网络流 | OceanEye's Blog

Description

XWW是个影响力很大的人，他有很多的追随者。这些追随者都想要加入XWW教成为XWW的教徒。但是这并不容易，需要通过XWW的考核。
XWW给你出了这么一个难题：XWW给你一个N*N的正实数矩阵A，满足XWW性。
称一个N*N的矩阵满足XWW性当且仅当：（1）A[N][N]=0；（2）矩阵中每行的最后一个元素等于该行前N-1个数的和；（3）矩阵中每列的最后一个元素等于该列前N-1个数的和。
现在你要给A中的数进行取整操作（可以是上取整或者下取整），使得最后的A矩阵仍然满足XWW性。同时XWW还要求A中的元素之和尽量大。

Input

第一行一个整数N,N ≤ 100。
接下来N行每行包含N个绝对值小于等于1000的实数，最多一位小数。

Output

输出一行，即取整后A矩阵的元素之和的最大值。无解输出No。

Sample Input

4
3.1 6.8 7.3 17.2
9.6 2.4 0.7 12.7
3.6 1.2 6.5 11.3
16.3 10.4 14.5 0

Sample Output

129

HINT

【数据规模与约定】

有10组数据，n的大小分别为10,20,30…100。

【样例说明】

样例中取整后满足XWW性的和最大的矩阵为：

3 7 8 18

10 3 0 13

4 1 7 12

17 11 15 0

朴素的建图，只是跑的网络流模式变了

然后就可以随便艹了

#include <cstdio>
#include <algorithm>
#include <cstring>
#include <cstdlib>
#include <cmath>
#include <vector>
#define ll long long
#define INF 1000000000
#define p(x) ('0'<=x&&x<='9')
#define For(i,l,r) for(int i=l;i<=r;i++)

char cc; int C;
template <class T>
void read( T &x )
{
	x=0; cc=getchar(); C=1;
	while(!p(cc)) { if(cc=='-') C=-1; cc=getchar(); }
	while(p(cc)) { x=x*10+cc-48; cc=getchar(); }
	x*=C;
}

using namespace std;
#define EE 80000
#define N 300
#define source 0
#define sink N-1
#define source_ N-2
#define sink_ N-3
struct Tedge
{
	int to,flow;
}edge[EE];
int e_tot,nxt[EE],fst[N];
#define E edge[i]
#define FLOW E.flow
#define TO E.to
#define NXT nxt[i]
#define calc(i) (n+i)
void add_e(int from,int to,int flow)
{
	static int &i=e_tot;
	TO=to; FLOW=flow; NXT=fst[from]; fst[from]=i++;
	TO=from; FLOW=0; NXT=fst[to]; fst[to]=i++;
}

double a[N][N];
int imp[N],in[N];
int n,S,T;
void init()
{
	int _;
	memset(fst,-1,sizeof(fst));
	read(n);
	For(i,1,n)
		for(int j=1;j<=n;j++) scanf("%lf",&a[i][j]);
	For(i,1,n-1)
		for(int j=1;j<n;j++)
		{
			_=(int)floor(a[i][j]);
			if(ceil(a[i][j])!=_) add_e(i,calc(j),1);
			in[i]-=_; in[calc(j)]+=_;
		}
	For(i,1,n-1)
	{
		_=floor(a[i][n]);
		in[i]+=_;
		in[source]-=_;
		if(ceil(a[i][n])!=_) add_e(source,i,1);
	}
	For(i,1,n-1)
	{
		_=floor(a[n][i]);
		in[sink]+=_;
		in[calc(i)]-=_;
		if(ceil(a[n][i])!=_) add_e(calc(i),sink,1);
	}
	add_e(sink,source,INF);
	For(i,0,N-1) if(in[i]) 
	{
		in[i]>0?add_e(source_,i,in[i]):add_e(i,sink_,-in[i]);
		imp[i]=e_tot-2;
	}
}
int cnt[N],d[N];
bool bfs()
{
	memset(d,0,sizeof(d));
	memset(cnt,0,sizeof(cnt));
	static int queue[65540],x;
	static unsigned short int he=0,ta=0;
	queue[++he]=T;
	d[T]=1;
	while(he!=ta)
	{
		x=queue[++ta]; cnt[d[x]]++;
		for(int i=fst[x];~i;i=NXT) if(!d[TO]&&edge[i^1].flow)
		{ d[TO]=d[x]+1; queue[++he]=TO; }
	}
	return d[S];
}
void cp(int &x,int y) { x>y?x=y:x; }
int p[N];

int Augment()
{
	static int node,c,i;
	node=T; c=INF;
	while(node!=S)
	{
		i=p[node]; cp(c,FLOW);
		node=edge[i^1].to;
	}
	node=T;
	while(node!=S)
	{
		i=p[node]; FLOW-=c;
		i^=1; FLOW+=c;
		node=TO;
	}
	return c;
}

int ISAP()
{
	static int node,cur[N],ret;
	static bool flag;
	if(!bfs()) return 0;
	node=S; ret=0;
	for(int i=0;i<N;i++) cur[i]=fst[i];
	while(d[S]<n*2+5)
	{
		if(node==T)
		{
			ret+=Augment();
			node=S;
		}
		flag=false;
		for(int i=cur[node];~i;i=NXT) if(d[TO]==d[node]-1&&FLOW)
		{
			p[TO]=i;
			cur[node]=i;
			node=TO;
			flag=true;
			break;
		}
		if(flag) continue;
		int M=N-1;
		if(!--cnt[d[node]]) break;
		for(int i=fst[node];~i;i=NXT) if(FLOW) cp(M,d[TO]+1);
		cnt[d[node]=M]++;
		cur[node]=fst[node];
		node==S?node:node=edge[p[node]^1].to;
	}
	return ret;
}

bool check()
{
	For(i,0,N-1) if(imp[i]) if(edge[imp[i]].flow) return false;
	return true;
}

int main()
{
	init();
	S=source_,T=sink_;
	ISAP();
//	printf("%d\n",ISAP());
	if(!check())
	{
		puts("-1");
		return 0;
	}
	S=source,T=sink;
	printf("%d\n",ISAP()*3);
	return 0;
}

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#include <cstdio>

#include <algorithm>

#include <cstring>

#include <cstdlib>

#include <cmath>

#include <vector>

#define ll long long

#define INF 1000000000

#define p(x) ('0'<=x&&x<='9')

#define For(i,l,r) for(int i=l;i<=r;i++)

char cc; int C;

template <class T>

void read( T &x )

{

x=0; cc=getchar(); C=1;

while(!p(cc)) { if(cc=='-') C=-1; cc=getchar(); }

while(p(cc)) { x=x*10+cc-48; cc=getchar(); }

x*=C;

}

using namespace std;

#define EE 80000

#define N 300

#define source 0

#define sink N-1

#define source_ N-2

#define sink_ N-3

struct Tedge

{

int to,flow;

}edge[EE];

int e_tot,nxt[EE],fst[N];

#define E edge[i]

#define FLOW E.flow

#define TO E.to

#define NXT nxt[i]

#define calc(i) (n+i)

void add_e(int from,int to,int flow)

{

static int &i=e_tot;

TO=to; FLOW=flow; NXT=fst[from]; fst[from]=i++;

TO=from; FLOW=0; NXT=fst[to]; fst[to]=i++;

}

double a[N][N];

int imp[N],in[N];

int n,S,T;

void init()

{

int _;

memset(fst,-1,sizeof(fst));

read(n);

For(i,1,n)

for(int j=1;j<=n;j++) scanf("%lf",&a[i][j]);

For(i,1,n-1)

for(int j=1;j<n;j++)

{

_=(int)floor(a[i][j]);

if(ceil(a[i][j])!=_) add_e(i,calc(j),1);

in[i]-=_; in[calc(j)]+=_;

