Bellman-Ford綆楁硶鎬濇兂
Bellman-Ford綆楁硶鑳藉湪鏇存櫘閬嶇殑鎯呭喌涓嬶紙瀛樺湪璐熸潈杈癸級瑙ｅ喅鍗曟簮鐐規(guī)渶鐭礬寰勯棶棰樸傚浜庣粰瀹氱殑甯︽潈錛堟湁鍚戞垨鏃犲悜錛夊浘 G=錛?/span>V,E錛夛紝鍏舵簮鐐逛負(fù)s錛屽姞鏉冨嚱鏁?/span> w鏄?/span> 杈歸泦 E 鐨勬槧灝勩傚鍥?/span>G榪愯Bellman-Ford綆楁硶鐨勭粨鏋滄槸涓涓竷?yōu)當(dāng)鍊鹼紝琛ㄦ槑鍥句腑鏄惁瀛樺湪鐫涓涓粠婧愮偣s鍙揪鐨勮礋鏉冨洖璺傝嫢涓嶅瓨鍦ㄨ繖鏍風(fēng)殑鍥炶礬錛岀畻娉曞皢緇欏嚭浠庢簮鐐?/span>s鍒?/span> 鍥?/span>G鐨勪換鎰忛《鐐?/span>v鐨勬渶鐭礬寰?/span>d[v]銆?/span>
Bellman-Ford綆楁硶嫻佺▼鍒嗕負(fù)涓変釜闃舵錛?/span>
錛?/span>1錛?/span> 鍒濆鍖栵細(xì)灝嗛櫎婧愮偣澶栫殑鎵鏈夐《鐐圭殑鏈鐭窛紱諱及璁″?/span> d[v] ←+∞, d[s] ←0;
錛?/span>2錛?/span> 榪唬姹傝В錛氬弽澶嶅杈歸泦E涓殑姣忔潯杈硅繘琛屾澗寮涙搷浣滐紝浣垮緱欏剁偣闆?/span>V涓殑姣忎釜欏剁偣v鐨勬渶鐭窛紱諱及璁″奸愭閫艱繎鍏舵渶鐭窛紱伙紱錛堣繍琛?/span>|v|-1嬈★級
錛?/span>3錛?/span> 媯楠岃礋鏉冨洖璺細(xì)鍒ゆ柇杈歸泦E涓殑姣忎竴鏉¤竟鐨勪袱涓鐐規(guī)槸鍚︽敹鏁涖傚鏋滃瓨鍦ㄦ湭鏀舵暃鐨勯《鐐癸紝鍒欑畻娉曡繑鍥?/span>false錛岃〃鏄庨棶棰樻棤瑙ｏ紱鍚﹀垯綆楁硶榪斿洖true錛屽茍涓斾粠婧愮偣鍙揪鐨勯《鐐?/span>v鐨勬渶鐭窛紱諱繚瀛樺湪 d[v]涓?/span>
綆楁硶鎻忚堪濡備笅錛?br>
2 E(G):杈圭殑闆嗗悎
3 S: 婧愰《鐐?br> 4 Dis[i]:琛ㄧずs鍒癷鐨勬渶鐭窛紱?鍒濆涓?/span>+∞
5 D[s]=0;
6 for (int i=0;i<|v|-1;i++)
7 for each (u,v)∈E(G)
8 if(dis[u]+w(u,v)<dis[v]
9 dis[v]=dis[u]+w(u,v);
10 for each (u,v)∈E(G)
11 if(d[v]>d[u]+w(u,v)
12 return false;//榪斿洖false,璇存槑瀛樺湪璐熸潈鍥炶礬
13 return true;
14
涓嬮潰緇欏嚭鎻忚堪鎬ц瘉鏄庯細(xì)
棣栧厛鎸囧嚭錛屽浘鐨勪換鎰忎竴鏉℃渶鐭礬寰勬棦涓嶈兘鍖呭惈璐熸潈鍥炶礬錛屼篃涓嶄細(xì)鍖呭惈姝ｆ潈鍥炶礬錛屽洜姝ゅ畠鏈澶氬寘鍚?/span>|v|-1鏉¤竟銆?/span>
鍏舵錛屼粠婧愮偣s鍙揪鐨勬墍鏈夐《鐐瑰鏋?/span> 瀛樺湪鏈鐭礬寰勶紝鍒欒繖浜涙渶鐭礬寰勬瀯鎴愪竴涓互s涓烘牴鐨勬渶鐭礬寰勬爲(wèi)銆?/span>Bellman-Ford綆楁硶鐨勮凱浠ｆ澗寮涙搷浣滐紝瀹為檯涓婂氨鏄寜欏剁偣璺濈s鐨勫眰嬈★紝閫愬眰鐢熸垚榪欐５鏈鐭礬寰勬爲(wèi)鐨勮繃紼嬨?/span>
