POJ--1300 -- Door Man [Determining Euler's path], Euler's path

POJ--1300 -- Door Man [Determining Euler's path], Euler's path

Link: http://poj.org/problem? Id = 1300

There are n rooms. Each room has several doors connected to other rooms. The butler starts from room m and wants to return to his residence (0 ), ask if there is a way to walk all the doors without repeating them.

Idea: Determine whether there is an Euler path, based on the nature of Euler's path and Euler's loop. There are two situations: one is the Euler loop, where the number of doors in all rooms is an even number, and the initial room is not 0 at this time, there is a required path, if the initial value is 0, no. The other is the Euler's path. There are only an odd number of doors in the two rooms, and the remaining two are even numbers. One of the two rooms is 0, the other is the current starting point, and the start point cannot be 0, the required path also exists. Otherwise, the path does not exist.

It hurts

#include<cstring>#include<string>#include<fstream>#include<iostream>#include<iomanip>#include<cstdio>#include<cctype>#include<algorithm>#include<queue>#include<map>#include<set>#include<vector>#include<stack>#include<ctime>#include<cstdlib>#include<functional>#include<cmath>using namespace std;#define PI acos(-1.0)#define MAXN 500100#define eps 1e-7#define INF 0x7FFFFFFF#define LLINF 0x7FFFFFFFFFFFFFFF#define seed 131#define mod 1000000007#define ll long long#define ull unsigned ll#define lson l,m,rt<<1#define rson m+1,r,rt<<1|1int in[30],out[30];char s[20],s1[200];int main(){    int i,j;    int m,n;    int a,flag,ans,fk;    while(scanf("%s",s)!=EOF){        if(s[0]=='E'&&strlen(s)>5)  break;        scanf("%d%d",&m,&n);        getchar();        ans = 0;        flag = 0;        fk = 0;        memset(in,0,sizeof(in));        for(i=0;i<n+1;i++){            gets(s1);            int p = 0;            while(sscanf(s1+p,"%d",&a)==1){                ans++;                in[a]++;                in[i]++;                while(s1[p]!='\0'&&s1[p]!=' ')  p++;                while(s1[p]!='\0'&&s1[p]==' ')  p++;            }        }        for(i=0;i<n;i++){            if(in[i]&1) flag++;        }        if(!flag){            if(!m)  fk = 1;            else    fk = 0;        }        else{            if(flag==2&&m!=0&&in[m]&1&&in[0]&1)   fk = 1;            else    fk = 0;        }        if(fk)  printf("YES %d\n",ans);        else    puts("NO");    }    return 0;}

What is the difference between the Euler's path and the Hamilton path?

Euler's path: if there is a path that passes through each side of the graph once and only once, this circuit is called Euler's path.

Hamilton path: given the distance (or weight) between n points and n points, a loop is obtained so that it passes through all points and passes through each point only once, the total distance (or total weight) of the entire loop (also known as path or border) is the smallest.

(Discrete Mathematics) What is the difference between the Euler's path (loop) and the Hamilton path (loop?

From their definitions, we can see the difference: Euler's path refers to the process of passing through each edge ......, While the Hamilton path is through every vertex ......