http://poj.org/problem?id=2679
Adventurous Driving
| Time Limit: 1000MS | Memory Limit: 65536K | |
| Total Submissions: 1596 | Accepted: 455 |
Description
After a period of intensive development of the transportation infrastructure, the government of Ruritania decides to take firm steps to strengthen citizens‘ confidence in the national road network and sets up a compensation scheme for adventurous driving (CSAD). Those driving on a road with holes, bumps and other entertaining obstacles get compensation; those driving on a decent road pay tax. These compensations and taxes are obtained and paid in cash on entry on each road and depend on the entry point on the road. What you get and pay driving on a road from A to B may be different from what you get and pay driving on the same road from B to A. The Ruritarian authorities call fee the amount of money paid as tax or obtained as compensation on entry on a road. A positive fee is a tax; a negative fee stands for compensation.
John Doe plans to take advantage of CSAD for saving money he needs to repair his old car. When driving from A to B, John follows a path he calls optimal: a path that is rewarding and has the minimal length out of the paths with the minimal weight from A to B. In John‘s opinion, a path is rewarding if all the roads in the path are rewarding, and a road (X,Y) is rewarding if it has the minimal entry fee out of the roads leaving X. The weight of a path is the sum of the entry fees paid along the path. The length of a path cumulates the length of the roads in the path. The problem is helping John to compute the weight and the length of an optimal path from A to B on a given map.
For example, on the illustrated road map vertices designate cities and edges stand for roads. The label fuv[L]fvu of the road (u,v) shows the fee fuv for driving from u to v, the fee fvu for driving from v to u, and the length L of the road. The path (0,2,4,3,5) from 0 to 5 is optimal: it is rewarding, has weight 2 (-1+3+0+0) and length 50 (5+10+5+30). The path (0,1,4,3,5), although rewarding and of weight 2, has length 51. The path (0,3,5) has weight 0 and length 20 but it is not rewarding.
Input
Write a program that reads several data sets from a text file. Each data set encodes a road map and starts with four integers: the number 1<=n<=1100 of towns on the map, the number 0<=m<=5000 of roads, the departure town 0<=A<=n-1, and the destination town 0<=B<=n-1. Follow m data quintuples (u,v,fuv[L]fvu), where u and v are town identifiers (integers in the range 0..n-1), 100<=fuv, fvu<=100 are integer fees for driving on the road (u,v), and 1<=L<=100 is the integer length of the road. The quintuples may occur in any order. Except the quintuples, which do not contain white spaces, white spaces may occur freely in input. Input data terminate with an end of file and are correct.
Output
For each data set, the program prints – from the beginning of a line – the weight and the length of an optimal path, according to John‘s oppinion, from A to B. If there is no optimal path from A to B the text VOID is printed. If the weight of the optimal path from A to B has no lower bound the text UNBOUND is printed.
Sample Input
3 3 0 2 (0,1,0[1]0) (0,2,1[1]0) (1,2,1[1]0) 3 3 0 2 (0,1,-1[1]1) (0,2,0[1]0) (1,2,0[1]1) 7 11 0 5 (0,1,-1[6]4) (0,2,-1[5]4) (0,3,0[1]0) (1,4,3[10]1) (2,4,3[10]1) (3,4,0[5]0) (3,5,0[30]0) (3,5,1[20]0) (4,6,0[3]1) (6,5,1[8]0) (6,6,0[2]-1)
Sample Output
VOID UNBOUND 2 50
Hint
An input/output sample is in the table above. The first data set encodes a road map with no optimal path from 0 to 2. The second data set corresponds to a map whose optimal path from 0 to 2 has an unbound weight. The third data set encodes the road map shown in the above figure.
