POJ1422 Air Raid

Air Raid

Description

Consider a town where all the streets are one-way and each street leads from one intersection to another. It is also known that starting from an intersection and walking through town‘s streets you can never reach the same intersection i.e. the town‘s streets form no cycles.

With these assumptions your task is to write a program that finds
the minimum number of paratroopers that can descend on the town and
visit all the intersections of this town in such a way that more than
one paratrooper visits no intersection. Each paratrooper lands at an
intersection and can visit other intersections following the town
streets. There are no restrictions about the starting intersection for
each paratrooper.

Input

Your
program should read sets of data. The first line of the input file
contains the number of the data sets. Each data set specifies the
structure of a town and has the format:

no_of_intersections

no_of_streets

S1 E1

S2 E2

......

Sno_of_streets Eno_of_streets

The first line of each data set contains a positive integer
no_of_intersections (greater than 0 and less or equal to 120), which is
the number of intersections in the town. The second line contains a
positive integer no_of_streets, which is the number of streets in the
town. The next no_of_streets lines, one for each street in the town, are
randomly ordered and represent the town‘s streets. The line
corresponding to street k (k <= no_of_streets) consists of two
positive integers, separated by one blank: Sk (1 <= Sk <=
no_of_intersections) - the number of the intersection that is the start
of the street, and Ek (1 <= Ek <= no_of_intersections) - the
number of the intersection that is the end of the street. Intersections
are represented by integers from 1 to no_of_intersections.

There are no blank lines between consecutive sets of data. Input data are correct.

Output

The
result of the program is on standard output. For each input data set the
program prints on a single line, starting from the beginning of the
line, one integer: the minimum number of paratroopers required to visit
all the intersections in the town.

Sample Input

2
4
3
3 4
1 3
2 3
3
3
1 3
1 2
2 3

Sample Output

2
1

Source

Dhaka 2002

【题解】

最小路径覆盖裸题

 1 #include <iostream>
 2 #include <cstdio>
 3 #include <cstdlib>
 4 #include <cstring>
 5
 6 inline void read(int &x)
 7 {
 8     x = 0;char ch = getchar(), c = ch;
 9     while(ch < ‘0‘ || ch > ‘9‘)c = ch, ch = getchar();
10     while(ch <= ‘9‘ && ch >= ‘0‘)x = x * 10 + ch - ‘0‘, ch = getchar();
11     if(c == ‘-‘)x = -x;
12 }
13
14 const int INF = 0x3f3f3f3f;
15
16 struct Edge
17 {
18     int u,v,next;
19     Edge(int _u, int _v, int _next){u = _u, v = _v, next = _next;}
20     Edge(){}
21 }edge[100000];
22
23 int head[10000], cnt;
24
25 inline void insert(int a, int b)
26 {
27     edge[++cnt] = Edge(a,b,head[a]);
28     head[a] = cnt;
29 }
30
31 int n,m,lk[10000],b[10000];
32
33 int dfs(int u)
34 {
35     for(register int pos = head[u];pos;pos = edge[pos].next)
36     {
37         int v = edge[pos].v;
38         if(b[v])continue;
39         b[v] = 1;
40         if(lk[v] == -1 || dfs(lk[v]))
41         {
42             lk[v] = u;
43             return 1;
44         }
45     }
46     return 0;
47 }
48
49 int xiongyali()
50 {
51     int ans = 0;
52     memset(lk, -1, sizeof(lk));
53     for(register int i = 1;i <= n;++ i)
54     {
55         memset(b, 0, sizeof(b));
56         ans += dfs(i);
57     }
58     return ans;
59 }
60
61 int t;
62
63 int main()
64 {
65     read(t);
66     for(;t;--t)
67     {
68         memset(edge, 0, sizeof(edge));
69         memset(head, 0, sizeof(head));
70         cnt = 0;
71         read(n), read(m);
72         register int tmp1,tmp2,i;
73         for(i = 1;i <= m;++ i)
74         {
75             read(tmp1), read(tmp2);
76             insert(tmp1, tmp2);
77         }
78         printf("%d\n", n - xiongyali());
79     }
80     return 0;
81 } 

POJ1422