题目链接:https://vjudge.net/problem/POJ-1797
题目大意
给定一张“城市-交通(V-E)”的无向图,每条道路的最大承重为 w,现在有一批货物要从 1 号城市运到 N 号城市,求每次所能运的重量的上限。
分析
根据短板效应,一条路上的最大承重等于路径上最小承重的道路所能承载的重量,题目就是求从 1->N 的所有道路中最大承重为多少?
把 Dijkstra算法的核心代码改改就行了。
代码如下
1 #include <cmath> 2 #include <ctime> 3 #include <iostream> 4 #include <string> 5 #include <vector> 6 #include <cstdio> 7 #include <cstdlib> 8 #include <cstring> 9 #include <queue> 10 #include <map> 11 #include <set> 12 #include <algorithm> 13 #include <cctype> 14 #include <stack> 15 #include <deque> 16 #include <list> 17 #include <sstream> 18 #include <cassert> 19 using namespace std; 20 21 #define INIT() ios::sync_with_stdio(false);cin.tie(0);cout.tie(0); 22 #define Rep(i,n) for (int i = 0; i < (n); ++i) 23 #define For(i,s,t) for (int i = (s); i <= (t); ++i) 24 #define rFor(i,t,s) for (int i = (t); i >= (s); --i) 25 #define ForLL(i, s, t) for (LL i = LL(s); i <= LL(t); ++i) 26 #define rForLL(i, t, s) for (LL i = LL(t); i >= LL(s); --i) 27 #define foreach(i,c) for (__typeof(c.begin()) i = c.begin(); i != c.end(); ++i) 28 #define rforeach(i,c) for (__typeof(c.rbegin()) i = c.rbegin(); i != c.rend(); ++i) 29 30 #define pr(x) cout << #x << " = " << x << " " 31 #define prln(x) cout << #x << " = " << x << endl 32 33 #define LOWBIT(x) ((x)&(-x)) 34 35 #define ALL(x) x.begin(),x.end() 36 #define INS(x) inserter(x,x.begin()) 37 #define UNIQUE(x) x.erase(unique(x.begin(), x.end()), x.end()) 38 #define REMOVE(x, c) x.erase(remove(x.begin(), x.end(), c), x.end()); // 删去 x 中所有 c 39 #define TOLOWER(x) transform(x.begin(), x.end(), x.begin(),::tolower); 40 #define TOUPPER(x) transform(x.begin(), x.end(), x.begin(),::toupper); 41 42 #define ms0(a) memset(a,0,sizeof(a)) 43 #define msI(a) memset(a,inf,sizeof(a)) 44 #define msM(a) memset(a,-1,sizeof(a)) 45 46 #define MP make_pair 47 #define PB push_back 48 #define ft first 49 #define sd second 50 51 template<typename T1, typename T2> 52 istream &operator>>(istream &in, pair<T1, T2> &p) { 53 in >> p.first >> p.second; 54 return in; 55 } 56 57 template<typename T> 58 istream &operator>>(istream &in, vector<T> &v) { 59 for (auto &x: v) 60 in >> x; 61 return in; 62 } 63 64 template<typename T1, typename T2> 65 ostream &operator<<(ostream &out, const std::pair<T1, T2> &p) { 66 out << "[" << p.first << ", " << p.second << "]" << " "; 67 return out; 68 } 69 70 inline int gc(){ 71 static const int BUF = 1e7; 72 static char buf[BUF], *bg = buf + BUF, *ed = bg; 73 74 if(bg == ed) fread(bg = buf, 1, BUF, stdin); 75 return *bg++; 76 } 77 78 inline int ri(){ 79 int x = 0, f = 1, c = gc(); 80 for(; c<48||c>57; f = c=='-'?