}

For(i,1,n-1)

{

_=floor(a[i][n]);

in[i]+=_;

in[source]-=_;

if(ceil(a[i][n])!=_) add_e(source,i,1);

}

For(i,1,n-1)

{

_=floor(a[n][i]);

in[sink]+=_;

in[calc(i)]-=_;

if(ceil(a[n][i])!=_) add_e(calc(i),sink,1);

}

add_e(sink,source,INF);

For(i,0,N-1) if(in[i])

{

in[i]>0?add_e(source_,i,in[i]):add_e(i,sink_,-in[i]);

imp[i]=e_tot-2;

}

int cnt[N],d[N];

bool bfs()

{

memset(d,0,sizeof(d));

memset(cnt,0,sizeof(cnt));

static int queue[65540],x;

static unsigned short int he=0,ta=0;

queue[++he]=T;

d[T]=1;

while(he!=ta)

{

x=queue[++ta]; cnt[d[x]]++;

for(int i=fst[x];~i;i=NXT) if(!d[TO]&&edge[i^1].flow)

{ d[TO]=d[x]+1; queue[++he]=TO; }

}

return d[S];

}

void cp(int &x,int y) { x>y?x=y:x; }

int p[N];

int Augment()

{

static int node,c,i;

node=T; c=INF;

while(node!=S)

{

i=p[node]; cp(c,FLOW);

node=edge[i^1].to;

}

node=T;

while(node!=S)

{

i=p[node]; FLOW-=c;

i^=1; FLOW+=c;

node=TO;

}

return c;

}

int ISAP()

{

static int node,cur[N],ret;

static bool flag;

if(!bfs()) return 0;

node=S; ret=0;

for(int i=0;i<N;i++) cur[i]=fst[i];

while(d[S]<n*2+5)

{

if(node==T)

{

ret+=Augment();

node=S;

}

flag=false;

for(int i=cur[node];~i;i=NXT) if(d[TO]==d[node]-1&&FLOW)

{

p[TO]=i;

cur[node]=i;

node=TO;

flag=true;

break;

}

if(flag) continue;

int M=N-1;

if(!--cnt[d[node]]) break;

for(int i=fst[node];~i;i=NXT) if(FLOW) cp(M,d[TO]+1);

cnt[d[node]=M]++;

cur[node]=fst[node];

node==S?node:node=edge[p[node]^1].to;

}

return ret;

}

bool check()

{

For(i,0,N-1) if(imp[i]) if(edge[imp[i]].flow) return false;

return true;

}

int main()

{

init();

S=source_,T=sink_;

ISAP();

// printf("%d\n",ISAP());

if(!check())

{

puts("-1");

return 0;

}

S=source,T=sink;

printf("%d\n",ISAP()*3);

return 0;

}

BZOJ3698

@OceanEye6年前

05/31

18:52

有上下界网络流的学习笔记

OceanEye 撰写有上下界网络流网络流费用流无回复

Link1 Link2

BZOJ3876

#include <cstdio>
#include <algorithm>
#include <cstring>
#include <cstdlib>
#include <cmath>
#include <vector>
#define ll long long
#define INF 1000000000
#define p(x) ('0'<=x&&x<='9')
#define For(i,l,r) for(int i=l;i<=r;i++)

char cc; int C;
template <class T>
void read( T &x )
{
	x=0; cc=getchar(); C=1;
	while(!p(cc)) { if(cc=='-') C=-1; cc=getchar(); }
	while(p(cc)) { x=x*10+cc-48; cc=getchar(); }
	x*=C;
}

using namespace std;
#define EE 40000
#define N 350
#define source 0
#define sink N-1
struct Tedge
{
	int to,flow,val;
}edge[EE];
#define E edge[i]
#define FLOW E.flow
#define TO E.to
#define VAL E.val
int fst[N],NXT[EE],e_tot;
int n;
void add_e(int from,int to,int flow,int val)
{
	static int &i=e_tot;
	TO=to; FLOW=flow; VAL=val; NXT[i]=fst[from]; fst[from]=i++;
	TO=from; FLOW=0; VAL=-val; NXT[i]=fst[to]; fst[to]=i++;
}
void init()
{
	int _,__,___;
	memset(fst,-1,sizeof(fst));
	read(n);
	for(int i=1;i<=n;i++)
	{
		read(_);
		if(i!=1)add_e(i,1,INF,0);
		if(_==0) continue;
		add_e(i,sink,_,0);
		while(_--)
		{
			read(__); read(___);
			add_e(i,__,INF,___);
			add_e(source,__,1,___);
		}
	}
}

int S,T,ans;
int d[N],p[N];
bool inq[N];

void Augment()
{
//	puts("1");
	static int node,c,i;
	node=T; c=INF;
	while(node!=S)
	{
		i=p[node];
		c=min(FLOW,c);
		node=edge[i^1].to;
	}
	node=T;
	while(node!=S)
	{
		i=p[node]; FLOW-=c; i^=1; FLOW+=c;
		node=TO;
	}
	ans+=c*d[T];
}

bool SPFA()
{
	static int Q[65540],x,i;
	static unsigned short int he=0,ta=0;
	memset(d,0x7f,sizeof(d));
	d[S]=0; inq[S]=true; Q[++he]=S;
	while(he!=ta)
	{
		x=Q[++ta]; inq[x]=0;
		for(i=fst[x];~i;i=NXT[i]) if(FLOW&&d[TO]>d[x]+VAL)
		{
			d[TO]=d[x]+VAL; p[TO]=i;
			if(!inq[TO]) inq[TO]=1,Q[++he]=TO;
		}
	}
	return d[T]<INF;
}

int main()
{
	init();
	S=source; T=sink;
	while(SPFA()) Augment();
	printf("%d",ans);
	return 0;
}

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#include <cstdio>

#include <algorithm>

#include <cstring>

#include <cstdlib>

#include <cmath>

#include <vector>

#define ll long long

#define INF 1000000000

#define p(x) ('0'<=x&&x<='9')

#define For(i,l,r) for(int i=l;i<=r;i++)

char cc; int C;

template <class T>

void read( T &x )

{

x=0; cc=getchar(); C=1;

while(!p(cc)) { if(cc=='-') C=-1; cc=getchar(); }

while(p(cc)) { x=x*10+cc-48; cc=getchar(); }

x*=C;

}

using namespace std;

#define EE 40000

#define N 350

#define source 0

#define sink N-1

struct Tedge

{

int to,flow,val;

}edge[EE];

#define E edge[i]

#define FLOW E.flow

#define TO E.to

#define VAL E.val

int fst[N],NXT[EE],e_tot;

int n;

void add_e(int from,int to,int flow,int val)

{

static int &i=e_tot;

TO=to; FLOW=flow; VAL=val; NXT[i]=fst[from]; fst[from]=i++;

TO=from; FLOW=0; VAL=-val; NXT[i]=fst[to]; fst[to]=i++;

}

void init()

{

int _,__,___;

memset(fst,-1,sizeof(fst));

read(n);

for(int i=1;i<=n;i++)

{

read(_);

if(i!=1)add_e(i,1,INF,0);

if(_==0) continue;

add_e(i,sink,_,0);

while(_--)

{

read(__); read(___);

add_e(i,__,INF,___);

add_e(source,__,1,___);

}

int S,T,ans;

int d[N],p[N];

bool inq[N];

void Augment()

{

// puts("1");

static int node,c,i;

node=T; c=INF;

while(node!=S)

{

i=p[node];

c=min(FLOW,c);

node=edge[i^1].to;

}

node=T;

while(node!=S)

{

i=p[node]; FLOW-=c; i^=1; FLOW+=c;

node=TO;

}

ans+=c*d[T];

}

bool SPFA()

{

static int Q[65540],x,i;

static unsigned short int he=0,ta=0;

memset(d,0x7f,sizeof(d));

d[S]=0; inq[S]=true; Q[++he]=S;

while(he!=ta)

