TJU 1325/PKU 2607 Fire Station
Time Limit: 3.0 Seconds Memory Limit: 65536K
Total Runs: 285 Accepted Runs: 80 Multiple test files
本题应该说是不难，但我却花费了一个上午。本题的思想就是最短路。值得注意的是有很多人都弄错了题意，本题的题意就是找到一个合适的点来安置Fire Station使得所有的intersections到离他们最近的Fire Station最长的那一个最短（原题是： minimize the maximum distance from any intersection to the nearest fire station.）
所有本题的思想就是用已给出的有Fire Station进行最短路求解，进行f 次之后算出每一个intersections到最近的Fire Station的距离。然后再从小到大一个一个的尝试，求出能最小化最大距离的那一个。
注意：由于本题可能有500个intersection所以如果用二维数组存储，有可能会超时，建议使用邻接表。
代码：
此代码在北大，和天津上均可过，下面还有一种简单的代码在北大上可过，但在天津上超时。
1
#include
<
stdio.h
>
2
#include
<
stdlib.h
>
3
#include
<
string
.h
>
4
#include
<
queue
>
5
using
namespace
std;
6
typedef
struct
t
7
{
8
int
data;
9
int
s;
10
struct
t
*
next;
11
}T;
12
struct
node
13
{
14
int
data;
15
T
*
next;
16
}g[
505
];
17
typedef
struct
qnode
18
{
19
int
s,data;
20
bool
operator
<
(
const
qnode
&
a)
const
21
{
22
return
a.s
<
s;
23
}
24
}NODE;
25
int
Index,zmin,n,Min[
505
];
26
void
dijkstra(
int
v0,
int
t)
27
{
28
priority_queue
<
NODE
>
qu;
29
NODE cur,next;
30
int
i,max,dist[
505
],visit[
505
],mark
=
0
;
31
cur.data
=
v0;cur.s
=
0
;
32
qu.push (cur);
33
T
*
p;
34
memset(dist,
-
1
,
sizeof
(dist));
35
memset(visit,
0
,
sizeof
(visit));
36
while
(
!
qu.empty ())
37
{
38
cur
=
qu.top ();
39
while
(visit[cur.data])
40
{
41
qu.pop();
42
if
(qu.empty ())
43
{
44
mark
=
1
;
45
break
;
46
}
47
cur
=
qu.top();
48
}
49
if
(mark)
50
break
;
51
qu.pop ();
52
visit[cur.data]
=
1
;
53
p
=
g[cur.data].next;
54
while
(p)
55
{
56
next.data
=
p
->
data;
57
if
(
!
visit[next.data]
&&
(dist[next.data]
==-
1
||
dist[next.data]
>
p
->
s
+
cur.s))
58
dist[next.data]
=
next.s
=
p
->
s
+
cur.s;
59
else
60
next.s
=
dist[next.data];
61
if
(
!
visit[p
->
data])
62
qu.push(next);
63
p
=
p
->
next;
64
}
65
}
66
if
(t
==
0
)
67
{
68
for
(i
=
1
;i
<=
n;i
++
)
69
{
70
if
(Min[i]
>
dist[i])
71
Min[i]
=
dist[i];
72
}
73
}
74
else
if
(t
==
1
)
75
{
76
dist[v0]
=
0
;
77
for
(i
=
1
;i
<=
n;i
++
)
78
{
79
if
(dist[i]
>
Min[i])
80
dist[i]
=
Min[i];
81
if
(dist[i]
>
max)
82
max
=
dist[i];
83
}
84
if
(max
<
zmin)
85
{
86
Index
=
v0;
87
zmin
=
max;
88
}
89
}
90
}
91
int
main()
92
{
93
int
f,i,x,y,s,mark[
505
]
=
{
0
},a[
105
]
=
{
0
};
94
scanf(
"
%d%d
"
,
&
f,
&
n);
95
for
(i
=
1
;i
<=
f;i
++
)
96
scanf(
"
%d
"
,
&
a[i]);
97
for
(i
=
1
;i
<=
n;i
++
)
98
{
99
g[i].next
=
NULL;
100
Min[i]
=
0xfffffff
;
101
}
102
T
*
p,
*
q;
103
zmin
=
0
;
104
while
(scanf(
"
%d%d%d
"
,
&
x,
&
y,
&
s)
!=
EOF)
105
{
106
p
=
(T
*
)malloc(
sizeof
(T));
107
q
=
(T
*
)malloc(
sizeof
(T));
108
p
->
data
=
y;
109
p
->
s
=
s;
110
p
->
next
=
g[x].next;
111
g[x].next
=
p;
112
g[x].data
=
x;
113
q
->
data
=
x;
114
q
->
s
=
s;
115
q
->
next
=
g[y].next;
116
g[y].next
=
q;
117
g[y].data
=
y;
118
}