鍦ㄥ姣忔潯杈硅繘琛?/span>1閬嶆澗寮涚殑鏃跺欙紝鐢熸垚浜嗕粠s鍑哄彂錛屽眰嬈¤嚦澶氫負(fù)1鐨勯偅浜涙爲(wèi)鏋濄備篃灝辨槸璇達(dá)紝鎵懼埌浜嗕笌s鑷沖鏈?/span>1鏉¤竟鐩歌仈鐨勯偅浜涢《鐐圭殑鏈鐭礬寰勶紱瀵規(guī)瘡鏉¤竟榪涜絎?/span>2閬嶆澗寮涚殑鏃跺欙紝鐢熸垚浜嗙2灞傛鐨勬爲(wèi)鏋濓紝灝辨槸璇存壘鍒頒簡緇忚繃2鏉¤竟鐩歌繛鐨勯偅浜涢《鐐圭殑鏈鐭礬寰?/span>……銆傚洜涓烘渶鐭礬寰勬渶澶氬彧鍖呭惈|v|-1 鏉¤竟錛屾墍浠ワ紝鍙渶瑕佸驚鐜?/span>|v|-1 嬈°?/span>
姣忓疄鏂戒竴嬈℃澗寮涙搷浣滐紝鏈鐭礬寰勬爲(wèi)涓婂氨浼?xì)鏈変竴灞傞《鐐硅揪鍒板叾鏈鐭窛紱伙紝姝ゅ悗榪欏眰欏剁偣鐨勬渶鐭窛紱誨煎氨浼?xì)涓鐩翠繚鎸佷笉鍙橈紝涓嶅啀鍙楀悗緇澗寮涙搷浣滅殑褰卞搷銆傦紙浣嗘槸錛屾瘡嬈¤繕瑕佸垽鏂澗寮涳紝榪欓噷嫻垂浜嗗ぇ閲忕殑鏃墮棿錛屾庝箞浼樺寲錛熷崟綰殑浼樺寲鏄惁鍙錛燂級
濡傛灉娌℃湁璐熸潈鍥炶礬錛岀敱浜庢渶鐭礬寰勬爲(wèi)鐨勯珮搴︽渶澶氬彧鑳芥槸|v|-1錛屾墍浠ユ渶澶氱粡榪?/span>|v|-1閬嶆澗寮涙搷浣滃悗錛屾墍鏈変粠s鍙揪鐨勯《鐐瑰繀灝嗘眰鍑烘渶鐭窛紱匯傚鏋?/span> d[v]浠嶄繚鎸?/span> +∞錛屽垯琛ㄦ槑浠?/span>s鍒?/span>v涓嶅彲杈俱?/span>
濡傛灉鏈夎礋鏉冨洖璺紝閭ｄ箞絎?/span> |v|-1 閬嶆澗寮涙搷浣滀粛鐒朵細(xì)鎴愬姛錛岃繖鏃訛紝璐熸潈鍥炶礬涓婄殑欏剁偣涓嶄細(xì)鏀舵暃銆?/span>
Bellman-Ford鐨勯槦鍒楀疄鐜?/span>SPFA
綆楁硶澶ц嚧嫻佺▼鏄敤涓涓槦鍒楁潵榪涜緇存姢銆傚垵濮嬫椂灝嗘簮鍔犲叆闃熷垪銆傛瘡嬈′粠闃熷垪涓彇鍑轟竴涓厓绱狅紝騫跺鎵鏈変笌浠栫浉閭?cè)潥勭偣杩涜?/span>鏉懼紱錛岃嫢鏌愪釜鐩擱偦鐨勭偣鏉懼紱鎴愬姛錛屽垯灝嗗叾鍏ラ槦銆傜洿鍒伴槦鍒椾負(fù)絀烘椂綆楁硶緇撴潫銆?/span>
榪欎釜綆楁硶錛岀畝鍗曠殑璇村氨鏄槦鍒椾紭鍖栫殑bellman-ford,鍒╃敤浜嗘瘡涓偣涓嶄細(xì)鏇存柊嬈℃暟澶鐨勭壒鐐瑰彂鏄庣殑姝ょ畻娉?/span>
SPFA鈥斺擲hortest Path Faster Algorithm錛屽畠鍙互鍦?/span>O(kE)鐨勬椂闂村鏉傚害鍐呮眰鍑烘簮鐐瑰埌鍏朵粬鎵鏈夌偣鐨勬渶鐭礬寰勶紝鍙互澶勭悊璐熻竟銆?/span>SPFA鐨勫疄鐜扮敋鑷蟲瘮Dijkstra鎴栬?/span>Bellman_Ford榪樿綆鍗曪細(xì)
璁?/span>Dist浠ｈ〃S鍒?/span>I鐐圭殑褰撳墠鏈鐭窛紱伙紝Fa浠ｈ〃S鍒?/span>I鐨勫綋鍓嶆渶鐭礬寰勪腑I鐐逛箣鍓嶇殑涓涓偣鐨勭紪鍙楓傚紑濮嬫椂Dist鍏ㄩ儴涓?/span>+∞錛屽彧鏈?/span>Dist[S]=0錛?/span>Fa鍏ㄩ儴涓?/span>0銆?/span>
緇存姢涓涓槦鍒楋紝閲岄潰瀛樻斁鎵鏈夐渶瑕佽繘琛岃凱浠ｇ殑鐐廣傚垵濮嬫椂闃熷垪涓彧鏈変竴涓偣S銆傜敤涓涓竷?yōu)當(dāng)鏁熬l勮褰曟瘡涓偣鏄惁澶勫湪闃熷垪涓?/span>
