蓝桥杯图论模板

1.树的直径

dfs版

#include<bits/stdc++.h>
using namespace std;

const int maxn = 1e5+5;
int vis[maxn],book[maxn];
vector<int> g[maxn]; 
int node = 1;
int path[maxn];
int n,m;
int ans = 0;

void init(){
	for(int i=1;i<=n;i++) {
		path[i] = -1;
		vis[i] = 0;
	}
}

void dfs(int x,int dis){
    vis[x] = 1; 
    for(int i=0;i<g[x].size();i++){
        int vv = g[x][i];
        if(!vis[vv]){
            path[vv] = x;
            if(dis + 1 > ans) {
            	node = vv;
            	ans = dis+1;
			}
            dfs(vv,dis+1);
        }
    }
    vis[x] = 0;
}


int main(){ 
	cin>>n>>m;
	for(int i=1;i<=m;i++){
		int u,v;
		cin>>u>>v;
		g[u].push_back(v);
		g[v].push_back(u);
	}
    dfs(1,0);
    int s1 = node; 
    ans = 0;
    init();
    dfs(node,0);
    int s2 = node;
    int maxDist = ans;
    cout<<s1<<" "<<s2<<" "<<maxDist;
    return 0;
}

bfs版

#include <iostream>
#include <vector>
#include <algorithm>
#include <queue>
using namespace std;

struct edge{
    int v,w;
    edge(int v,int w){
        this -> v = v;
        this -> w = w;
    }
};
vector<edge> vec[10001];
int d[10001],ans;
bool vis[10001];
int node; // 记录第一次dfs最远的点
void bfs(int u){
    queue<int> q;
    q.push(u);
    while(!q.empty()){
        int x = q.front();
        vis[x] = 1;
        q.pop();
        for(int i = 0;i < (int)vec[x].size();i++){
            int y = vec[x][i].v;
            if(vis[y]) continue;
            d[y] = d[x] + vec[x][i].w;
            if(d[y] > ans){
                ans = d[y];
                node = y;
            }
            q.push(y);
        }
    }
}
int main(){
    // freopen("test.txt","r",stdin);
    int u,v,w;
    while(scanf("%d%d%d",&u,&v,&w) == 3){
        vec[u].push_back(edge(v,w));
        vec[v].push_back(edge(u,w));
    }
    memset(vis,0,sizeof(vis));
    ans = 0;
    d[1] = 0;
    bfs(1);
    memset(vis,0,sizeof(vis));
    ans = 0;
    d[node] = 0;
    bfs(node);
    printf("%d\n",ans);
    return 0;
}

2.带权并查集

#include<bits/stdc++.h>
using namespace std;

const int maxn = 1e6+10;

int n,m;//n个顶点 m条边 
int father[maxn]; //元素父亲节点 
int size[maxn];//集合大小 
int maxs[maxn];//集合最大值 
int dist[maxn];//元素x到它所在集合根节点的距离 
int setNums = 0;//集合总数 

//初始化 
void init(){
	setNums = n;
	for(int i=1;i<=n;i++){
		father[i] = i;
		size[i] = 1;
		maxs[i] = i;
		dist[i] = 0;
	}
}

//查找 
int find(int x){
	if(father[x] == x){
		return x;
	}
	int y = father[x];
	father[x] = find(y);
	dist[x] += dist[y]; //x到根的距离 需要加上y到根的距离 
	return father[x];
}

//合并 
void join(int x,int y){
	int a = find(x);
	int b = find(y);
	if(a != b){
		setNums--;
		father[a] = b;
		dist[a] = size[b];
		size[b] += size[a];
		maxs[b] = max(maxs[a],maxs[b]);
	}
}