{

x=Q[++ta]; inq[x]=0;

for(i=fst[x];~i;i=NXT[i]) if(FLOW&&d[TO]>d[x]+VAL)

{

d[TO]=d[x]+VAL; p[TO]=i;

if(!inq[TO]) inq[TO]=1,Q[++he]=TO;

}

return d[T]<INF;

}

int main()

{

init();

S=source; T=sink;

while(SPFA()) Augment();

printf("%d",ans);

return 0;

}

BZOJ2502

#include <cstdio>
#include <algorithm>
#include <cstring>
#include <queue>
#define ll long long
#define INF 10000000
#define p(x) ('0'<=x&&x<='9')
#define For(i,l,r) for(int i=l;i<=r;i++)
char cc; int C;
template <class T>
void read( T &x )
{
	x=0; cc=getchar(); C=1;
	while(!p(cc)) { if(cc=='-') C=-1; cc=getchar(); }
	while(p(cc)) { x=x*10+cc-48; cc=getchar(); }
	x*=C;
}
void cp(int &x,int y) { x>y?x=y:x=x; }
using namespace std;
#define EE 40000
#define N 150
#define source 0
#define sink (N-1)
#define sink_ (N-2)
#define source_ (N-3)
struct Tedge
{
	int to,flow;
}edge[EE];
int e_tot,fst[N],nxt[EE];
#define E edge[i]
#define FLOW E.flow
#define TO E.to
#define NXT nxt[i]
void add_e(int from,int to,int flow)
{
	static int &i=e_tot;
	FLOW=flow; TO=to; NXT=fst[from]; fst[from]=i++;
	FLOW=0; TO=from; NXT=fst[to]; fst[to]=i++;
}
int o[N],n;
void init()
{
	memset(fst,-1,sizeof(fst));
	int _,__;
	read(n);
	For(i,1,n)
	{
		add_e(source,i,INF);
		read(_); o[i]-=_;
		if(_==0) add_e(i,sink,INF);
		while(_--)
		{
			read(__);
			o[__]++;
			add_e(i,__,INF);
		}
	}
	For(i,1,n)
	{
		if(o[i]<0) add_e(i,sink_,-o[i]);
		else add_e(source_,i,o[i]);
	}
}

int m[N],d[N],p[N],cur[N],S,T;

bool bfs()
{
	static queue <int> Q; static int x,i;
	Q.push(T); d[T]=1;
	while(!Q.empty())
	{
		x=Q.front(); Q.pop(); m[d[x]]++;
		for(i=fst[x];~i;i=NXT) if((edge[i^1].flow)&&!d[TO])
		{
			d[TO]=d[x]+1;
			Q.push(TO);
		}
	}
	return d[S];
}

void Augment()
{
	static int node,c,i;
	node=T; c=INF;
	while(node!=S){
		i=p[node]; cp(c,FLOW);
		node=edge[i^1].to;
	}
	node=T;
	while(node!=S)
	{
		i=p[node]; FLOW-=c; i^=1; FLOW+=c;
		node=TO;
	}
	return;
}

void ISAP()
{
	memset(m,0,sizeof(m)); memset(d,0,sizeof(d));
	int node=S,M,i; bool flag;
	For(i,0,N-1) cur[i]=fst[i];
	while(d[S]<=n+4)
	{
		if(node==T)
		{
			Augment();
			node=S;
		}
		flag=false;
		for(i=cur[node];~i;i=NXT) if(d[TO]==d[node]-1&&FLOW)
		{
			p[TO]=i;
			cur[node]=i;
			node=TO;
			flag=true;
			break;
		}
		if(flag) continue;
		if(!--m[d[node]]) return;
		M=N-1;
		for(cur[node]=i=fst[node];~i;i=NXT)
			if(FLOW) cp(M,d[TO]+1);
		m[d[node]=M]++;
		node=(node!=S?edge[p[node]^1].to:node);
	}
}

int main()
{
	freopen("BZOJ2502.in","r",stdin);
	init();
	S=source_; T=sink_;
	ISAP();
	add_e(sink,source,INF);
	ISAP();
	printf("%d\n",edge[e_tot-1].flow);
	return 0;
}

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#include <cstdio>

#include <algorithm>

#include <cstring>

#include <queue>

#define ll long long

#define INF 10000000

#define p(x) ('0'<=x&&x<='9')

#define For(i,l,r) for(int i=l;i<=r;i++)

char cc; int C;

template <class T>

void read( T &x )

{

x=0; cc=getchar(); C=1;

while(!p(cc)) { if(cc=='-') C=-1; cc=getchar(); }

while(p(cc)) { x=x*10+cc-48; cc=getchar(); }

x*=C;

}

void cp(int &x,int y) { x>y?x=y:x=x; }

using namespace std;

#define EE 40000

#define N 150

#define source 0

#define sink (N-1)

#define sink_ (N-2)

#define source_ (N-3)

struct Tedge

{

int to,flow;

}edge[EE];

int e_tot,fst[N],nxt[EE];

#define E edge[i]

#define FLOW E.flow

#define TO E.to

#define NXT nxt[i]

void add_e(int from,int to,int flow)

{

static int &i=e_tot;

FLOW=flow; TO=to; NXT=fst[from]; fst[from]=i++;

FLOW=0; TO=from; NXT=fst[to]; fst[to]=i++;

}

int o[N],n;

void init()

{

memset(fst,-1,sizeof(fst));

int _,__;

read(n);

For(i,1,n)

{

add_e(source,i,INF);

read(_); o[i]-=_;

if(_==0) add_e(i,sink,INF);

while(_--)

{

read(__);

o[__]++;

add_e(i,__,INF);

}

For(i,1,n)

{

if(o[i]<0) add_e(i,sink_,-o[i]);

else add_e(source_,i,o[i]);

}

int m[N],d[N],p[N],cur[N],S,T;

bool bfs()

{

static queue <int> Q; static int x,i;

Q.push(T); d[T]=1;

while(!Q.empty())

{

x=Q.front(); Q.pop(); m[d[x]]++;

for(i=fst[x];~i;i=NXT) if((edge[i^1].flow)&&!d[TO])

{

d[TO]=d[x]+1;

Q.push(TO);

}

return d[S];

}

void Augment()

{

static int node,c,i;

node=T; c=INF;

while(node!=S){

i=p[node]; cp(c,FLOW);

node=edge[i^1].to;

}

node=T;

while(node!=S)

{

i=p[node]; FLOW-=c; i^=1; FLOW+=c;

node=TO;

}

return;

}

void ISAP()

{

memset(m,0,sizeof(m)); memset(d,0,sizeof(d));

int node=S,M,i; bool flag;

For(i,0,N-1) cur[i]=fst[i];

while(d[S]<=n+4)

{

if(node==T)

{

Augment();

node=S;

}

flag=false;

for(i=cur[node];~i;i=NXT) if(d[TO]==d[node]-1&&FLOW)

{

p[TO]=i;

cur[node]=i;

node=TO;

flag=true;

break;

}

if(flag) continue;

if(!--m[d[node]]) return;

M=N-1;

for(cur[node]=i=fst[node];~i;i=NXT)

if(FLOW) cp(M,d[TO]+1);

m[d[node]=M]++;

node=(node!=S?edge[p[node]^1].to:node);

}

int main()

{

freopen("BZOJ2502.in","r",stdin);

init();

S=source_; T=sink_;

ISAP();

add_e(sink,source,INF);

ISAP();

printf("%d\n",edge[e_tot-1].flow);

return 0;

