pku1149 最大流（EK算法）
用EK就能做。
盗用大牛讲解：
题目大意：
详解见：原创博客
这题关键：建一个超级源点，连上所有的商人，边权置为每个顾客能打开的猪圈里猪的总数，建一个超级汇点，每个顾客都连上这个汇点，权值为每个顾客的购买上限，如果猪圈i先被顾客p1打开，紧接着又被p2打开，加一条从p1到p2的边，边权为INF。
我EK写了两遍：
第一个：407ms
代码
#include
<
queue
>
#include
<
stdio.h
>
using
namespace
std;
#define
NN 104
#define
INF 0x5fffffff
int
M, N;
int
c[NN][NN];
int
mark[NN];
int
pre[NN];
void
CreateGraph()
{
int
i, j, cnt, t, x[
1004
], flag[
1004
];
for
(i
=
0
; i
<=
N
+
1
; i
++
){
for
(j
=
0
; j
<=
N
+
1
; j
++
){
c[i][j]
=
0
;
}
}
for
(i
=
1
; i
<=
M; i
++
){
scanf(
"
%d
"
,
&
x[i]);
flag[i]
=
-
1
;
//
标记第i个猪圈刚被哪个商人打开过
}
for
(i
=
1
; i
<=
N; i
++
){
scanf(
"
%d
"
,
&
cnt);
for
(j
=
1
; j
<=
cnt; j
++
){
scanf(
"
%d
"
,
&
t);
if
(flag[t]
!=
-
1
){
c[flag[t]][i]
=
INF;
}
else
{
c[
0
][i]
+=
x[t];
}
flag[t]
=
i;
}
scanf(
"
%d
"
,
&
t);
c[i][N
+
1
]
=
t;
}
}
int
Bfs()
{
int
que[NN];
memset(mark,
0
,
sizeof
(mark));
mark[
0
]
=
1
;
que[
0
]
=
0
;
int
cur, i;
int
flow
=
INF;
int
j, num
=
1
;
for
(j
=
0
; j
<
num; j
++
) {
cur
=
que[j];
for
(i
=
0
; i
<=
N
+
1
; i
++
){
if
(c[cur][i]
>
0
&&
!
mark[i]){
mark[i]
=
1
;
if
(c[cur][i]
<
flow){
flow
=
c[cur][i];
}
pre[i]
=
cur;
if
(i
==
N
+
1
){
return
flow;
}
que[num
++
]
=
i;
}
}
}
return
-
1
;
}
void
Edmonds_Karp()
{
int
maxFlow
=
0
;
int
flow, tmp;
while
((flow
=
Bfs())
!=
-
1
){
maxFlow
+=
flow;
tmp
=
N
+
1
;
while
(tmp
!=
0
){
c[pre[tmp]][tmp]
-=
flow;
c[tmp][pre[tmp]]
+=
flow;
tmp
=
pre[tmp];
}
}
printf(
"
%d\n
"
, maxFlow);
}
int
main()
{
scanf(
"
%d%d
"
,
&
M,
&
N);
CreateGraph();
Edmonds_Karp();
return
0
;
}
第二个：16ms
代码
#include
<
queue
>
#include
<
stdlib.h
>
#include
<
stdio.h
>
using
namespace
std;
#define
NN 104
#define
INF 0x5fffffff
int
M, N;
int
c[NN][NN];
int
mark[NN];
int
pre[NN];
void
CreateGraph()
{
int
i, j, cnt, t, x[
1004
], flag[
1004
];
for
(i
=
0
; i
<=
N
+
1
; i
++
){
for
(j
=
0
; j
<=
N
+
1
; j
++
){
c[i][j]
=
0
;
}
}
for
(i
=
1
; i
<=
M; i
++
){
scanf(
"
%d
"
,
&
x[i]);
flag[i]
=
-
1
;
//
标记第i个猪圈刚被哪个商人打开过
}
for
(i
=
1
; i
<=
N; i
++
){
scanf(
"
%d
"
,
&
cnt);
for
(j
=
1
; j
<=
cnt; j
++
){
scanf(
"
%d
"
,
&
t);
if
(flag[t]
!=
-
1
){
c[flag[t]][i]
=
INF;
}
else
{
c[
0
][i]
+=
x[t];
}
flag[t]
=
i;
}
scanf(
"
%d
"
,
&
t);
c[i][N
+
1
]
=
t;
}
}
int
Bfs()
{
int
que[NN];
memset(mark,
0
,
sizeof
(mark));
mark[
0
]
=
1
;
que[
0
]
=
0
;
int
cur, i;
int
j, num
=
1
;
for
(j
=
0
; j
<
num; j
++
) {
cur
=
que[j];
for
(i
=
0
; i
<=
N
+
1
; i
++
){
if
(c[cur][i]
>
0
&&
!
mark[i]){
mark[i]
=
1
;
pre[i]
=
cur;
if
(i
==
N
+
1
){
return
1
;
}
que[num
++
]
=
i;
}
}
}
return
-
1
;
}
void
Edmonds_Karp()
{
int
maxFlow
=
0
;
int
flow, tmp;
while
(Bfs()
==
1
){
/*
查找最小增流的时候，只查找最短路径上的点
*/
flow
=
INF;
tmp
=
N
+
1
;
while
(tmp
!=
0
){
if
(c[pre[tmp]][tmp]
<
flow){
flow
=
c[pre[tmp]][tmp];
}
tmp
=
pre[tmp];
}
maxFlow
+=
flow;
tmp
=
N
+
1
;
while
(tmp
!=
0
){
c[pre[tmp]][tmp]
-=
flow;
c[tmp][pre[tmp]]
+=
flow;
tmp
=
pre[tmp];
}
}
printf(
"
%d\n
"
, maxFlow);
}
int
main()
{
scanf(
"
%d%d
"
,
&
M,
&
N);
CreateGraph();
Edmonds_Karp();
//
system("pause");
return
0
;
}
两个代码的区别在于，在查找最小的流值的增量时候，第一个是在搜到的所有节点中找，第二个是在最短路径上找的，范围比第一个小，增量就增加的快，BFS的次数就减少了。