queue<node, vector<node>, greater<node>> pq;
    pq.push({s, 0});
    dis[s] = 0;
    while(!pq.empty()) {
      int u = pq.top().id;
      pq.pop();
      if (vis[u]) continue;
      vis[u] = true;
      for (int i = head[u]; i; i = edge[i].next) {
        int v = edge[i].to;
        if (dis[v] > dis[u] + edge[i].w) {
          dis[v] = dis[u] + edge[i].w;
          pq.push({v, dis[v]});
        }
      }
    }
    

• Kruscal生成树

  • std::sort(e + 1, e + e_cnt + 1);
    int ans = 0, t_cnt = 0;
    for (int i = 1; i <= n; ++ i) fa[i] = i;
    for (int i = 1; i <= e_cnt; ++ i) {
      int fau = findfa(e[i].u);
      int fav = findfa(e[i].v);
      if (fau != fav) {
        fa[fav] = fau; // attention! use fa[find(v)], not fa[v]
        ans += e[i].w;
        t_cnt ++;
      }
    }