-1:f, c=gc()); 81 for(; c>47&&c<58; x = x*10 + c - 48, c=gc()); 82 return x*f; 83 } 84 85 template<class T> 86 inline string toString(T x) { 87 ostringstream sout; 88 sout << x; 89 return sout.str(); 90 } 91 92 inline int toInt(string s) { 93 int v; 94 istringstream sin(s); 95 sin >> v; 96 return v; 97 } 98 99 //min <= aim <= max 100 template<typename T> 101 inline bool BETWEEN(const T aim, const T min, const T max) { 102 return min <= aim && aim <= max; 103 } 104 105 typedef long long LL; 106 typedef unsigned long long uLL; 107 typedef pair< double, double > PDD; 108 typedef pair< int, int > PII; 109 typedef pair< int, PII > PIPII; 110 typedef pair< string, int > PSI; 111 typedef pair< int, PSI > PIPSI; 112 typedef set< int > SI; 113 typedef set< PII > SPII; 114 typedef vector< int > VI; 115 typedef vector< double > VD; 116 typedef vector< VI > VVI; 117 typedef vector< SI > VSI; 118 typedef vector< PII > VPII; 119 typedef map< int, int > MII; 120 typedef map< LL, int > MLLI; 121 typedef map< int, string > MIS; 122 typedef map< int, PII > MIPII; 123 typedef map< PII, int > MPIII; 124 typedef map< string, int > MSI; 125 typedef map< string, string > MSS; 126 typedef map< PII, string > MPIIS; 127 typedef map< PII, PII > MPIIPII; 128 typedef multimap< int, int > MMII; 129 typedef multimap< string, int > MMSI; 130 //typedef unordered_map< int, int > uMII; 131 typedef pair< LL, LL > PLL; 132 typedef vector< LL > VL; 133 typedef vector< VL > VVL; 134 typedef priority_queue< int > PQIMax; 135 typedef priority_queue< int, VI, greater< int > > PQIMin; 136 const double EPS = 1e-8; 137 const LL inf = 0x3fffffff; 138 const LL infLL = 0x3fffffffffffffffLL; 139 const LL mod = 20100713; 140 const int maxN = 1e3 + 7; 141 const LL ONE = 1; 142 const LL evenBits = 0xaaaaaaaaaaaaaaaa; 143 const LL oddBits = 0x5555555555555555; 144 145 struct Edge{ 146 // u->v 147 int u, v, w; 148 }; 149 150 istream& operator>> (istream &in, Edge &x) { 151 in >> x.u >> x.v >> x.w; 152 return in; 153 } 154 155 int T, N, M; 156 157 VI V[maxN]; 158 int maxW[maxN]; 159 vector< Edge > E; 160 bool vis[maxN]; 161 162 inline void addEdge(Edge &x) { 163 V[x.u].PB(E.size()); 164 E.PB(x); 165 } 166 167 void init() { 168 For(i, 1, N) V[i].clear(); 169 ms0(maxW); 170 E.clear(); 171 172 ms0(vis); 173 } 174 175 void Dijkstra() { 176 priority_queue< PII > Q; // 大顶堆 177 Q.push(MP(inf, 1)); 178 maxW[1] = inf; 179 180 while(!Q.empty()) { 181 PII tmp = Q.top(); Q.pop(); 182 if(vis[tmp.sd]) continue; 183 vis[tmp.sd] = 1; 184 if(tmp.sd == N) return; 185 186 Rep(i, V[tmp.sd].size()) { 187 Edge &e = E[V[tmp.sd][i]]; 188 if(vis[e.v]) continue; 189 190 if(min(maxW[tmp.sd], e.w) > maxW[e.v]) { 191 maxW[e.v] = min(maxW[tmp.sd], e.w); 192 Q.push(MP(maxW[e.v], e.v)); 193 } 194 } 195 } 196 } 197 198 int main(){ 199 //freopen("MyOutput.txt","w",stdout); 200 //freopen("input.txt","r",stdin); 201 INIT(); 202 cin >> T; 203 For(cases, 1, T) { 204 cin >> N >> M; 205 init(); 206 Rep(i, M) { 207 Edge t; 208 cin >> t; 209 addEdge(t); 210 swap(t.u, t.v); 211 addEdge(t); 212 } 213 214 Dijkstra(); 215 216 cout << "Scenario #" << cases << ": "; 217 cout << maxW[N] << " "; 218 } 219 return 0; 220 }