}

BZOJ2055

#include <cstdio>
#include <algorithm>
#include <cstring>
#include <cstdlib>
#include <cmath>
#define ll long long
#define INF 1000000000
#define p(x) ('0'<=x&&x<='9')
#define For(i,l,r) for(int i=l;i<=r;i++)

char cc; int C;
template <class T>
void read( T &x )
{
	x=0; cc=getchar(); C=1;
	while(!p(cc)) { if(cc=='-') C=-1; cc=getchar(); }
	while(p(cc)) { x=x*10+cc-48; cc=getchar(); }
	x*=C;
}
void cp(int &x,int y) { x>y?x=y:x; }
using namespace std;
#define EE 80010
#define N 210
#define source 0
#define sink (N-1)
#define source_ (N-2)
#define sink_ (N-3)
#define calc(i) (i+n)
struct Tedge
{
	int to,flow,val;
}edge[EE];
int fst[N],nxt[EE],e_tot;
#define E edge[i]
#define FLOW E.flow
#define TO E.to
#define VAL E.val
#define NXT nxt[i]
void add_e(int from,int to,int flow,int val)
{
	static int &i=e_tot;
	TO=to; FLOW=flow; VAL=val; 
	NXT=fst[from]; fst[from]=e_tot++;
	TO=from; FLOW=0; VAL=-val;
	NXT=fst[to]; fst[to]=e_tot++;
}

int n,m,v[N];

void init()
{
	int _;
	memset(fst,-1,sizeof(fst));
	read(n); read(m);
	add_e(sink,source,m,0);
	for(int i=1;i<=n;i++)
	{
		add_e(source,i,INF,0);
		add_e(calc(i),sink,INF,0);
		read(_);
		add_e(source_,calc(i),_,0);
		add_e(i,sink_,_,0);
	}
	For(i,1,n-1)
		for(int j=i+1;j<=n;j++)
		{
			read(_); if(!~_) continue;
			add_e(calc(i),j,INF,_);
		}
}

int ans,d[N],p[N],S,T;
bool inq[N];

void Augment()
{
	static int node,c,i;
	node=T; c=INF;
	while(node!=S)
	{
		i=p[node];
		cp(c,FLOW); node=edge[i^1].to;
	}
	node=T;
	while(node!=S)
	{
		i=p[node]; FLOW-=c; i^=1; FLOW+=c;
		node=TO;
	}
	ans+=c*d[T];
}

bool SPFA()
{
	static int Q[65540],i;
	static unsigned short int he=0,ta=0,x;
	memset(d,0x7f,sizeof(d));
	Q[++he]=S; d[S]=0;
	while(he!=ta)
	{
		x=Q[++ta]; inq[x]=false;
		for(i=fst[x];~i;i=NXT)
			if(FLOW&&d[TO]>d[x]+VAL)
			{
				d[TO]=d[x]+VAL; p[TO]=i;
				if(!inq[TO]) inq[TO]=true,Q[++he]=TO;
			}
	}
	if(d[T]>INF) return false;
	Augment();
	return true;
}

int main()
{
	init();
	S=source_; T=sink_;
	while(SPFA());
	printf("%d",ans);
	return 0;
}

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#include <cstdio>

#include <algorithm>

#include <cstring>

#include <cstdlib>

#include <cmath>

#define ll long long

#define INF 1000000000

#define p(x) ('0'<=x&&x<='9')

#define For(i,l,r) for(int i=l;i<=r;i++)

char cc; int C;

template <class T>

void read( T &x )

{

x=0; cc=getchar(); C=1;

while(!p(cc)) { if(cc=='-') C=-1; cc=getchar(); }

while(p(cc)) { x=x*10+cc-48; cc=getchar(); }

x*=C;

}

void cp(int &x,int y) { x>y?x=y:x; }

using namespace std;

#define EE 80010

#define N 210

#define source 0

#define sink (N-1)

#define source_ (N-2)

#define sink_ (N-3)

#define calc(i) (i+n)

struct Tedge

{

int to,flow,val;

}edge[EE];

int fst[N],nxt[EE],e_tot;

#define E edge[i]

#define FLOW E.flow

#define TO E.to

#define VAL E.val

#define NXT nxt[i]

void add_e(int from,int to,int flow,int val)

{

static int &i=e_tot;

TO=to; FLOW=flow; VAL=val;

NXT=fst[from]; fst[from]=e_tot++;

TO=from; FLOW=0; VAL=-val;

NXT=fst[to]; fst[to]=e_tot++;

}

int n,m,v[N];

void init()

{

int _;

memset(fst,-1,sizeof(fst));

read(n); read(m);

add_e(sink,source,m,0);

for(int i=1;i<=n;i++)

{

add_e(source,i,INF,0);

add_e(calc(i),sink,INF,0);

read(_);

add_e(source_,calc(i),_,0);

add_e(i,sink_,_,0);

}

For(i,1,n-1)

for(int j=i+1;j<=n;j++)

{

read(_); if(!~_) continue;

add_e(calc(i),j,INF,_);

}

int ans,d[N],p[N],S,T;

bool inq[N];

void Augment()

{

static int node,c,i;

node=T; c=INF;

while(node!=S)

{

i=p[node];

cp(c,FLOW); node=edge[i^1].to;

}

node=T;

while(node!=S)

{

i=p[node]; FLOW-=c; i^=1; FLOW+=c;

node=TO;

}

ans+=c*d[T];

}

bool SPFA()

{

static int Q[65540],i;

static unsigned short int he=0,ta=0,x;

memset(d,0x7f,sizeof(d));

Q[++he]=S; d[S]=0;

while(he!=ta)

{

x=Q[++ta]; inq[x]=false;

for(i=fst[x];~i;i=NXT)

if(FLOW&&d[TO]>d[x]+VAL)

{

d[TO]=d[x]+VAL; p[TO]=i;

if(!inq[TO]) inq[TO]=true,Q[++he]=TO;

}

if(d[T]>INF) return false;

Augment();

return true;

}

int main()

{

init();

S=source_; T=sink_;

while(SPFA());

printf("%d",ans);

return 0;

}

有上下界网络流的学习笔记

@OceanEye6年前

05/9

21:15

BZOJ4808

OceanEye 撰写 BZOJ 最小割网络流无回复

题目名字很有趣

但是看完题面会发现这就是个黑白染色最小割

网络流大法好，ISAP直接跑

好像这几道题是一个系列的233

#include <cstdio>
#include <algorithm>
#include <cstdlib>
#include <cstring>
#include <queue>
#define ll long long 
#define INF 1000000000
char cc; int C;
#define p(x) ('0'<=x&&x<='9')
template <class T>
void read( T &x )
{
	cc=getchar(); C=1; x=0;
	while(!p(cc)) { if(cc=='-') C=-1; cc=getchar(); }
	while(p(cc)) { x=x*10+cc-48; cc=getchar(); }
	x*=C;
}
using namespace std;

