我正在从 topcoder 站点学习 push-relabel 算法：http: //community.topcoder.com/tc ?module=Static&d1=tutorials&d2=maxflowPushRelabel 我认为实现有问题。节点饱和时如何将多余的流量推回节点。例如：
在找到从 1 到 3 的最大流量时，在某一阶段我需要将流量从 2 推回到 1（因为 2 没有出边）。但在先进先出算法的代码实现中，第16行的循环从0 to G[u].size(). 既然 2 没有从 2 到 1 的任何边，它怎么能把流量推回到 1 呢？
如果需要，这是我糟糕的实现：
#define DEBUG //comment when you have to disable all debug macros.
#define LOCAL
#define NDEBUG //comment when all assert statements have to be disabled.
#include <iostream>
#include <cstring>
#include <sstream>
#include <cstdlib>
#include <cstdio>
#include <cmath>
#include <vector>
#include <set>
#include <map>
#include <bitset>
#include <climits>
#include <ctime>
#include <algorithm>
#include <functional>
#include <stack>
#include <queue>
#include <list>
#include <deque>
#include <sys/time.h>
#include <iomanip>
#include <cstdarg>
#include <utility> //std::pair
#include <cassert>
#define tr(c,i) for(typeof(c.begin()) i = (c).begin(); i != (c).end(); i++)
#define present(c,x) ((c).find(x) != (c).end())
#define all(x) x.begin(), x.end()
#define pb push_back
#define mp make_pair
#define log2(x) (log(x)/log(2))
#define ARRAY_SIZE(arr) (1[&arr]-arr)
#define INDEX(arr,elem) (lower_bound(all(arr),elem)-arr.begin())
#define lld long long int
#define MOD 1000000007
#define gcd __gcd
#define equals(a,b) (a.compare(b)==0) //for strings only
using namespace std;
struct Graph{
lld numV;
vector<lld> *adj;
lld **flow, **cap, **cf, *height, *excess;
inline void SET0(lld *array)
{
for(lld i=0;i<=numV;i++)
array[i]=0;
}
Graph(lld _numV)
{
numV=_numV;
lld i;
/* allocating memory....*/
flow = new lld*[numV+1];
for(i=0;i<=numV;i++)
flow[i] = new lld[numV+1], SET0(flow[i]);
cap = new lld*[numV+1];
for(i=0;i<=numV;i++)
cap[i] = new lld[numV+1], SET0(cap[i]);
cf = new lld*[numV+1];
for(i=0;i<=numV;i++)
cf[i] = new lld[numV+1], SET0(cf[i]);
height = new lld[numV+1];
excess = new lld[numV+1];
SET0(height);
SET0(excess);
adj = new vector<lld>[numV+1];
}
void addEdge(lld u, lld v, lld uv)
{
adj[u].push_back(v);
cap[u][v] = uv;
cf[u][v] = uv;
}
void initialize_preflow(lld source)
{
lld i, v;
height[source] = numV-1;
tr(adj[source],it)
{
v = *it;
flow[source][v] = cap[source][v];
flow[v][source] = -cap[source][v];
excess[v] += cap[source][v];
excess[source] -=cap[source][v];
cf[source][v] = cap[source][v]-flow[source][v];
cf[v][source] = cap[v][source]-flow[v][source];
}
}
void push(lld u, lld v)
{
lld push_val = min(cf[u][v], excess[u]);
flow[u][v] += push_val;
flow[v][u] = -flow[u][v];
excess[u] -=push_val;
excess[v] +=push_val;
cf[u][v] = cap[u][v]-flow[u][v];
cf[v][u] = cap[v][u]-flow[v][u];
}
lld max_flow(lld source, lld sink)
{
initialize_preflow(source);
queue<lld> q;
bool considered[numV+1];
lld u, v, m, i;
memset(considered, false, sizeof(considered));
tr(adj[source], it)
{
v = *it;
if(v!=sink)
{
q.push(v);
considered[v] = true;
}
}
bool flag;
u = -1;
while(!q.empty())
{
u = q.front();
m = -1;
for(i=0;i<adj[u].size() && excess[u]>0; i++)
{
v = adj[u][i];
if(cf[u][v]>0)
{
if(height[u]>height[v])
{
push(u,v);
if(!considered[v] && v!=sink && v!=source)
{
considered[v] = true;
q.push(v);
}
}
else if(m==-1) m = height[v];
else m = min(m, height[v]);
}
}
if(adj[u].empty()) {q.pop();continue;}
if(excess[u]!=0) height[u] = m+1;
else
{
q.pop();
considered[u] = false;
}
}
return excess[sink];
}
};
template<class T>
inline void inputInt(T &n )
{
n=0;
T ch=getchar_unlocked();
while( ch < '0' || ch > '9' )
ch=getchar_unlocked();
while( ch >= '0' && ch <= '9' )
n = (n<<3)+(n<<1) + ch-'0', ch=getchar_unlocked();
}
int main()
{
#ifdef LOCAL
freopen("input.in","r",stdin);
#endif
lld e,u,v,n,c;
//cout<<"V:"<<endl;
cin>>n>>e;
Graph g(n);
while(e--)
{
inputInt(u);
inputInt(v);
inputInt(c);
if(u!=v)
{
if(g.cf[u][v])
g.cf[u][v]=g.cf[v][u]=g.cap[u][v]=g.cap[v][u]+c;
else g.addEdge(u,v,c);
}
}
cout<<g.max_flow(1,n)<<endl;
}