Five kinds of storage methods of graphs "graph theory"

Use three ways to realize the storage of graphs to adapt to different situations.

Reference: ACM-ICPC Programming Series--Graph theory and application

Mode 1: adjacency matrix

Adjacency matrix is the simplest and most common one of the data structure of the graph.

Implementation: The two-dimensional array map[maxn][maxn],map[i][j] represents the distance from point I to to J.

Initialize: map[i][i] = 0,map[i][j] = INF (i!=j), read in data map[i][j] = W.

Time complexity: Initialize O (n^2), map requires O (m), Total time complexity O (n^2).

Advantages and disadvantages: simple and intuitive, can be directly queried between the point I and Point J whether there is an edge, the traversal efficiency is low, not

Can store the renumbering, low initialization efficiency, large graph overhead, suitable for dense graphs with less storage points.

Way 2: The Forward star

#include <iostream> #include <algorithm> #include <cstdio> #include <cstring>using namespace    std;const int MAXN = 100;const int MAXM = 100;int head[maxn];//The position of the first edge of the storage starting point of i struct node{int from;//start int to;//end point  int w;//weight Value};node edge[maxm];bool cmp (node A,node b)//edge Sort {if (A.from = b.from && a.to = = b.to) return    A.W < B.W;    if (A.from = = B.from) return a.to < b.to; return A.from < B.from;}    int main () {int n,m;    CIN >> n >> m;    for (int i = 0; i < m; i++) {cin >> edge[i].from >> edge[i].to >> edge[i].w;    } sort (edge,edge+m,cmp);    memset (head,-1,sizeof (head));    Head[edge[0].from] = 0; for (int i = 1; i < m; i++)//Determine starting point for I first edge position {if (edge[i].from! = edge[i-1].from) Head[edge[i].from]    = i; } for (int i = 1; I <= n; i++)//traversal diagram {//k is the starting position for the I-node edge for (int k = Head[i]; edge[k].from = i &AMP;&A mp K < M;         k++) {   cout << edge[k].from << ' << edge[k].to << ' << edge[k].w << Endl; }} return 0;} /*7 81 1 11 3 11 3 23 5 13 6 14 6 12 4 11 2 1*/

Mode 3: Adjacency table-Dynamic Build table

#include <iostream> #include <algorithm> #include <cstdio> #include <cstring>using namespace std;const int maxn = 100;struct edgenode<span style= "white-space:pre" ></span>//adjacency table node {int To;<span style = "White-space:pre" ></span>//end int W;<span style= "white-space:pre" ></span>//weight EdgeNode *next; <span style= "White-space:pre" ></span>//pointer to next edge};struct vnode<span style= "White-space:pre" > </span>//Start table Node {int From;<span style= "White-space:pre" ></span>//start Edgenode *first;<span style= "White-space:pre" ></span>//adjacency table head pointer};    Vnode adjlist[maxn];<span style= "White-space:pre" ></span>//the adjacency table of the entire graph int main () {int n,m,x,y,w;    CIN >> n >> m;        for (int i = 0; i < m; i++)//read in graph {cin >> x >> y >> w;        Edgenode *p = new Edgenode ();        P->to = y;        P->w = W;        P->next = Adjlist[x].first; Adjlist[x].first = p;   } cout << Endl;            for (int i = 1; I <= n; i++)//traverse diagram {for (Edgenode *k = Adjlist[i].first; K! = NULL; k = k->next)    cout << i << ' << k->to << ' << k->w << Endl; } return 0;}

Method 4: Adjacency table--vector simulation linked list implementation

#include <iostream> #include <algorithm> #include <vector> #include <cstdio> #include < cstring>using namespace Std;const int maxn = 100;const int maxm = 100;struct edgenode<span style= "White-space:pre" &G t;</span>//Edge table node type {int To;<span style= "white-space:pre" ></span>//endpoint int w;<span style= "white-sp    Ace:pre "></span>//weight value};vector<edgenode> map[maxn];int main () {Edgenode E;    int n,m,x,y,w;    CIN >> n >> m; for (int i = 0; i < m; i++) <span style= "White-space:pre" ></span>//read in diagram {cin >> x >> y        >> W;        e.to = y;        E.W = W;    Map[x].push_back (e);    } cout << Endl; for (int i = 1; I <= n; i++) <span style= "White-space:pre" ></span>//traverse diagram {for (vector &LT;EDGENODE&G T;::iterator k = Map[i].begin (); K!=map[i].end ();            k++) {Edgenode t = *k; cout << i << ' << t.to << ' &Lt;< T.W << Endl; }} return 0;}

Mode 5: Adjacency table--chain forward star ★

#include <iostream> #include <algorithm> #include <cstdio> #include <cstring>using namespace std;const int MAXN = 100;const int maxm = 100;int head[maxn];struct edgenode{    int to;    int W;    int next;}; Edgenode Edges[maxm];int Main () {    int n,m,x,y,w;    CIN >> n >> m;    memset (head,-1,sizeof (head));    for (int i = 0; i < m; i++)    {        cin >> x >> y >> w;        edges[i].to = y;        EDGES[I].W = W;        Edges[i].next = head[x];        HEAD[X] = i;    }    cout << Endl;    for (int i = 1, i <= N; i++)    {for        (int k = head[i]; k!=-1; k = edges[k].next)            cout << i << ' ' << edges[k].to << ' << edges[k].w << Endl;    }    return 0;}

Five kinds of storage methods of graphs "graph theory"