【01分数规划】 ZOJ 2676 Network Wars

#include <iostream>
#include <cstdio>
#include <cstring>
#include <string>
#include <cmath>
#include <algorithm>
#include <queue>
#include <stack>
#include <vector>
#include <deque>
#include <set>
#include <map>
using namespace std;
#define ll long long
#pragma comment(linker, "/STACK:102400000,102400000")
#define mod (ll)4294967296
const int MAXN = 51222;//点数的最大值
const int MAXM = 22222;//边数的最大值
const int INF = 0x3f3f3f3f;
const double eps = 1e-4;
struct Edge
{
int to,next;
double cap,flow;
}edge[MAXM];//注意是MAXM
int tol;
int head[MAXN];
int gap[MAXN],dep[MAXN],cur[MAXN];
void init()
{
tol = 0;
memset(head,-1,sizeof (head));
}
void addedge (int u,int v,double w,double rw = 0)
{
edge[tol].to = v; edge[tol].cap = w; edge[tol].flow = 0;
edge[tol].next = head[u]; head[u] = tol++;
edge[tol].to = u; edge[tol].cap = w; edge[tol].flow = 0;
edge[tol].next = head[v]; head[v] = tol++;
}
int Q[MAXN];
void BFS(int start,int end)
{
memset(dep,-1,sizeof(dep));
memset(gap,0,sizeof(gap));
gap[0] = 1;
int front = 0, rear = 0;
dep[end] = 0;
Q[rear++] = end;
while(front != rear)
{
int u = Q[front++];
for(int i = head[u]; i !=  -1; i = edge[i].next)
{
int v = edge[i]. to;
if(dep[v] != -1)continue;

if(edge[i^1].cap-edge[i^1].flow<=eps) continue;//end开始所以取反向边
Q[rear++] = v;
dep[v] = dep[u] + 1;
gap[dep[v]]++;
}
}
return ;
}
int S[MAXN];
double sap(int start,int end, int N)
{
BFS(start,end);
memcpy(cur,head,sizeof(head));
int top = 0;
int u = start;
double ans = 0;
int i;
while(dep[start] < N)
{
if(u == end)
{
double Min = INF*1.0;
int inser;
for( i = 0;i < top;i++)
{
if(Min > edge[S[i]].cap - edge[S[i]].flow)
{
Min = edge[S[i]].cap - edge[S[i]].flow;
inser = i;
}
}
for( i = 0;i < top;i++)
{
edge[S[i]]. flow += Min;
edge[S[i]^1].flow -= Min;
}
ans += Min;
top = inser;
u = edge[S[top]^1].to;
continue;
}
bool flag =  false;
int v;
for( i = cur[u]; i != -1; i = edge[i]. next)
{
v = edge[i]. to;
if(edge[i].cap - edge[i].flow && dep[v]+1 == dep[u])
{
flag =  true;
cur[u] = i;
break;
}
}
if(flag)
{
S[top++] = cur[u];
u = v;
continue;
}
int Min = N;
for( i = head[u]; i !=  -1; i = edge[i].next)
{
if(edge[i].cap - edge[i].flow && dep[edge[i].to] < Min)
{
Min = dep[edge[i].to];
cur[u] = i;
}
}
gap[dep[u]]--;
if(!gap[dep[u]]) return ans;
dep[u] = Min + 1;
gap[dep[u]]++;
if(u != start)u = edge[S[--top]^1].to;
}
return ans;
}
int a[MAXN],b[MAXN];
double c[MAXN];
int main()
{
int n,m;
while(scanf("%d%d",&n,&m)!=EOF)
{
init();
double l=INF*1.0,r=0;
for(int i=1;i<=m;i++)
{
scanf("%d%d%lf",&a[i],&b[i],&c[i]);
l=min(l,c[i]),r=max(r,c[i]);
}
while(r-l>eps)
{
init();
double lr=(l+r)/2.0,flow=0;
for(int i=1;i<=m;i++)
{
if(c[i]<=lr)
flow+=c[i]-lr;
else
addedge(a[i],b[i],c[i]-lr,0);
}
flow+=sap(1,n,n);
if(flow>0) l=lr;
else r=lr;
}
init();
for(int i=1;i<=m;i++)
if(c[i]>r) addedge(a[i],b[i],c[i]-r,0);
else addedge(0,0,0,0);
sap(1,n,n);
BFS(1,n);
vector<int>ans;
for(int i=1;i<=m;i++)
{
if(c[i]<=r||((dep[a[i]]==-1)^(dep[b[i]]==-1)))
ans.push_back(i);
}
printf("%d\n",ans.size());
for(int i=0;i<ans.size();++i)
{
if(i>0) printf(" ");
printf("%d",ans[i]);
}
printf("\n");
}
return 0;
}
/*
6 8
1 2 3
1 3 3
2 4 2
2 5 2
3 4 2
3 5 2
5 6 3
4 6 3
4 5
1 2 2
1 3 2
2 3 1
2 4 2
3 4 2
*/