姣忔榪唬錛屽彇鍑洪槦澶寸殑鐐?/span>v錛屼緷嬈℃灇涓句粠v鍑哄彂鐨勮竟v->u錛岃杈圭殑闀垮害涓?/span>len錛屽垽鏂?/span>Dist[v]+len鏄惁灝忎簬Dist[u]錛岃嫢灝忎簬鍒欐敼榪?/span>Dist[u]錛屽皢Fa[u]璁頒負(fù)v錛屽茍涓旂敱浜?/span>S鍒?/span>u鐨勬渶鐭窛紱誨彉灝忎簡錛屾湁鍙兘u鍙互鏀硅繘鍏跺畠鐨勭偣錛屾墍浠ヨ嫢u涓嶅湪闃熷垪涓紝灝卞皢瀹冩斁鍏ラ槦灝俱傝繖鏍蜂竴鐩磋凱浠ｄ笅鍘葷洿鍒伴槦鍒楀彉絀猴紝涔熷氨鏄?/span>S鍒版墍鏈夌殑鏈鐭窛紱婚兘紜畾涓嬫潵錛岀粨鏉熺畻娉曘傝嫢涓涓偣鍏ラ槦嬈℃暟瓚呰繃n錛屽垯鏈夎礋鏉冪幆銆?/span>
SPFA 鍦ㄥ艦寮忎笂鍜屽搴︿紭鍏堟悳绱㈤潪甯哥被浼鹼紝涓嶅悓鐨勬槸瀹藉害浼樺厛鎼滅儲涓竴涓偣鍑轟簡闃熷垪灝變笉鍙兘閲嶆柊榪涘叆闃熷垪錛屼絾鏄?/span>SPFA涓竴涓偣鍙兘鍦ㄥ嚭闃熷垪涔嬪悗鍐嶆琚斁鍏ラ槦鍒楋紝涔熷氨鏄竴涓偣鏀硅繘榪囧叾瀹冪殑鐐逛箣鍚庯紝榪囦簡涓孌墊椂闂村彲鑳芥湰韜鏀硅繘錛屼簬鏄啀嬈＄敤鏉ユ敼榪涘叾瀹冪殑鐐癸紝榪欐牱鍙嶅榪唬涓嬪幓銆傝涓涓偣鐢ㄦ潵浣滀負(fù)榪唬鐐瑰鍏跺畠鐐硅繘琛屾敼榪涚殑騫沖潎嬈℃暟涓?/span>k錛屾湁鍔炴硶璇佹槑瀵逛簬閫氬父鐨勬儏鍐碉紝k鍦?/span>2宸﹀彸
2 闃熷垪 queue<int> q;
3 Inque[i] 鏍囪i鏄惁鍦ㄩ槦鍒楅噷錛屽垵濮嬫墍鏈変負(fù)false
4 S: 婧愰《鐐?br> 5 Dis[i]:琛ㄧずs鍒癷鐨勬渶鐭窛紱?鍒濆涓?/span>+∞
6
7 Dis[s]=0;
8 q.push(s);
9 inque[s]=true;
10 while(q.size()>0)
11 {
12 Int t=q.front();
13 q.pop();
14 inque[t]=false;
15 for t’s adjacent vertex v
16 if(dis[t]+w(t,v)<dis[v])
17 {
18 Dis[v]=dis[t]+w(t,v);
19 If(!inque[v])
20 {
21 q.push(v);
22 inque[v]=true;
23 }
24 }
25
26 }
27
USACO 3.2 Sweet Butter
Sweet Butter
Farmer John has discovered the secret to making the sweetest butter in all of Wisconsin: sugar. By placing a sugar cube out in the pastures, he knows the N (1 <= N <= 500) cows will lick it and thus will produce super-sweet butter which can be marketed at better prices. Of course, he spends the extra money on luxuries for the cows.
