稠密图（邻接矩阵），并查集，最短路径（Dijkstra，spfa），最小生成树（kruskal，prim）
全部函数通过杭电 1142，1162，1198，1213等题目测试。
#include<iostream> #include<vector> #include<queue> #include<stack> #include<algorithm> #include<stdio.h> #include<stdlib.h> using namespace std; /* //函数集合声明下，方便查看 void Dijkstra(const denseGraph& dg, int s); void spfa(const denseGraph& dg, int s); weightType prim(const denseGraph& dg, int s); void makeSet(int x); int findSet(int x); void unionSet(int x, int y); weightType kruskal(const denseGraph& dg); */ //稠密图，邻接矩阵表示 #define N 1000 //表示顶点数最大值 #define NOEDGE 1000000 //表示无边，用于距离类求解中 typedef double weightType; //表示带边权的类型 //定义带权边类 struct edge{ int v, w; weightType val; edge(int v = -1, int w = -1, weightType val = NOEDGE) :v(v), w(w), val(val){} }; //定义稠密图类 struct denseGraph{ int Vcnt, Ecnt; //顶点数，边数 bool dg; //有向图 ? vector< vector<weightType> > adj; //邻接矩阵 denseGraph(int v, bool dg = false) :adj(v), Vcnt(v), Ecnt(0), dg(dg){ for (int i = 0; i < v; ++i) adj[i].assign(v, NOEDGE); } void insert(edge e){ int v = e.v, w = e.w; weightType val = e.val; if (adj[v][w] == NOEDGE) ++Ecnt; adj[v][w] = val; if (!dg) adj[w][v] = val; } void show(){ printf("Vcnt = %d, Ecnt = %d, Directed : %d\n", Vcnt, Ecnt, dg); for (int i = 0; i < Vcnt; ++i){ for (int j = 0; j < Vcnt-1; ++j) cout << adj[i][j] << ' '; cout << adj[i][Vcnt - 1] << endl; } } }; //Dijkstra算法 weightType dDijkstra[N]; //存放所有顶点到 s 的最短路径距离 int pDijkstra[N]; //pDijkstra[i],路径存在时，存放节点 i 的前驱，不存在时，-1 void Dijkstra(const denseGraph &dg, int s) { bool visit[N]; //集合 S ,visit[i]=true, i 属于集合 S for (int i = 0; i < dg.Vcnt; ++i){ //初始化 visit[i] = false; dDijkstra[i] = dg.adj[s][i]; pDijkstra[i] = dDijkstra[i] == NOEDGE ? -1 : s; } visit[s] = true; dDijkstra[s] = 0; for (int i = 0; i < dg.Vcnt - 1; ++i){ //dg.Vcnt-1次选点 int min = NOEDGE; int v = 0; for (int j = 0; j < dg.Vcnt; ++j){ //选距离最近点 if (!visit[j] && dDijkstra[j] < min){ v = j; min = dDijkstra[j]; } } visit[v] = true; for (int j = 0; j < dg.Vcnt; ++j){ //更新与 v 直接相连的顶点 if (!visit[j] && min + dg.adj[v][j] < dDijkstra[j]){ dDijkstra[j] = min + dg.adj[v][j]; pDijkstra[j] = v; } } } } //最短路径 SPFA算法 weightType dSpfa[N]; int pSpfa[N]; void spfa(const denseGraph& dg, int s) { bool visit[N]; for (int i = 0; i < dg.Vcnt; ++i){ visit[i] = false; dSpfa[i] = NOEDGE; pSpfa[i] = -1; } dSpfa[s] = 0; int u; queue<int> q; q.push(s); while (!q.empty()){ u = q.front(); q.pop(); for (int i = 0; i < dg.Vcnt; ++i){ if (dSpfa[u] + dg.adj[u][i] < dSpfa[i]){ dSpfa[i] = dSpfa[u] + dg.adj[u][i]; pSpfa[i] = u; if (!visit[i]) q.push(i); } } } } //最小生成树 