#define N 205
#define E 800000
#define S 0
#define T 40009

struct Tedge
{
	int from,to,cap,flow;
}edge[E];
int e_tot,NXT[E],fst[40010];
#define TO edge[i].to
#define FROM edge[i].from
#define FL (edge[i].cap-edge[i].flow)
void add_e(int _,int __,int cap)
{
	edge[e_tot].from=_; edge[e_tot].to=__; edge[e_tot].cap=cap; edge[e_tot].flow=0;
	NXT[e_tot]=fst[_]; fst[_]=e_tot++;
	edge[e_tot].from=__; edge[e_tot].to=_; edge[e_tot].cap=cap; edge[e_tot].flow=cap;
	NXT[e_tot]=fst[__]; fst[__]=e_tot++;
}

int d[40010],p[40010],cur[40010],cnt[40010];
int mp[N][N],n,m,tot;

bool bfs()
{
	int x,i;
	d[T]=1;
	queue <int> Q;
	Q.push(T);
	while(!Q.empty())
	{
		x=Q.front(); Q.pop();
		cnt[d[x]]++;
		for(i=fst[x];~i;i=NXT[i])
		{
			if(d[TO]||FL) continue;
			d[TO]=d[x]+1;
			Q.push(TO);
		}
	}
	return d[S]!=0;
}

int Augment()
{
	int node,ret,i;
	node=T; ret=INF;
	while(node!=S)
	{
		i=p[node];
		ret=min(ret,FL);
		node=FROM;
	}
	node=T;
	while(node!=S)
	{
		i=p[node];
		edge[i].flow+=ret;
		edge[i^1].flow-=ret;
		node=FROM;
	}
	return ret;
}

int ISAP()
{
	if(!bfs()) return 0;
	int node=S,ret=0,M,i;
	bool flag;
	for(int i=0;i<40010;i++) cur[i]=fst[i];
	while(d[S]<=tot+2)
	{
		if(node==T)
		{
			ret+=Augment();
			node=S;
		}
		flag=false;
		for(i=cur[node];~i;i=NXT[i])
			if(d[TO]==d[node]-1&&FL)
			{
				flag=true;
				p[TO]=cur[node]=i;
				node=TO;
				break;
			}
		if(flag) continue;
		M=tot+5;
		for(cur[node]=i=fst[node];~i;i=NXT[i])
			if(FL) M=min(M,d[TO]+1);
		if(!--cnt[d[node]]) return ret;
		cnt[d[node]=M]++;
		node!=S?node=edge[p[node]].from:node=S;
	}
	return ret;
}

const int _x[8]={1,1,2,2,-1,-1,-2,-2},_y[8]={2,-2,1,-1,2,-2,1,-1};

#define calc(x,y) ( (x-1)*m+y )

void pre()
{
	memset(fst,-1,sizeof(fst));
	read(n); read(m);
	for(int i=1;i<=n;i++)
		for(int j=1;j<=m;j++) read(mp[i][j]);
	int x,y,pt;
	for(int i=1;i<=n;i++)
		for(int j=1;j<=m;j++)
		{
			if(mp[i][j]) continue;
			tot++;
			pt=calc(i,j);
			if((i^j)&1)
			{
				add_e(S,pt,1);
				for(int k=0;k<8;k++)
				{
					x=_x[k]+i; y=_y[k]+j;
					if(mp[x][y])continue;
					if(x>n||x<=0||y>m||y<=0) continue;
					add_e(pt,calc(x,y),INF);
				}
			}
			else
				add_e(pt,T,1);
		}
}

int main()
{
//	freopen("BZOJ4808.in","r",stdin);
	pre();
	printf("%d",tot-ISAP());
	return 0;
}

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#include <cstdio>

#include <algorithm>

#include <cstdlib>

#include <cstring>

#include <queue>

#define ll long long

#define INF 1000000000

char cc; int C;

#define p(x) ('0'<=x&&x<='9')

template <class T>

void read( T &x )

{

cc=getchar(); C=1; x=0;

while(!p(cc)) { if(cc=='-') C=-1; cc=getchar(); }

while(p(cc)) { x=x*10+cc-48; cc=getchar(); }

x*=C;

}

using namespace std;

#define N 205

#define E 800000

#define S 0

#define T 40009

struct Tedge

{

int from,to,cap,flow;

}edge[E];

int e_tot,NXT[E],fst[40010];

#define TO edge[i].to

#define FROM edge[i].from

#define FL (edge[i].cap-edge[i].flow)

void add_e(int _,int __,int cap)

{

edge[e_tot].from=_; edge[e_tot].to=__; edge[e_tot].cap=cap; edge[e_tot].flow=0;

NXT[e_tot]=fst[_]; fst[_]=e_tot++;

edge[e_tot].from=__; edge[e_tot].to=_; edge[e_tot].cap=cap; edge[e_tot].flow=cap;

NXT[e_tot]=fst[__]; fst[__]=e_tot++;

}

int d[40010],p[40010],cur[40010],cnt[40010];

int mp[N][N],n,m,tot;

bool bfs()

{

int x,i;

d[T]=1;

queue <int> Q;

Q.push(T);

while(!Q.empty())

{

x=Q.front(); Q.pop();

cnt[d[x]]++;

for(i=fst[x];~i;i=NXT[i])

{

if(d[TO]||FL) continue;

d[TO]=d[x]+1;

Q.push(TO);

}

return d[S]!=0;

}

int Augment()

{

int node,ret,i;

node=T; ret=INF;

while(node!=S)

{

i=p[node];

ret=min(ret,FL);

node=FROM;

}

node=T;

while(node!=S)

{

i=p[node];

edge[i].flow+=ret;

edge[i^1].flow-=ret;

node=FROM;

}

return ret;

}

int ISAP()

{

if(!bfs()) return 0;

int node=S,ret=0,M,i;

bool flag;

for(int i=0;i<40010;i++) cur[i]=fst[i];

while(d[S]<=tot+2)

{

if(node==T)

{

ret+=Augment();

node=S;

}

flag=false;

for(i=cur[node];~i;i=NXT[i])

if(d[TO]==d[node]-1&&FL)

{

flag=true;

p[TO]=cur[node]=i;

node=TO;

break;

}

if(flag) continue;

M=tot+5;

for(cur[node]=i=fst[node];~i;i=NXT[i])

if(FL) M=min(M,d[TO]+1);

if(!--cnt[d[node]]) return ret;

cnt[d[node]=M]++;

node!=S?node=edge[p[node]].from:node=S;

}

return ret;

}

const int _x[8]={1,1,2,2,-1,-1,-2,-2},_y[8]={2,-2,1,-1,2,-2,1,-1};

#define calc(x,y) ( (x-1)*m+y )

void pre()

{

memset(fst,-1,sizeof(fst));

read(n); read(m);

for(int i=1;i<=n;i++)

for(int j=1;j<=m;j++) read(mp[i][j]);

int x,y,pt;

for(int i=1;i<=n;i++)

for(int j=1;j<=m;j++)

{

if(mp[i][j]) continue;

tot++;

pt=calc(i,j);

if((i^j)&1)

{

add_e(S,pt,1);

for(int k=0;k<8;k++)

{

x=_x[k]+i; y=_y[k]+j;

if(mp[x][y])continue;

if(x>n||x<=0||y>m||y<=0) continue;

add_e(pt,calc(x,y),INF);

}

else

add_e(pt,T,1);

}

int main()

{

// freopen("BZOJ4808.in","r",stdin);

pre();

printf("%d",tot-ISAP());

return 0;

}

BZOJ4808

@OceanEye6年前

05/2

20:04

BZOJ1324

OceanEye 撰写最小割网络流无回复

有些炸裂的题解

题目是一道最大点独立集，比较裸的那种

最大点独立集=最小点覆盖集的补集

然后套最小点覆盖集用sum-tot_flow即可

#include <cstdio>
#include <algorithm>
#include <cstring>
#include <cstdlib>
#include <iostream>
#include <queue>
#define ll long long
#define INF 1000000000
#define p(x) ('0'<=x&&x<='9')

char cc; int C;
template <class T>
void read( T &x )
{
	x=0; cc=getchar(); C=1;
	while(!p(cc)) { if(cc=='-') C=-1; cc=getchar(); }
	while(p(cc)) { x=x*10+cc-48; cc=getchar(); }
	x*=C;
}

using namespace std;
#define E 100010
#define N 10050

struct Tedge
{
	int from,to,cap,flow;
}edge[E];
#define TO edge[i].to
#define FROM edge[i].from
#define FLO (edge[i].cap-edge[i].flow)
int e_tot,fst[N],NXT[E];
#define calc(x,y) ((x-1)*m+y)
#define S 0
#define T N-1

void add_e(int _,int __,int ___)
{
	edge[e_tot].to=__; edge[e_tot].from=_; edge[e_tot].cap=___; edge[e_tot].flow=0;
	NXT[e_tot]=fst[_]; fst[_]=e_tot++;
	edge[e_tot].to=_; edge[e_tot].from=__; edge[e_tot].cap=___; edge[e_tot].flow=___;
	NXT[e_tot]=fst[__]; fst[__]=e_tot++;
}