//查询集合总数量 
int findSetnum(){
	return setNums;
}

//查询x所在集合的大小(元素数量)
int findSize(int x){
	return size(find(x));
}

//查询x所在集合中的最大值 
int findSetMax(int x){
	return maxs(find(x));
}

//查询x到它的集合的根 的距离
int findDist(int x){
	return dist[x];
}

int main(){
	
	return 0;
} 

3.最短路

floyd

#include<bits/stdc++.h>
using namespace std;

const int maxn = 1010;
int g[maxn][maxn];
const int inf = 0x3f3f3f3f;

void init(){
	for(int i=1;i<=n;i++){
		for(int j=1;j<=n;j++){
			if(i==j) g[i][j] = 0;
			else g[i][j] == inf;
		}
	}
}

void floyd(){
	for(int i=1;i<=n;i++){
		for(int j=1;j<=n;j++){
			for(int k=1;k<=n;k++){
				if(g[i][j] > g[i][k] + g[k][i]){
					g[i][j] = g[i][k] + g[k][i];
				}
			}
		}
	}
}

int main(){
	init();
	floyd();
	return 0;
}

SPFA

void spfa(int s){
	memset(inq,0,sizeof(inq));
	memset(d,0x3f3f3f3f,sizeof(d));
	d[s] = 0;
	inq[s] = true;
	queue<int> q;
	q.push(s);
	while(!q.empty()){
		int u = q.front();
		q.pop();
		inq[u] = false;
		for(int i=0;i<v[u].size();i++){
			int vv = v[u][i].x;
			if(d[vv] >  d[u] + v[u][i].w){
				d[vv] = d[u] + v[u][i].w;
				if(!inq[vv]){
					q.push(vv);
					inq[vv] = 1;
				}
			}
		}
	}
}

dijkstra

bool dijkstra(int s){
	memset(vst,0,sizeof(vst));
	memset(dist,0x3f3f3f3f,sizeof(dist));
	dist[s] = 0;
	for(int i=0;i<n;i++){
		int v,min_w = inf;
		for(int j=0;j<n;j++){
			if(!vst[j] && dist[j] < min_w){
				min_w = dist[j];
				v = j;
			}
		}
		if(min_w == inf){ //有顶点无法从原点到达 
			return false;
		}
		vst[v] = true;
		for(int j=p[v];j!=-1;j=e[j].next){
			int x = e[j].v;
			if(!vst[x] && dist[v] + e[j].w < dist[x]){
				dist[x] = dist[v] + e[j].w;
			}
		}
	}
}

bool dijkstra(int s){
	memset(vst,0,sizeof(vst));
	memset(dist,0x3f3f3f3f,sizeof(dist));
	priority_queue<node> min_heap;
	dist[s] = 0;
	min_heap.push(node(s,0));
	while(!min_heap.empty()){
		int v = min_heap.top().u;
		min_heap.pop();
		if(vst[v]) continue;
		vst[v] = true;
		for(int j=p[v];j!=-1;j++){
			int x = e[j].v;
			if(!vst[x] && dist[v] + e[j].w < dist[x]){
				dist[x] = dist[v] + e[j].w;
				min_heap.push(node(x,dist[x]));
			}
		}
	}
	return true;
} 

4.tarjan

#include<bits/stdc++.h>
using namespace std;


const int maxn = 1e5+5;
vector<int> g[maxn];
int belong[maxn],scc = 0;
int idx = 0;
int dfn[maxn],low[maxn];
bool ins[maxn];
stack<int> s;

void tarjan(int u){
	dfn[u] = low[u] = ++idx;
	s.push(u);
	ins[u] = 1;
	for(int i=0;i<g[u].size();i++){
		int v = g[u][i];
		if(!dfn[v]){
			tarjan(v);
			low[u] = min(low[u],low[v]);
		}else if(ins[v]){
			low[u] = min(low[u],dfn[v]);
		}
	}
	int vv;
	if(dfn[u] == low[u]){
		++scc;
		do{
			vv = s.top();
			belong[vv] = scc;
			ins[vv] = false;
			s.pop();
		}while(vv != u);
	}
}


int main(){
	int n,m;
	cin>>n>>m;
	memset(dfn,0,sizeof(dfn));
	memset(low,0,sizeof(low));
	idx = 0;
	for(int i=1;i<=m;i++){
		int u,v;
		cin>>u>>v;
		g[u].push_back(v);
	}
	for(int i=1;i<=n;i++){
		if(!dfn[i]){
			tarjan(i);
		}
	}
	for(int i=1;i<=scc;i++){
		cout<<"block "<<i<<": ";
		for(int j=1;j<=n;j++){
			if(belong[j] == i){
				cout<<j<<" ";
			}
		}
		cout<<endl;
	}
	return 0;
}
/*
4 4
1 2
2 3
3 1
2 4
*/