最大流(push-relable)算法
预流推进算法(push-relable)，时间复杂度O(V^2E)
1
//
The push-relable algorithm code due to CLRS chapter 26
2
#include
<
iostream
>
3
#include
<
list
>
4
using
namespace
std;
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const
int
N
=
100
;
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int
n;
//
vertex number
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int
e[N];
//
residual flow of the vertex
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int
h[N];
//
height of the vertex
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int
c[N][N];
//
capacity of the edge
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int
f[N][N];
//
flow of the edge
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list
<
int
>
ev;
//
excess flow vertex
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list
<
int
>
edge[N];
//
edge link list
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bool
flag[N];
//
lable whether the vertex is in the flow list
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inline
void
Push(
int
u,
int
v)
//
push flow from edge (u, v)
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{
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int
df
=
min(e[u], c[u][v]
-
f[u][v]);
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f[u][v]
+=
df;
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f[v][u]
=
-
f[u][v];
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e[u]
-=
df;
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e[v]
+=
df;
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}
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void
Relable(
int
u)
//
re-lable heght of vertex u
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{
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h[u]
=
n
*
2
-
1
;
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for
(list
<
int
>
::iterator iter
=
edge[u].begin(); iter
!=
edge[u].end(); iter
++
)
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{
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if
(c[u][
*
iter]
>
f[u][
*
iter]
&&
h[
*
iter]
<
h[u])
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h[u]
=
h[
*
iter];
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}
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h[u]
++
;
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}
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void
Discharge(
int
u)
//
discharge the residual flow of vertex u
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{
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list
<
int
>
::iterator iter
=
edge[u].begin();
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while
(e[u]
>
0
)
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{
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if
(iter
==
edge[u].end())
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{
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Relable(u);
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iter
=
edge[u].begin();
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}
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if
(h[u]
==
h[
*
iter]
+
1
&&
c[u][
*
iter]
>
f[u][
*
iter])
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{
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Push(u,
*
iter);
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if
(e[
*
iter]
>
0
&&
!
flag[
*
iter])
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ev.push_back(
*
iter);
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}
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++
iter;
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}
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}
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void
Init_PreFlow()
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{
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ev.clear();
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h[
0
]
=
n;
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e[
0
]
=
0
;
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memset(flag,
0
,
sizeof
(flag));
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memset(f,
0
,
sizeof
(f));
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flag[
0
]
=
flag[n
-
1
]
=
true
;
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for
(
int
u
=
1
; u
<
n; u
++
)
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{
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f[
0
][u]
=
c[
0
][u];
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f[u][
0
]
=
-
f[
0
][u];
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e[u]
=
c[
0
][u];
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if
(e[u]
>
0
&&
!
flag[u])
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{
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ev.push_back(u);
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flag[u]
=
true
;
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}
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}
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//
construct link list
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for
(
int
u
=
0
; u
<
n; u
++
)
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for
(
int
v
=
u
+
1
; v
<
n; v
++
)
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{
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if
(c[u][v]
>
0
||
c[v][u]
>
0
)
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{
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edge[u].push_back(v);
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edge[v].push_back(u);
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}
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}
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}
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int
Push_Relable()
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{
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Init_PreFlow();
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while
(
!
ev.empty())
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{
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int
u
=
ev.front();
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Discharge(u);
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ev.pop_front();
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flag[u]
=
false
;
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}
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return
e[n
-
1
];
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}
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int
main()
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{
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int
m, u, v, w;
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while
(scanf(
"
%d%d
"
,
&
m,
&
n)
!=
EOF)
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{
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memset(c,
0
,
sizeof
(c));
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for
(
int
i
=
0
; i
<
m; i
++
)
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{
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scanf(
"
%d%d%d
"
,
&
u,
&
v,
&
w);
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c[u][v]
=
w;
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}
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printf(
"
Max Flow is %d\n
"
, Push_Relable());
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}
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return
0
;
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}