int dist[N],cnt[N],cur[N],p[N];

bool bfs()
{
	int x;
	queue <int> Q;
	dist[T]=1;
	cnt[1]=1;
	Q.push(T);
	while(!Q.empty())
	{
		x=Q.front(); Q.pop();
		for(int i=fst[x];~i;i=NXT[i])
		{
			if(dist[TO]||FLO) continue;
			cnt[dist[TO]=dist[x]+1]++;
			Q.push(TO);
		}
	}
	return dist[S]!=0;
}

int Augment()
{
	static int ret,node,i;
	ret=INF; node=T;
	while(node!=S)
	{
		i=p[node];
		ret=min(ret,FLO);
		node=FROM;
	}
	node=T;
	while(node!=S)
	{
		i=p[node];
		edge[i].flow+=ret; edge[i^1].flow-=ret;
		node=FROM;
	}
	return ret;
}

int ISAP()
{
	if(!bfs()) return 0;
	int node=S,ret=0;
	bool flag;
	for(int i=0;i<N;i++) cur[i]=fst[i];
	while(dist[S]<N)
	{
		if(node==T)
		{
			ret+=Augment();
			node=S;
		}
		flag=false;
		for(int i=cur[node];~i;i=NXT[i])
		{
			if(dist[TO]!=dist[node]-1||!FLO) continue;
			flag=true;
			p[TO]=i;
			cur[node]=i;
			node=TO;
			break;
		}
		if(flag) continue;
		int M=N+5;
		cur[node]=fst[node];
		for(int i=fst[node];~i;i=NXT[i])
		{
			if(!FLO) continue;
			M=min(dist[TO]+1,M);
		}
		if(!--cnt[dist[node]]) return ret;
		dist[node]=M;
		cnt[M]++;
		if(node!=S) node=edge[p[node]].from;
	}
	return ret;
}

int a[105][105],tot,n,m;

const int _x[4]={0,0,1,-1},_y[4]={1,-1,0,0};

void pre()
{
	memset(fst,-1,sizeof(fst));
	read(n); read(m);
	for(int i=1;i<=n;i++)
		for(int j=1;j<=m;j++) read(a[i][j]),tot+=a[i][j];
	int _,__;
	for(int i=1;i<=n;++i)
		for(int j=1;j<=m;++j)
		{
			if((i^j)&1)
			{
				add_e(calc(i,j),T,a[i][j]);
				continue;
			}
			add_e(S,calc(i,j),a[i][j]);
			for(int k=0;k<4;k++)
			{
				_=i+_x[k]; __=j+_y[k];
				if(_<=0||_>n||__<=0||__>m) continue;
				add_e(calc(i,j),calc(_,__),INF);
			}
		}
}

int main()
{
	pre();
	printf("%d",tot-ISAP());
	return 0;
}

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#include <cstdio>

#include <algorithm>

#include <cstring>

#include <cstdlib>

#include <iostream>

#include <queue>

#define ll long long

#define INF 1000000000

#define p(x) ('0'<=x&&x<='9')

char cc; int C;

template <class T>

void read( T &x )

{

x=0; cc=getchar(); C=1;

while(!p(cc)) { if(cc=='-') C=-1; cc=getchar(); }

while(p(cc)) { x=x*10+cc-48; cc=getchar(); }

x*=C;

}

using namespace std;

#define E 100010

#define N 10050

struct Tedge

{

int from,to,cap,flow;

}edge[E];

#define TO edge[i].to

#define FROM edge[i].from

#define FLO (edge[i].cap-edge[i].flow)

int e_tot,fst[N],NXT[E];

#define calc(x,y) ((x-1)*m+y)

#define S 0

#define T N-1

void add_e(int _,int __,int ___)

{

edge[e_tot].to=__; edge[e_tot].from=_; edge[e_tot].cap=___; edge[e_tot].flow=0;

NXT[e_tot]=fst[_]; fst[_]=e_tot++;

edge[e_tot].to=_; edge[e_tot].from=__; edge[e_tot].cap=___; edge[e_tot].flow=___;

NXT[e_tot]=fst[__]; fst[__]=e_tot++;

}

int dist[N],cnt[N],cur[N],p[N];

bool bfs()

{

int x;

queue <int> Q;

dist[T]=1;

cnt[1]=1;

Q.push(T);

while(!Q.empty())

{

x=Q.front(); Q.pop();

for(int i=fst[x];~i;i=NXT[i])

{

if(dist[TO]||FLO) continue;

cnt[dist[TO]=dist[x]+1]++;

Q.push(TO);

}

return dist[S]!=0;

}

int Augment()

{

static int ret,node,i;

ret=INF; node=T;

while(node!=S)

{

i=p[node];

ret=min(ret,FLO);

node=FROM;

}

node=T;

while(node!=S)

{

i=p[node];

edge[i].flow+=ret; edge[i^1].flow-=ret;

node=FROM;

}

return ret;

}

int ISAP()

{

if(!bfs()) return 0;

int node=S,ret=0;

bool flag;

for(int i=0;i<N;i++) cur[i]=fst[i];

while(dist[S]<N)

{

if(node==T)

{

ret+=Augment();

node=S;

}

flag=false;

for(int i=cur[node];~i;i=NXT[i])

{

if(dist[TO]!=dist[node]-1||!FLO) continue;

flag=true;

p[TO]=i;

cur[node]=i;

node=TO;

break;

}

if(flag) continue;

int M=N+5;

cur[node]=fst[node];

for(int i=fst[node];~i;i=NXT[i])

{

if(!FLO) continue;

M=min(dist[TO]+1,M);

}

if(!--cnt[dist[node]]) return ret;

dist[node]=M;

cnt[M]++;

if(node!=S) node=edge[p[node]].from;

}

return ret;

}

int a[105][105],tot,n,m;

const int _x[4]={0,0,1,-1},_y[4]={1,-1,0,0};

void pre()

{

memset(fst,-1,sizeof(fst));

read(n); read(m);

for(int i=1;i<=n;i++)

for(int j=1;j<=m;j++) read(a[i][j]),tot+=a[i][j];

int _,__;

for(int i=1;i<=n;++i)

for(int j=1;j<=m;++j)

{

if((i^j)&1)

{

add_e(calc(i,j),T,a[i][j]);

continue;

}

add_e(S,calc(i,j),a[i][j]);

for(int k=0;k<4;k++)

{

_=i+_x[k]; __=j+_y[k];

if(_<=0||_>n||__<=0||__>m) continue;

add_e(calc(i,j),calc(_,__),INF);

}

int main()

{

pre();

printf("%d",tot-ISAP());

return 0;

}

BZOJ1324

@OceanEye6年前

04/28

23:34

BZOJ1497

OceanEye 撰写最小割网络流无回复

最小割

从源点向每个人连收益大小的边

人向站连大小为INF的边

站向汇连大小为成本的边

这个时候的割有三种情况：

1.把收益割掉了，此时支出>收入

2.把支出割掉了，此时支出<收入

3.支出和收入同时割掉了，支出=收入

总的答案就是sum-割

#include <cstdio>
#include <algorithm>
#include <cstring>
#include <cstdlib>
#include <iostream>
#include <queue>
#define ll long long
#define INF 1000000000
#define p(x) ('0'<=x&&x<='9')

char cc; int C;
template <class T>
void read( T &x )
{
	x=0; cc=getchar(); C=1;
	while(!p(cc)) { if(cc=='-') C=-1; cc=getchar(); }
	while(p(cc)) { x=x*10+cc-48; cc=getchar(); }
	x*=C;
}

using namespace std;
#define E 400000
#define N 70050

struct Tedge
{
	int from,to,cap,flow;
}edge[E];