119
for
(i
=
1
;i
<=
f;i
++
)
120
{
121
if
(mark[a[i]])
122
continue
;
123
mark[a[i]]
=
1
;
124
dijkstra(a[i],
0
);
125
126
}
127
for
(i
=
1
;i
<=
n;i
++
)
128
{
129
if
(Min[i]
>
zmin)
130
zmin
=
Min[i];
131
}
132
Index
=
1
;
133
for
(i
=
1
;i
<=
n;i
++
)
134
{
135
if
(mark[i])
136
continue
;
137
dijkstra(i,
1
);
138
}
139
printf(
"
%d\n
"
,Index);
140
return
0
;
141
}
代码：
代码
1
#include
<
stdio.h
>
2
#include
<
string
.h
>
3
#include
<
stdlib.h
>
4
#define
MAX 0xfffffff
5
int
Min[
505
],n;
6
int
rmin,Index;
7
typedef
struct
t
8
{
9
int
data;
10
int
s;
11
struct
t
*
next;
12
}T;
13
struct
node
14
{
15
int
data;
16
T
*
next;
17
}g[
505
];
18
void
dijkstra(
int
v0,
int
t)
19
{
20
int
distance[
505
],s[
505
],mindis,i,j,u,max
=
0
;
21
memset(distance,
-
1
,
sizeof
(distance));
22
memset(s,
0
,
sizeof
(s));
23
T
*
p;
24
p
=
g[v0].next;
25
while
(p)
26
{
27
distance[p
->
data]
=
p
->
s;
28
p
=
p
->
next;
29
}
30
s[v0]
=
1
;
31
for
(i
=
1
;i
<
n;i
++
)
32
{
33
mindis
=
MAX;
34
for
(j
=
1
;j
<=
n;j
++
)
35
{
36
if
(
!
s[j]
&&
distance[j]
!=-
1
&&
distance[j]
<
mindis)
37
{
38
u
=
j;
39
mindis
=
distance[j];
40
}
41
}
42
s[u]
=
1
;
43
p
=
g[u].next;
44
while
(p)
45
{
46
if
(
!
s[p
->
data]
&&
(p
->
s
+
distance[u]
<
distance[p
->
data]
||
distance[p
->
data]
==-
1
))
47
distance[p
->
data]
=
p
->
s
+
distance[u];
48
p
=
p
->
next;
49
}
50
}
51
if
(t
==
0
)
52
{
53
for
(i
=
1
;i
<=
n;i
++
)
54
{
55
if
(distance[i]
<
Min[i])
56
Min[i]
=
distance[i];
57
}
58
}
59
else
if
(t
==
1
)
60
{
61
distance[v0]
=
0
;
62
for
(i
=
1
;i
<=
n;i
++
)
63
{
64
if
(distance[i]
>
Min[i])
65
distance[i]
=
Min[i];
66
if
(distance[i]
>
max)
67
max
=
distance[i];
68
}
69
if
(max
<
rmin)
70
{
71
Index
=
v0;
72
rmin
=
max;
73
}
74
75
}
76
}
77
int
main()
78
{
79
int
a[
105
]
=
{
0
},i,b,c,s,f,mark[
505
];
80
memset(mark,
0
,
sizeof
(mark));
81
scanf(
"
%d%d
"
,
&
f,
&
n);
82
for
(i
=
1
;i
<=
f;i
++
)
83
{
84
scanf(
"
%d
"
,
&
a[i]);
85
}
86
for
(i
=
1
;i
<=
n;i
++
)
87
{
88
g[i].next
=
NULL;
89
Min[i]
=
0xfffffff
;
90
}
91
rmin
=
0
;
92
T
*
p,
*
q;
93
while
(scanf(
"
%d%d%d
"
,
&
b,
&
c,
&
s)
!=
EOF)
94
{
95
p
=
(T
*
)malloc(
sizeof
(T));
96
q
=
(T
*
)malloc(
sizeof
(T));
97
p
->
data
=
c;
98
p
->
s
=
s;
99
p
->
next
=
g[b].next;
100
g[b].next
=
p;
101
g[b].data
=
b;
102
q
->
data
=
b;
103
q
->
s
=
s;
104
q
->
next
=
g[c].next;
105
g[c].next
=
q;
106
g[c].data
=
c;
107
}
108
for
(i
=
1
;i
<=
f;i
++
)
109
{
110
if
(mark[a[i]]
==
0
)
111
{
112
mark[a[i]]
=
1
;
113
dijkstra(a[i],
0
);
114
}
115
}
116
for
(i
=
1
;i
<=
n;i
++
)
117
{
118
if
(Min[i]
>
rmin)
119
rmin
=
Min[i];
120
}
121
Index
=
1
;
122
for
(i
=
1
;i
<=
n;i
++
)
123
{
124
if
(mark[i])
125
continue
;
126
dijkstra(i,
1
);
127
}
128
printf(
"
%d\n
"
,Index);
129
return
0
;
130
}