模板|欧拉路径与欧拉回路

1.判断无向图的欧拉回路和欧拉路径

#include <iostream>
#include <cstring>
using namespace std;
const int MAX_N = 100;
const int MAX_M = 10000;
struct edge {
    int v, next;
    int len;
} E[MAX_M];
int p[MAX_N], eid;
void init() {
    memset(p, -1, sizeof(p));
    eid = 0;
}
void insert(int u, int v) {
    E[eid].v = v;
    E[eid].next = p[u];
    p[u] = eid++;
}
int n,m;
int degree[MAX_N];
int cnt;
bool vis[MAX_N];
void dfs(int u){
    vis[u] = true;
    cnt++;
    for(int i=p[u];i!=-1;i=E[i].next){
        int v = E[i].v;
        if(!vis[v]){
            dfs(v);
        }
    }
}

void euler(){
    dfs(1);
    if(cnt!=n){
		cout<<"It doesn't have an euler path!"<<endl;
        return;
    }
    int cntodd = 0;
    for(int i=1;i<=n;i++){
		if(degree[i]%2 == 1){
            cntodd++;
        }
    }
    if(cntodd == 0){
		cout<<"It has an euler circuit!"<<endl;
    }else if(cntodd == 2){
        cout<<"It has an euler path!"<<endl;
    }else{
		cout<<"It doesn't have an euler path!"<<endl;
    }
}


int main() {
    init();
    memset(degree,0,sizeof(degree));
    cin>>n>>m;
    for(int i=0;i<m;i++){
        int u,v;
        cin>>u>>v;
        insert(u,v);
        insert(v,u);
        degree[u]++;
        degree[v]++;
    }
    euler();
    return 0;
}

2.判断无向图的欧拉回路和欧拉路径

#include <iostream>
#include <cstring>
using namespace std;
const int MAX_N = 100;
const int MAX_M = 10000;
struct edge {
    int v, next;
    int len;
} E[MAX_M];
int p[MAX_N], eid;
void init() {
    memset(p, -1, sizeof(p));
    eid = 0;
}
void insert(int u, int v) {
    E[eid].v = v;
    E[eid].next = p[u];
    p[u] = eid++;
}

int n,m;
int degree[MAX_N];

int euler(){
    int first = 0,last = 0;
    for(int i = 1;i <= n;i++){
        if(degree[i]<-1 || degree[i] > 1){
            cout<<"It doesn't have an euler path!"<<endl;
            return 0;
        }else if(degree[i] == -1){
            if(first != 0){
                cout<<"It doesn't have an euler path!"<<endl;
                return 0;
            }else{
                first = i;
            }
        }else if(degree[i] == 1){
			if(last != 0 ){
                cout<<"It doesn't have an euler path!"<<endl;
                return 0;
            }else{
                last = i;
            }
        }
    }
    if(first == 0 && last == 0){
        cout<<"It has an eluer circuit!"<<endl;
        return 1;
    }else if(first != 0 && last != 0){
        cout<<"It has an euler path!"<<endl;
        return first;
    }
}

int main() {
    init();
    memset(degree,0,sizeof(degree));
    cin>>n>>m;
    for(int i=0;i<m;i++){
        int u,v;
        cin>>u>>v;
        insert(u,v);
        degree[u]--;
        degree[v]++;
    }
    euler();
    return 0;
}

3.找出有向图的欧拉回路

#include <iostream>
#include <cstring>
#include <stack>
using namespace std;
const int MAX_N = 100;
const int MAX_M = 10000;
struct edge {
    int v, next;
    int len;
} E[MAX_M];
int p[MAX_N], eid;
void init() {
    memset(p, -1, sizeof(p));
    eid = 0;
}
void insert(int u, int v) {
    E[eid].v = v;
    E[eid].next = p[u];
    p[u] = eid++;
}
int n, m;
int degree[MAX_N];
int euler() {
    int first = 0, last = 0;
    for (int i = 1; i <= n; i++) {
        if (degree[i] < -1 || degree[i] > 1) {
            return 0;
        } else if (degree[i] == -1) {
            if (first != 0) {
                return 0;
            } else {
                first = i;
            }
        } else if (degree[i] == 1) {
            if (last != 0) {
                return 0;
            } else {
                last = i;
            }
        }
    }
    if (first == 0 && last == 0) {
        return 1;
    } else if (first != 0 && last != 0) {
        return first;
    } else {
        return 0;
    }
}

stack<int> path;
void dfs(int u){
	while(p[u] != -1){
        int v = E[p[u]].v;
        p[u] = E[p[u]].next;//删除这条边就是把p[u]赋值位E[p[u]].next
        dfs(v);
    }
    path.push(u);
}

bool euler_find(){
    int start;
    start = euler();
    if(start == 0){
        return false;
    }else{
        dfs(start);
        return path.size() == m + 1;
    }
}

int main() {
    init();
    memset(degree,0,sizeof(degree));
    cin>>n>>m;
    for(int i=0;i<m;i++){
        int u,v;
        cin>>u>>v;
        insert(u,v);
        degree[u]--;
        degree[v]++;
	}
    if(!euler_find()){
        cout<<"It doesn't have an euler path!"<<endl;
    }else{
        while(!path.empty()){
            cout<<path.top()<<endl;
            path.pop();
        }
    }
    return 0;
}