UVA 1599 Ideal Path

  1 #include <bits/stdc++.h>
  2 using namespace std;
  3  
  4 #define INIT() ios::sync_with_stdio(false);cin.tie(0);cout.tie(0);
  5 #define Rep(i,n) for (int i = 0; i < (n); ++i)
  6 #define For(i,s,t) for (int i = (s); i <= (t); ++i)
  7 #define rFor(i,t,s) for (int i = (t); i >= (s); --i)
  8 #define ForLL(i, s, t) for (LL i = LL(s); i <= LL(t); ++i)
  9 #define rForLL(i, t, s) for (LL i = LL(t); i >= LL(s); --i)
 10 #define foreach(i,c) for (__typeof(c.begin()) i = c.begin(); i != c.end(); ++i)
 11 #define rforeach(i,c) for (__typeof(c.rbegin()) i = c.rbegin(); i != c.rend(); ++i)
 12  
 13 #define pr(x) cout << #x << " = " << x << "  "
 14 #define prln(x) cout << #x << " = " << x << endl
 15  
 16 #define LOWBIT(x) ((x)&(-x))
 17  
 18 #define ALL(x) x.begin(),x.end()
 19 #define INS(x) inserter(x,x.begin())
 20 #define UNIQUE(x) x.erase(unique(x.begin(), x.end()), x.end())
 21 #define REMOVE(x, c) x.erase(remove(x.begin(), x.end(), c), x.end()); // 删去 x 中所有 c 
 22 #define TOLOWER(x) transform(x.begin(), x.end(), x.begin(),::tolower);
 23 #define TOUPPER(x) transform(x.begin(), x.end(), x.begin(),::toupper);
 24  
 25 #define ms0(a) memset(a,0,sizeof(a))
 26 #define msI(a) memset(a,0x7f,sizeof(a))
 27 #define msM(a) memset(a,-1,sizeof(a))
 28 
 29 #define MP make_pair
 30 #define PB push_back
 31 #define ft first
 32 #define sd second
 33  
 34 template<typename T1, typename T2>
 35 istream &operator>>(istream &in, pair<T1, T2> &p) {
 36     in >> p.first >> p.second;
 37     return in;
 38 }
 39  
 40 template<typename T>
 41 istream &operator>>(istream &in, vector<T> &v) {
 42     for (auto &x: v)
 43         in >> x;
 44     return in;
 45 }
 46 
 47 template<typename T>
 48 ostream &operator<<(ostream &out, vector<T> &v) {
 49     Rep(i, v.size()) out << v[i] << " \n"[i == v.size()];
 50     return out;
 51 }
 52  
 53 template<typename T1, typename T2>
 54 ostream &operator<<(ostream &out, const std::pair<T1, T2> &p) {
 55     out << "[" << p.first << ", " << p.second << "]" << "\n";
 56     return out;
 57 }
 58 
 59 inline int gc(){
 60     static const int BUF = 1e7;
 61     static char buf[BUF], *bg = buf + BUF, *ed = bg;
 62     
 63     if(bg == ed) fread(bg = buf, 1, BUF, stdin);
 64     return *bg++;
 65 } 
 66 
 67 inline int ri(){
 68     int x = 0, f = 1, c = gc();
 69     for(; c<48||c>57; f = c==‘-‘?-1:f, c=gc());
 70     for(; c>47&&c<58; x = x*10 + c - 48, c=gc());
 71     return x*f;
 72 }
 73 
 74 template<class T>
 75 inline string toString(T x) {
 76     ostringstream sout;
 77     sout << x;
 78     return sout.str();
 79 }
 80 
 81 inline int toInt(string s) {
 82     int v;
 83     istringstream sin(s);
 84     sin >> v;
 85     return v;
 86 }
 87 
 88 //min <= aim <= max
 89 template<typename T>
 90 inline bool BETWEEN(const T aim, const T min, const T max) {
 91     return min <= aim && aim <= max;
 92 }
 93  
 94 typedef long long LL;
 95 typedef unsigned long long uLL;
 96 typedef pair< double, double > PDD;
 97 typedef pair< int, int > PII;
 98 typedef pair< int, PII > PIPII;
 99 typedef pair< string, int > PSI;
100 typedef pair< int, PSI > PIPSI;
101 typedef set< int > SI;
102 typedef set< PII > SPII;
103 typedef vector< int > VI;
104 typedef vector< double > VD;