题意：给出一个有向图，每条边有一个费用和长度。给出一个起点一个终点。要求从起点走到终点，每个点的出边必须走费用最小的或者并列最小的，如果按照要求不能走到终点，就输出VOID。然后如果走过的路费用可以无限小，那么就输出 BOUND，否则就计算从起点到终点的最小费用和最小长度，费用最小优先，同样小就长度最小优先。
思路：这题一开始看不懂题意，觉得貌似挺水的，看懂题意后一直在第三个样例跑成负环，后来从别人那里才知道这题是要从起点到终点的路径判断，而平时写的是对于整个图判断。首先把每个点最小费用的出边记录下来，把大于这个最小费用的出边删除，这样的图才符合条件。因为要判断从起点到终点的路径是否有负环，平时写的都是对于整个图的判断负环，所以要建立一个反向图，跑一下DFS，用一个vis数组记录从终点跑出去可以经过哪些点，如果不可以经过的话，一定是不会出现在路径上的，那么就删除这些点之后跑SPFA就可以判断负环了，如果不是负环就可以输出最小的 fee 和 dis。
这里学习到好多vector的东西。。
1 #include <cstdio>
2 #include <cstring>
3 #include <algorithm>
4 #include <queue>
5 #include <vector>
6 #define INF 0x3f3f3f3f
7 using namespace std;
8 #define N 1110
9 struct edge
10 {
11 int l, w, v;
12 edge () {}
13 edge (int v, int w, int l) : v(v), w(w), l(l) {}
14 };
15 int st, ed, lfee[N], vis[N], dis[N], fee[N], cnt[N], n, m;
16 vector <vector<edge> > G, R;
17 //就是vector<edge> G[N];
18
19 void add(vector<vector<edge> > &G, int u, int v, int w, int l)
20 {
21 G[u].push_back(edge(v, w, l));
22 }
23
24 //删除不是最小费用的边
25 void edge_clear()
26 {
27 for(int i = 0; i < n; i++) {
28 for(vector<edge>::iterator p = G[i].begin(); p != G[i].end(); ) {
29 if(p->w > lfee[i]) {
30 p = G[i].erase(p);
31 } else {
32 p++;
33 }
34 }
35 }
36 }
37
38 //删除从起点到终点不会走过的点
39 void node_clear()
40 {
41 for(int i = 0; i < n; i++) {
42 if(!vis[i]) {
43 G[i].clear();
44 continue;
45 }
46 for(vector<edge>::iterator p = G[i].begin(); p != G[i].end(); ) {
47 if(!vis[p->v]) {
48 p = G[i].erase(p);
49 } else {
50 p++;
51 }
52 }
53 }
54 }
55
56 //将图翻转
57 void reg()
58 {
59 R = vector<vector<edge> > (n);
60 for(int i = 0; i < n; i++) {
61 for(vector<edge>::iterator p = G[i].begin(); p != G[i].end(); p++) {
62 add(R, p->v, i, p->w, p->l);
63 }
64 }
65 }
66
67 //标记从终点走出去可以经过哪些点
68 void dfs(int u)
69 {
70 vis[u] = 1;
71 for(int i = 0; i < R[u].size(); i++) {
72 int v = R[u][i].v;
73 if(!vis[v]) dfs(v);
74 }
75 }
76
77 bool spfa()
78 {
79 for(int i = 0; i <= n; i++) {
80 dis[i] = INF; fee[i] = INF;
81 }
82 memset(vis, 0, sizeof(vis));
83 memset(cnt, 0, sizeof(cnt));
84 dis[st] = 0;
85 fee[st] = 0;
86 vis[st] = 1;
87 queue <int> que;
88 while(!que.empty()) que.pop();
89 que.push(st);
90 while(!que.empty()) {
91 int u = que.front(); que.pop();
92 cnt[u]++;
93 if(cnt[u] > n) return false;
94 vis[u] = 0;
95 for(int i = 0; i < G[u].size(); i++) {
96 int v = G[u][i].v, w = G[u][i].w, l = G[u][i].l;
97 if(fee[v] >= fee[u] + w) {
98 if(fee[v] > fee[u] + w) {
99 fee[v] = fee[u] + w;
100 dis[v] = dis[u] + l;
101 if(!vis[v]) {
102 vis[v] = 1;
103 que.push(v);
104 }
105 } else if(dis[v] > dis[u] + l) {
106 dis[v] = dis[u] + l;
107 if(!vis[v]) {
108 vis[v] = 1;
109 que.push(v);
110 }
111 }
112 }
113 }
114 }
115 }
116
117 int main()
118 {
119 while(~scanf("%d%d%d%d", &n, &m, &st, &ed)) {
120 memset(lfee, INF, sizeof(lfee));
121 G.clear(); R.clear();
122 G = vector<vector<edge> > (n);
123 for(int i = 0; i < m; i++) {
124 int u, v, uv, vu, l;
125 scanf(" (%d,%d,%d[%d]%d)", &u, &v, &uv, &l, &vu);
126 add(G, u, v, uv, l);
127 add(G, v, u, vu, l);
128 if(lfee[u] > uv) lfee[u] = uv;
129 if(lfee[v] > vu) lfee[v] = vu;
130 //记录出边的最小的费用
131 }
132
133 memset(vis, 0, sizeof(vis));
134 edge_clear();
135 reg();
136 dfs(ed);
137 if(!vis[st]) {
138 printf("VOID\n");
139 continue;
140 }
141 node_clear();
142 bool flag = spfa();
143 if(!flag) printf("UNBOUND\n");
144 else printf("%d %d\n", fee[ed], dis[ed]);
145 }
146 return 0;
147 }