#define FROM edge[i].from
#define TO edge[i].to
#define FLO (edge[i].cap-edge[i].flow)

int e_tot,fst[N],NXT[E];
int n,m,tot;

void add_e(int _,int __,int ___)
{
	edge[e_tot].from=_; edge[e_tot].to=__; edge[e_tot].cap=___; edge[e_tot].flow=0;
	NXT[e_tot]=fst[_]; fst[_]=e_tot++;
	edge[e_tot].from=__; edge[e_tot].to=_; edge[e_tot].cap=___; edge[e_tot].flow=___;
	NXT[e_tot]=fst[__]; fst[__]=e_tot++;
}

#define calc(x) (x+m)
#define S 0
#define T N-1

void pre()
{
	memset(fst,-1,sizeof(fst));
	read(n); read(m);
	int _,__,___;
	for(int i=1;i<=n;i++)
	{
		read(_);
		add_e(calc(i),T,_);
	}
	for(int i=1;i<=m;i++)
	{
		read(_); read(__); read(___);
		add_e(S,i,___);
		tot+=___;
		add_e(i,calc(__),INF);
		add_e(i,calc(_),INF);
	}
}


int dist[N],p[N],cur[N],cnt[N];

int Augment()
{
	int node,cur,i;
	cur=INF; node=T;
	while(node!=S)
	{
		i=p[node];
		cur=min(cur,FLO);
		node=FROM;
	}
	node=T;
	while(node!=S)
	{
		i=p[node];
		edge[i].flow+=cur;
		edge[i^1].flow-=cur;
		node=FROM;
	}
	return cur;
}

bool bfs()
{
	int x;
	dist[T]=1;
	queue<int> Q; Q.push(T);
	while(!Q.empty())
	{
		x=Q.front(); Q.pop();
		for(int i=fst[x];~i;i=NXT[i])
			if(!FLO&&!dist[TO])
			{
				Q.push(TO);
				dist[TO]=dist[x]+1;
			}
	}
	return dist[S]!=0;
}

int ISAP()
{
	int node=S,ret=0;
	bool flag;
	if(!bfs()) return false;
	for(int i=0;i<N;i++)
	{
		cur[i]=fst[i];
		if(dist[i]) cnt[dist[i]]++;
	}
	while(dist[S]<=n*2+2)
	{
		if(node==T)
		{
			ret+=Augment();
			node=S;
		}
		flag=false;
		for(int i=cur[node];~i;i=NXT[i])
			if(dist[TO]==dist[node]-1&&FLO)
			{
				p[TO]=cur[node]=i;
				node=TO;
				flag=true;
				break;
			}
		if(flag) continue;
		int M=N-1;
		cur[node]=fst[node];
		for(int i=fst[node];~i;i=NXT[i])
		{
			if(!FLO) continue;
			M=min(M,dist[TO]+1);
		}
		if(!--cnt[dist[node]]) break;
		cnt[dist[node]=M]++;
		if(node!=S) node=edge[p[node]].from;
	}
	return ret;
}

int main()
{
	pre();
	printf("%d\n",tot-ISAP());
	return 0;
}

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#include <cstdio>

#include <algorithm>

#include <cstring>

#include <cstdlib>

#include <iostream>

#include <queue>

#define ll long long

#define INF 1000000000

#define p(x) ('0'<=x&&x<='9')

char cc; int C;

template <class T>

void read( T &x )

{

x=0; cc=getchar(); C=1;

while(!p(cc)) { if(cc=='-') C=-1; cc=getchar(); }

while(p(cc)) { x=x*10+cc-48; cc=getchar(); }

x*=C;

}

using namespace std;

#define E 400000

#define N 70050

struct Tedge

{

int from,to,cap,flow;

}edge[E];

#define FROM edge[i].from

#define TO edge[i].to

#define FLO (edge[i].cap-edge[i].flow)

int e_tot,fst[N],NXT[E];

int n,m,tot;

void add_e(int _,int __,int ___)

{

edge[e_tot].from=_; edge[e_tot].to=__; edge[e_tot].cap=___; edge[e_tot].flow=0;

NXT[e_tot]=fst[_]; fst[_]=e_tot++;

edge[e_tot].from=__; edge[e_tot].to=_; edge[e_tot].cap=___; edge[e_tot].flow=___;

NXT[e_tot]=fst[__]; fst[__]=e_tot++;

}

#define calc(x) (x+m)

#define S 0

#define T N-1

void pre()

{

memset(fst,-1,sizeof(fst));

read(n); read(m);

int _,__,___;

for(int i=1;i<=n;i++)

{

read(_);

add_e(calc(i),T,_);

}

for(int i=1;i<=m;i++)

{

read(_); read(__); read(___);

add_e(S,i,___);

tot+=___;

add_e(i,calc(__),INF);

add_e(i,calc(_),INF);

}

int dist[N],p[N],cur[N],cnt[N];

int Augment()

{

int node,cur,i;

cur=INF; node=T;

while(node!=S)

{

i=p[node];

cur=min(cur,FLO);

node=FROM;

}

node=T;

while(node!=S)

{

i=p[node];

edge[i].flow+=cur;

edge[i^1].flow-=cur;

node=FROM;

}

return cur;

}

bool bfs()

{

int x;

dist[T]=1;

queue<int> Q; Q.push(T);

while(!Q.empty())

{

x=Q.front(); Q.pop();

for(int i=fst[x];~i;i=NXT[i])

if(!FLO&&!dist[TO])

{

Q.push(TO);

dist[TO]=dist[x]+1;

}

return dist[S]!=0;

}

int ISAP()

{

int node=S,ret=0;

bool flag;

if(!bfs()) return false;

for(int i=0;i<N;i++)

{

cur[i]=fst[i];

if(dist[i]) cnt[dist[i]]++;

}

while(dist[S]<=n*2+2)

{

if(node==T)

{

ret+=Augment();

node=S;

}

flag=false;

for(int i=cur[node];~i;i=NXT[i])

if(dist[TO]==dist[node]-1&&FLO)

{

p[TO]=cur[node]=i;

node=TO;

flag=true;

break;

}

if(flag) continue;

int M=N-1;

cur[node]=fst[node];

for(int i=fst[node];~i;i=NXT[i])

{

if(!FLO) continue;

M=min(M,dist[TO]+1);

}

if(!--cnt[dist[node]]) break;

cnt[dist[node]=M]++;

if(node!=S) node=edge[p[node]].from;

}

return ret;

}

int main()

{

pre();

printf("%d\n",tot-ISAP());

return 0;

}

BZOJ1497

@OceanEye6年前

04/8

00:03

BZOJ1834

OceanEye 撰写 ISAP 模板网络流费用流无回复

嘛……几万年没好好写过网络流了……
gap优化真的强，把我的1s的代码降成了0.05s
相信前面榜上的就是gap的吧……

/**************************************************************
    Problem: 1834
    User: OceanEYe
    Language: C++
    Result: Accepted
    Time:56 ms
    Memory:1948 kb
****************************************************************/
 