FJ is a sly farmer. Like Pavlov of old, he knows he can train the cows to go to a certain pasture when they hear a bell. He intends to put the sugar there and then ring the bell in the middle of the afternoon so that the evening's milking produces perfect milk.
FJ knows each cow spends her time in a given pasture (not necessarily alone). Given the pasture location of the cows and a description of the paths the connect the pastures, find the pasture in which to place the sugar cube so that the total distance walked by the cows when FJ rings the bell is minimized. FJ knows the fields are connected well enough that some solution is always possible.
PROGRAM NAME: butter
INPUT FORMAT
- Line 1: Three space-separated integers: N, the number of pastures: P (2 <= P <= 800), and the number of connecting paths: C (1 <= C <= 1,450). Cows are uniquely numbered 1..N. Pastures are uniquely numbered 1..P.
- Lines 2..N+1: Each line contains a single integer that is the pasture number in which a cow is grazing. Cow i's pasture is listed on line i+1.
- Lines N+2..N+C+1: Each line contains three space-separated integers that describe a single path that connects a pair of pastures and its length. Paths may be traversed in either direction. No pair of pastures is directly connected by more than one path. The first two integers are in the range 1..P; the third integer is in the range (1..225).
SAMPLE INPUT (file butter.in)
3 4 5 2 3 4 1 2 1 1 3 5 2 3 7 2 4 3 3 4 5
INPUT DETAILS
This diagram shows the connections geometrically: 
OUTPUT FORMAT
- Line 1: A single integer that is the minimum distance the cows must walk to a pasture with a sugar cube.
SAMPLE OUTPUT (file butter.out)
8 OUTPUT DETAILS: Putting the cube in pasture 4 means: cow 1 walks 3 units; cow 2 walks 5 units; cow 3 walks 0 units -- a total of 8.
瑙ｇ瓟:
榪欓亾棰樼洿鎺ョ敤涓鑸殑Dijkstra綆楁硶O(P2),涓鍏辮皟鐢≒嬈ijkstra,鎬諱綋澶嶆潅搴(P3),p=800,鑲畾瓚呮椂,鍦ㄨ繖閲岀敤SPFA綆楁硶,O(k*c),k鏄?宸﹀彸鐨勫父鏁?