105 typedef vector< VI > VVI;
106 typedef vector< SI > VSI;
107 typedef vector< PII > VPII;
108 typedef map< int, int > MII;
109 typedef map< int, string > MIS;
110 typedef map< int, PII > MIPII;
111 typedef map< PII, int > MPIII;
112 typedef map< string, int > MSI;
113 typedef map< string, string > MSS;
114 typedef map< PII, string > MPIIS;
115 typedef map< PII, PII > MPIIPII;
116 typedef multimap< int, int > MMII;
117 typedef multimap< string, int > MMSI;
118 //typedef unordered_map< int, int > uMII;
119 typedef pair< LL, LL > PLL;
120 typedef vector< LL > VL;
121 typedef vector< VL > VVL;
122 typedef priority_queue< int > PQIMax;
123 typedef priority_queue< int, VI, greater< int > > PQIMin;
124 const double EPS = 1e-8;
125 const LL inf = 0x7fffffff;
126 const LL infLL = 0x7fffffffffffffffLL;
127 const LL mod = 1e9 + 7;
128 const int maxN = 1e5 + 7;
129 const LL ONE = 1;
130 const LL evenBits = 0xaaaaaaaaaaaaaaaa;
131 const LL oddBits = 0x5555555555555555;
132 
133 struct Edge{
134     int from, to, c;
135 };
136 
137 int m, n, k;
138 vector< Edge > e;
139 VI v[maxN];
140 // path[i] 表示第 i 条边能取到的颜色的最小值 
141 int d[maxN], path[maxN];
142 bool vis[maxN];
143 
144 inline void addEdge(Edge &x) {
145     v[x.from].PB(e.size());
146     e.PB(x);
147     swap(x.from, x.to);
148     v[x.from].PB(e.size());
149     e.PB(x);
150 }
151 
152 inline void bfs1() {
153     queue< int > Q;
154     d[n] = 0;
155     ms0(vis);
156     vis[n] = 1;
157     Q.push(n);
158     
159     while(!Q.empty()) {
160         int tmp = Q.front(); Q.pop();
161         
162         foreach(i, v[tmp]) {
163             Edge &x = e[*i];
164             if(vis[x.to]) continue;
165             vis[x.to] = 1;
166             
167             d[x.to] = d[tmp] + 1;
168             
169             if(x.to == 1) return;
170             Q.push(x.to);
171         }
172     }
173 }
174 
175 inline void bfs2() {
176     queue< PII > Q;
177     // memset 是以8个bit为单位初始化的！！！ 
178     msI(path);
179     path[0] = 0;
180     ms0(vis);
181     Q.push(PII(1, 0));
182     
183     while(!Q.empty()) {
184         // tmpv 为当前顶点， tmpc为到达当前顶点的边的颜色 
185         int tmpv = Q.front().ft, tmpc = Q.front().sd; Q.pop();
186         
187         if(path[k - d[tmpv]] < tmpc || vis[tmpv]) continue;
188         vis[tmpv] = 1; // 到达一个节点的路径可能有多条，不记录的话会被重复访问，复杂度指数上升 
189         
190         foreach(i, v[tmpv]) {
191             Edge &x = e[*i];
192             if(d[tmpv] - 1 != d[x.to] || d[x.to] == 0 && x.to != n) continue; 
193             path[k - d[x.to]] = min(path[k - d[x.to]], x.c);
194             
195             Q.push(PII(x.to, x.c));
196         }
197     }
198 }
199 
200 int main(){
201     //freopen("MyOutput.txt","w",stdout);
202     //freopen("input.txt","r",stdin);
203     //INIT();
204     while(~scanf("%d%d", &n, &m)) {
205         e.clear();
206         For(i, 1, n) v[i].clear(); 
207         
208         Rep(i, m) {
209             Edge t;
210             scanf("%d%d%d", &t.from, &t.to, &t.c);
211             addEdge(t);
212         }
213         
214         bfs1();
215         k = d[1];
216         
217         bfs2();
218         
219         printf("%d\n", k);
220         For(i, 1, k) printf("%d%c", path[i], " \n"[i == k]);
221     }
222     return 0;
223 }