prim weightType dPrim[N]; //存放所有顶点到 s 的最短路径距离 weightType prim(const denseGraph& dg, int s) { weightType sum = 0; bool visit[N]; for (int i = 0; i < dg.Vcnt; ++i){ //初始化 visit[i] = false; dPrim[i] = dg.adj[s][i]; } visit[s] = true; dPrim[s] = 0; for (int i = 0; i < dg.Vcnt - 1; ++i){ weightType min = NOEDGE; int v = 0; for (int j = 0; j < dg.Vcnt; ++j){ //选点 if (!visit[j] && dPrim[j] < min){ v = j; min = dPrim[j]; } } sum += min; visit[v] = true; for (int j = 0; j < dg.Vcnt; ++j){ if (!visit[j] && dg.adj[v][j] < dPrim[j]){ dPrim[j] = dg.adj[v][j]; } } } return sum; } //并查集实现，点集[0,1,2,3,4,...,n-1] int parentSet[N]; int rankSet[N]; void makeSet(int x) { parentSet[x] = x; rankSet[x] = 0; } void linkSet(int x, int y) { if (rankSet[x] > rankSet[y]) parentSet[y] = x; else { parentSet[x] = y; if (rankSet[x] == rankSet[y]) ++rankSet[y]; } } int findSet(int x) { vector<int> v; while (parentSet[x] != x){ v.push_back(x); x = parentSet[x]; } for (int i = 0; i < v.size(); ++i) parentSet[v[i]] = x; return x; } void unionSet(int x, int y) { linkSet(findSet(x), findSet(y)); } //最小生成树 kruskal bool kruskalComp(const edge& a, const edge& b) { return a.val < b.val; } weightType kruskal(const denseGraph& dg) { weightType sum = 0; edge e; vector<edge> ve; for (int i = 0; i < dg.Vcnt; ++i) for (int j = 0; j <= i; ++j) if (dg.adj[i][j]!=NOEDGE) ve.push_back(edge(i, j, dg.adj[i][j])); if (dg.dg){ for (int i = 0; i < dg.Vcnt; ++i) for (int j = i + 1; j < dg.Vcnt; ++j) if(dg.adj[i][j]!=NOEDGE) ve.push_back(edge(i, j, dg.adj[i][j])); } sort(ve.begin(), ve.end(), kruskalComp); for (int i = 0; i < dg.Vcnt; ++i) makeSet(i); for (int i = 0; i < ve.size(); ++i){ e = ve[i]; int x = findSet(e.v); int y = findSet(e.w); if (x != y){ unionSet(x, y); sum += e.val; } } return sum; } /*测试数据 5 6 1 3 2 1 4 2 3 4 3 1 5 12 4 2 34 5 2 24 7 8 1 3 1 1 4 1 3 7 1 7 4 1 7 5 1 6 7 1 5 2 1 6 2 1 */ int main() { int v, w, val, n, m; cin >> n >> m; denseGraph dg(n,true); while (m--){ cin >> v >> w >> val; dg.insert(edge(v - 1, w - 1, val)); } dg.show(); cout << endl; for (int i = 0; i < dg.Vcnt; ++i){ spfa(dg, i); Dijkstra(dg, i); for (int i = 0; i < dg.Vcnt; ++i) cout << dSpfa[i] << ' '; cout << endl; for (int i = 0; i < dg.Vcnt; ++i) cout << dDijkstra[i] << ' '; cout << endl; for (int i = 0; i < dg.Vcnt; ++i) cout << pSpfa[i] << ' '; cout << endl; for (int i = 0; i < dg.Vcnt; ++i) cout << pDijkstra[i] << ' '; cout << endl << endl; } for (int i = 0; i < dg.Vcnt; ++i) cout << prim(dg, i) << endl; cout << kruskal(dg) << endl; }