璋冪敤p嬈?鏁翠綋澶嶆潅搴(p*c*k).鍦?.2縐掑彲浠ュ緱鍑鴻В.闄勫師鐮?/pre>/*
ID: kuramaw1
PROG: butter
LANG: C++
*/
#include <fstream>
#include <queue>
using std::ifstream;
using std::ofstream;
using std::queue;
using std::endl;
using std::vector;
#define MAX_EDGE 1451
#ifndef INT_MAX
#define INT_MAX 2147483647
#endif
struct graph
{
struct Edge
{
short n; // next adjacent edge
short v; // to which vertex
short c; // weight
Edge(const short _n=-1,const short _v=-1,const short _c=0):n(-n),v(_v),c(-c)
{
}
Edge(const Edge &e):n(e.n),v(e.v),c(e.c)
{
}
Edge & operator =(const Edge &e)
{
n=e.n;
v=e.v;
c=e.c;
return *this;
}
};
struct Ver
{
short w;
short e;//frist e
Ver(const short _w=0,const short _e=-1):w(_w),e(_e)
{
}
Ver(const Ver &v):w(v.w),e(v.e)
{
}
Ver & operator =(const Ver &v)
{
w=v.w;
e=v.e;
return *this;
}
};
typedef std::vector<Edge> EdgeSet;
typedef std::vector<Ver> VertSet;
VertSet _V;
EdgeSet _E;
// interfaces
inline void Reset(const short &n)
{
_V.resize(n);
_E.clear();
_E.reserve(MAX_EDGE);
}
inline void IncVetWei(const short &i)
{
_V[i].w++;
}
inline void InsertEdge(short u, short v, short c)
{
Edge e;
e.v = v, e.c = c, e.n = _V[u].e;
_V[u].e = _E.size();
_E.push_back(e);
e.v = u, e.c = c, e.n = _V[v].e;
_V[v].e = _E.size();
_E.push_back(e);
}
int short_dis_sum(const short &s)
{
vector<int> dis;
queue<short> q;
vector<bool> b_in_que;
dis.resize(_V.size(),INT_MAX);
b_in_que.resize(_V.size(),false);
q.push(s);
dis[s]=0;
b_in_que[s]=true;
while(q.size()>0)
{
short t=q.front();
q.pop();
b_in_que[t]=false;
short e=_V[t].e;
while(e!=-1)
{
Edge &edge=_E[e];
if(dis[t]+edge.c<dis[edge.v])
{
dis[edge.v]=dis[t]+edge.c;
if(!b_in_que[edge.v])
{
q.push(edge.v);
b_in_que[edge.v]=true;
}
}
e=edge.n;
}
}
int sum(0);
for(short i=0;i<dis.size();i++)
if(_V[i].w>0)
{
sum+=_V[i].w*dis[i];
}
return sum;
}
};
graph g;
short n,p,c;
int main()
{
ifstream in("butter.in");
in>>n>>p>>c;
g.Reset(p);
for(short i=0;i<n;i++)
{
short v;
in>>v;
g.IncVetWei(v-1);
}
for(short i=0;i<c;i++)
{
short u,v,w;
in>>u>>v>>w;
g.InsertEdge(u-1,v-1,w);
}
in.close();
int min_dis=INT_MAX;
for(int i=0;i<p;i++)
{
int dis=g.short_dis_sum(i);
if(dis<min_dis)
min_dis=dis;
}
//out
ofstream out("butter.out");
out<<min_dis<<endl;
out.close();
}
]]>
緇欏畾涓涓棤鍚戝浘G,涓鏉¤礬寰勭粡榪囧浘G鐨勬瘡涓鏉¤竟,涓斾粎緇忚繃涓嬈?span lang=EN-US>,榪欐潯璺緞縐頒負(fù)嬈ф媺璺緞(Eulerian Tour),濡傛灉嬈ф媺璺緞鐨勮搗濮嬮《鐐瑰拰緇堢偣鏄悓涓欏剁偣,鍒欑О涓烘鎷夊洖璺?span lang=EN-US>(Eulerian circuit).
綆楁硶:
鏃犲悜鍥?span lang=EN-US>G瀛樺湪嬈ф媺璺緞鐨勫厖瑕佹潯浠?span lang=EN-US>:鍥?span lang=EN-US>G鏄繛閫氱殑,涓旇嚦澶氶櫎涓や釜鐐瑰(鍙互涓?span lang=EN-US>0涓?span lang=EN-US>,榪炴帴鍥句笉鍙兘鏈変笖浠呮湁涓涓《鐐圭殑搴︿負(fù)濂囨暟)鍏跺畠鎵鏈夐《鐐圭殑搴︿負(fù)鍋舵暟.
鏃犲悜鍥?span lang=EN-US>G瀛樺湪嬈ф媺鍥炶礬鐨勫厖瑕佹潯浠?span lang=EN-US>:鍥?span lang=EN-US>G鏄繛閫氱殑涓旀墍鏈夐《鐐圭殑搴︿負(fù)鍋舵暟;
綆楁硶鎻忚堪:
2 pos: int
3
find_eulerian_circuit()
4 {
5 pos=0;
6 find_circuit(1);
7 }
8
find_eulerian_tour()
9 {
10 find a vertex i ,the degree of which is odd
11 pos=0;
12 find_circuit(i);
13 }
14
find_circuit(vertex i)
15 {
16 while(exist j,(i,j) is the edge of G)
17 {
18 remove edge(i,j);
19 find_circuit(j);
20 }
21 tour[pos++]=i;
22 }
23
USACO 3.2 Riding the fence,灝辨槸涓涓眰嬈ф媺璺緞鐨勯棶棰?span>.
