18 National Day map of the Hui-si School

Graph theory

1. Basic Concepts

　　

　　

2. Storage of graphs

　　

3. Path

　　

4. Free Tree

　　

5 a tree and a two-fork tree

　　

6. Graph traversal

　　

7. Connectivity

　　

8. Topology sequencing

　　

9. Euler path

　　

10. Shortest circuit

　　

　　(1) Dijkstra

　　

voidDijkstraintx) { for(inti =1; I <= N; i++) Dis[i] =A[x][i]; DIS[X]=1; F[X] =1;  for(inti =1; I <= N; i++) {Minn=0;  for(intj =1; J <= N; J + +)            if(F[j] = =0&& Dis[j] >Minn) {k=J; Minn=Dis[j]; } F[k]=1; if(k = = y) Break;  for(intj =1; J <= N; J + +)            if(F[j] = =0&& Dis[k] * A[k][j] >Dis[j]) dis[j]= Dis[k] *A[k][j]; }}

　　(2) Bellman-ford

Constantly adding edges in the shortest way

Complexity of Time: O (VE)

 for (int i = n; i;--i)      for (int j = n; j;--J)         = Min (Dis[v[j]], Dis[u[j]] + w[j]);

　　(3) Folyd

can be considered as DP while finding the shortest path between each point pair

Complexity of Time: O (n3)

 for (int1; k <= N; + +k    )  for (int1; i <= N; + +i        )  for (int1; j <= N; + +j            ) = Min (Dis[i][j], dis[i][k] + dis[k][j]);

　　(4) SPFA

Although the teacher did not say, but I usually write this ...

voidSPFA (intx) { for(inti =1; I <= N; ++i) dis[i]= MAXN, vis[i] =0; DIS[X]=0; VIS[X] =1; Q.push (x);  while(!Q.empty ()) {        inty = Q.front (); Q.pop (); Vis[y] =0;  for(inti = head[y]; I i =Net[i]) {            intt =To[i]; if(Dis[t] > Dis[y] +Cap[i]) {Dis[t]= Dis[y] +Cap[i]; if(!vis[t]) vis[t] =1, Q.push (t); }        }    }}

　　(5) Johnson's right to re-empower

　　

　　(6) Application: Differential constraint system

　　

11. Strongly Connected components

　　

12. Side Double Connected components

　　

13. Point Double connected components

　　

14. Minimum spanning tree MST

　　(1) MST basic theorem

　　

　　(2) MST solution method

　　

//The other two will not write Qwq//this is Kruskal .structNond {intu, V, W;} E[M];intFindintx) {returnFA[X] = = x? X:FA[X] =find (Fa[x]);}BOOLCMP (Nond x, Nond y) {returnX.W <Y.W;}voidKruskal () {sort (e+1, e+k+1, CMP);  for(inti =1; I <= K; ++i) {intx = Find (e[i].u), y =find (E[I].V); if(x = = y)Continue; FA[X]=y; ++tot; Sum+=E[I].W; if(tot = = N-1) Break; }    return ;}

　　(3) The nature of MST

　　

15. Recent Public ancestor LCA

　　(1) defining a given two points U and V, the LCA (U, v) is the deepest of all the common ancestors of two points

　　(2) Seeking the law

　　

18 National Day map of the Hui-si School