Algorithm review--Euler circuit (uoj117)

Topic:

Exercises

Euler's Loop correlation theorem (see other materials for definitions and certifications):

1. Euler circuit

(1) The direction graph: All points of the degree is equal to the degree of the graph is Eulerian graph (existence of the Euler circuit) necessary and sufficient conditions.

(2) No direction diagram: The degree of all points is even the necessary and sufficient conditions for the graph to be Eulerian graph (existence of the Euler circuit).

2. Euler pathway

(1) The direction of the graph: In addition to two points (one point out of the degree of +1==, the other point into the degree of +1==) the other point out degree is equal to the degree of the graph is a semi-Eulerian graph (existence Oraton road) necessary and sufficient conditions.

(2) No direction diagram: In addition to two points (two points are odd) the other point of the degree is even for the figure is half Eulerian graph (existence Oraton Road) sufficient and necessary conditions.

The above theorem is used to determine whether a Euler circuit or a path exists.

Then there are two inferences:

Yes, that's it. • Back to this problem, a very naked template problem ... However, the data of the Uoj are taught to behave ·

Pay attention to the, or it will time out. Optimized with cur similar to network streams (see Code for details)

Code:

#include <iostream>#include<cstdio>#include<cstdlib>#include<cmath>#include<ctime>#include<cctype>#include<cstring>#include<string>#include<algorithm>using namespacestd;Const intn=1e5+5;Const intm=5e5+5;intfirst[n],go[m*2],next[m*2],tot=0;intn,m,t,ru[n],chu[n],stack[m*2],cnt;BOOLVisit[m];inlinevoidComb (intAintb) {next[++tot]=first[a],first[a]=tot,go[tot]=b;} InlinevoidDFS1 (intu) {   for(int&e=first[u];e;e=Next[e]) {    if(!Visit[e]) {Visit[e]=true; if(e%2==1) Visit[e+1]=true; Elsevisit[e-1]=true; intt=e;      DFS1 (Go[e]); stack[++cnt]=T; }}}inlinevoidDFS2 (intu) {   for(int&e=first[u];e;e=Next[e]) {    if(!Visit[e]) {Visit[e]=true; intt=e;      DFS2 (Go[e]); stack[++cnt]=T; }  }}intMain () {//freopen ("a.in", "R", stdin);scanf"%d",&T); intb; scanf ("%d%d",&n,&m); if(t==1)//the situation of the non-direction diagram  {      for(intI=1; i<=m;i++) {scanf ("%d%d",&a,&b);      Comb (A, b);      Comb (b,a); RU[B]++; Chu[a]++; }     for(intI=1; i<=n;i++)      if((Ru[i]+chu[i])%2==1) {cout<<"NO"<<Endl; return 0; }     for(intI=1; i<=n;i++)    {      if(First[i]) {DFS1 (i);  Break; }    }    if(cnt!=m) {cout<<"NO"<<Endl; return 0; } cout<<"YES"<<Endl;  for(inti=cnt;i>=1; i--)    {        if(stack[i]%2==1) cout<< (stack[i]+1)/2<<" "; Elsecout<<stack[i]/2*(-1) <<" "; }    return 0; }  Else  {     for(intI=1; i<=m;i++) {scanf ("%d%d",&a,&b);      Comb (A, b); RU[B]++; Chu[a]++; }     for(intI=1; i<=n;i++)      if(ru[i]!=Chu[i]) {cout<<"NO"<<Endl; return 0; }      for(intI=1; i<=n;i++)     {       if(First[i]) {DFS2 (i);  Break; }     }    if(cnt!=m) {cout<<"NO"<<Endl; return 0; } cout<<"YES"<<Endl;  for(inti=cnt;i>=1; i--) cout<<stack[i]<<" "; return 0; }}

Algorithm review--Euler circuit (uoj117)