闂鎻忚堪:
Farmer John owns a large number of fences that must be repaired annually. He traverses the fences by riding a horse along each and every one of them (and nowhere else) and fixing the broken parts.
Farmer John is as lazy as the next farmer and hates to ride the same fence twice. Your program must read in a description of a network of fences and tell Farmer John a path to traverse each fence length exactly once, if possible. Farmer J can, if he wishes, start and finish at any fence intersection.
Every fence connects two fence intersections, which are numbered inclusively from 1 through 500 (though some farms have far fewer than 500 intersections). Any number of fences (>=1) can meet at a fence intersection. It is always possible to ride from any fence to any other fence (i.e., all fences are "connected").
Your program must output the path of intersections that, if interpreted as a base 500 number, would have the smallest magnitude.
There will always be at least one solution for each set of input data supplied to your program for testing.
PROGRAM NAME: fence
INPUT FORMAT
|
Line 1: |
The number of fences, F (1 <= F <= 1024) |
|
Line 2..F+1: |
A pair of integers (1 <= i,j <= 500) that tell which pair of intersections this fence connects. |
SAMPLE INPUT (file fence.in)
9
1 2
2 3
3 4
4 2
4 5
2 5
5 6
5 7
4 6
OUTPUT FORMAT
The output consists of F+1 lines, each containing a single integer. Print the number of the starting intersection on the first line, the next intersection's number on the next line, and so on, until the final intersection on the last line. There might be many possible answers to any given input set, but only one is ordered correctly.
SAMPLE OUTPUT (file fence.out)
1
2
3
4
2
5
4
6
5
7
瑙ｇ瓟:綆鍗曠殑嬈ф媺璺緞闂,鍥鵑噰鐢ㄩ偦鎺ヨ〃瀛樺偍,闄勫師鐮?span>ID: kuramaw1
PROG: fence
LANG: C++
*/
#include <fstream>
using std::ifstream;
using std::ofstream;
using std::endl;
#ifdef _DEBUG
#include <iostream>
using std::cout;
#endif
#define MAX_V 500
#define MAX_EDGE 1025
#define MAX(a,b) ((a)>(b)?(a):(b))
struct grapha
{
struct node
{
short v;
node * next;
node(const short _v=-1):v(_v),next(NULL)
{
}
};
struct ver
{
node * r;
short d;//degree
ver():d(0)
{
r=new node();
}
~ver()
{
node * n=r;
while(n!=NULL)
{
node * t=n;
n=n->next;
delete t;
}
}
inline void add_neighbor(const short &v)
{
node * t=new node(v);
node * p=r;
node * n=p->next;
while(n!=NULL && v>n->v)
{
p=n;
n=n->next;
}
p->next=t;
t->next=n;
d++;
}
inline void remove_neighbor(const short &v)
{
node * p=r;
node * n=p->next;
while(n!=NULL && v!=n->v)
{
p=n;
n=n->next;
}
if(n!=NULL)
{
p->next=n->next;
delete n;
d--;
}
}
};
ver v[MAX_V];
short n;
short * tour;
short pos;
grapha():n(0),tour(NULL)
{
}
void add_edge(const short &_u,const short &_v)
{
v[_u-1].add_neighbor(_v-1);
v[_v-1].add_neighbor(_u-1);
short t=MAX(_u,_v);
if(t>n)
n=t;
}
void find_tour(const short &s)
{
while(v[s].d>0)
{
short j=v[s].r->next->v;
v[s].remove_neighbor(j);
v[j].remove_neighbor(s);
find_tour(j);
}
tour[pos++]=s+1;
}
void Eulerian_tour(short * _tour)
{
tour=_tour;
pos=0;
bool b=false;
for(int i=0;i<n;i++)
if(v[i].d % 2!=0)
{
find_tour(i);
b=true;
break;
}
if(!b)
find_tour(0);
}
};
grapha g;
short tour[MAX_EDGE];
short f;
int main()
{
ifstream in("fence.in");
in>>f;
for(short i=0;i<f;i++)
{
short u,v;
in>>u>>v;
g.add_edge(u,v);
}
//do
g.Eulerian_tour(tour);
//out
ofstream out("fence.out");
for(int i=f;i>=0;i--)
out<<tour[i]<<endl;
out.close();
}
]]>