#include <cstdio>
#include <algorithm>
#include <cstring>
#include <cstdlib>
#include <vector>
#include <queue>
#include <set>
#define p(x) ('0'<=x&&x<='9')
#define INF 100000000
char cc; int C;
template <class T>
void read(T &x)
{
    cc=getchar(); C=1; x=0;
    while(!p(cc))
    {
        if(cc=='-') C=-1;
        cc=getchar();
    }
    while(p(cc)) x=x*10+cc-48,cc=getchar();
    x*=C;
}
template <class T>
void MN(T &x,T y) { x>y?x=y:x=x; }
 
using namespace std;
#define N 1005
#define E 10010
 
struct Tedge
{
    int from,to,cap,flow;
    int val;
}edge[E<<2];
#define TO edge[i].to
#define VAL edge[i].val
#define SIZ (edge[i].cap-edge[i].flow)
#define CAP edge[i].cap
int fst[N],NXT[E<<2],e_tot;
void add_e(int _,int __,int ___,int ____)
{
    edge[e_tot].to=__; edge[e_tot].cap=___; edge[e_tot].from=_; edge[e_tot].val=____;
    NXT[e_tot]=fst[_]; fst[_]=e_tot++;
    edge[e_tot].to=_; edge[e_tot].cap=___; edge[e_tot].flow=___; edge[e_tot].from=__; edge[e_tot].val=-____;
    NXT[e_tot]=fst[__]; fst[__]=e_tot++;
}
 
int S,T;
struct rec
{
    int a,b,c,d;
    rec(int _,int __,int ___,int ____): a(_),b(__),c(___),d(____) {}
};
 
vector <rec> R; 
int n,m,k;
void init1()
{
    read(n); read(m); read(k);
    S=1; T=n;
    int _,__,___,____;
    memset(fst,-1,sizeof(fst));
    for(int i=1;i<=m;i++)
    {
        read(_); read(__); read(___); read(____);
        add_e(_,__,___,0);
        R.push_back(rec(_,__,___,____));
    }
}
//
bool vis[N];
int d[N],cnt[N],p[N],pre[N],ans;
int Augment()
{
    int r=T,c=INF,i;
    while(r!=S)
    {
        i=pre[r];
        MN(c,CAP-SIZ);
        r=TO;
    }
    r=T;
    while(r!=S)
    {
        i=pre[r];
        edge[i].flow-=c; edge[i^1].flow+=c;
        r=TO;
    }
    return c;
}
void ISAP()
{
    int node=S,c;
    for(int i=1;i<=n;i++) p[i]=fst[i];
    bool flag;
    while(d[S]<=n)
    {
        if(node==T)
        {
            ans+=Augment();
            node=S;
        }
        //solve
        flag=false;
        for(int i=p[node];~i;i=NXT[i])
        {
            if(d[TO]!=d[node]-1||SIZ==0) continue;
            p[node]=i;
            pre[TO]=i^1;
            node=TO;
            flag=true;
            break;
        }
        if(flag) continue;
        c=n+10;
        for(int i=fst[node];~i;i=NXT[i])
        {
            if(!SIZ) continue;
            MN(c,d[TO]+1);
        }
        if(--cnt[d[node]]==0)
        {
            printf("%d ",ans);
            return;
        }
        cnt[d[node]=c]++;
        p[node]=fst[node];
        if(node!=S)node=edge[pre[node]].to;
        //retreat
    }
    printf("%d ",ans);
}
queue<int> Q;
void bfs()
{
    int x;
    memset(vis,0,sizeof(vis));
    d[T]=1; Q.push(T); vis[T]^=1;
    while(!Q.empty())
    {
        x=Q.front(); Q.pop(); 
        cnt[d[x]]++;
        for(int i=fst[x];~i;i=NXT[i])
        {
            if(vis[TO]||SIZ) continue;
            d[TO]=d[x]+1;
            Q.push(TO);
            vis[TO]^=1;
        }
    }
}
//
int dis[N],cost;
void init2()
{
    int _,__,___,____;
    for(int i=0;i<m;i++)
    {
        _=R[i].a;
        __=R[i].b;
        ____=R[i].d;
        add_e(_,__,INF,____);
    }
}
int Augment2()
{
    int r=T,c=0,i;
    while(r!=S)
    {
        i=pre[r];
        edge[i].flow--; edge[i^1].flow++;
        c+=edge[i^1].val;
        r=TO;
    }
    return c;
}
void SPFA()
{
    memset(dis,0x7f,sizeof(dis));
    memset(vis,false,sizeof(vis));
    dis[S]=0; Q.push(S); vis[S]=true;
    int x,i;
    while(!Q.empty())
    {
        x=Q.front(); Q.pop(); vis[x]=false;
        for(i=fst[x];~i;i=NXT[i])
        {
            if(!SIZ) continue;
            if(dis[TO]<=dis[x]+VAL) continue;
            dis[TO]=dis[x]+VAL;
            pre[TO]=i^1;
            if(vis[TO]) continue;
            vis[TO]=true;
            Q.push(TO);
        }
    }
    cost+=Augment2();
}
//
int main()
{
    init1();
    bfs();
    ISAP();
    init2();
    for(int i=1;i<=k;i++) SPFA();
    printf("%d\n",cost);
    return 0;
}

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/**************************************************************

Problem: 1834

User: OceanEYe

Language: C++

Result: Accepted

Time:56 ms

Memory:1948 kb

****************************************************************/

#include <cstdio>

#include <algorithm>

#include <cstring>

#include <cstdlib>

#include <vector>

#include <queue>

#include <set>

#define p(x) ('0'<=x&&x<='9')

#define INF 100000000

char cc; int C;

template <class T>

void read(T &x)

{

cc=getchar(); C=1; x=0;

while(!p(cc))

{

if(cc=='-') C=-1;

cc=getchar();

}

while(p(cc)) x=x*10+cc-48,cc=getchar();

x*=C;

}

template <class T>

void MN(T &x,T y) { x>y?x=y:x=x; }

using namespace std;

#define N 1005

#define E 10010

struct Tedge

{

int from,to,cap,flow;

int val;

}edge[E<<2];

#define TO edge[i].to

#define VAL edge[i].val

#define SIZ (edge[i].cap-edge[i].flow)

#define CAP edge[i].cap

int fst[N],NXT[E<<2],e_tot;

void add_e(int _,int __,int ___,int ____)

{

edge[e_tot].to=__; edge[e_tot].cap=___; edge[e_tot].from=_; edge[e_tot].val=____;

NXT[e_tot]=fst[_]; fst[_]=e_tot++;

edge[e_tot].to=_; edge[e_tot].cap=___; edge[e_tot].flow=___; edge[e_tot].from=__; edge[e_tot].val=-____;

NXT[e_tot]=fst[__]; fst[__]=e_tot++;

}

int S,T;

struct rec

{

int a,b,c,d;

rec(int _,int __,int ___,int ____): a(_),b(__),c(___),d(____) {}

};

vector <rec> R;

int n,m,k;

void init1()

{

read(n); read(m); read(k);

S=1; T=n;

int _,__,___,____;

memset(fst,-1,sizeof(fst));

for(int i=1;i<=m;i++)

{

read(_); read(__); read(___); read(____);

add_e(_,__,___,0);

R.push_back(rec(_,__,___,____));

}

bool vis[N];

int d[N],cnt[N],p[N],pre[N],ans;

int Augment()

{

int r=T,c=INF,i;

while(r!=S)

{

i=pre[r];

MN(c,CAP-SIZ);

r=TO;

}

r=T;

while(r!=S)

{

i=pre[r];

edge[i].flow-=c; edge[i^1].flow+=c;

r=TO;

}

return c;

}

void ISAP()

{

int node=S,c;

for(int i=1;i<=n;i++) p[i]=fst[i];

bool flag;

while(d[S]<=n)

{

if(node==T)

{

ans+=Augment();

node=S;

}

//solve

flag=false;

for(int i=p[node];~i;i=NXT[i])

{

if(d[TO]!=d[node]-1||SIZ==0) continue;

p[node]=i;

pre[TO]=i^1;

node=TO;

flag=true;

break;

}

if(flag) continue;

c=n+10;

for(int i=fst[node];~i;i=NXT[i])

{

if(!SIZ) continue;

MN(c,d[TO]+1);

}

if(--cnt[d[node]]==0)

{

printf("%d ",ans);

return;

}

cnt[d[node]=c]++;

p[node]=fst[node];

if(node!=S)node=edge[pre[node]].to;

//retreat

}

printf("%d ",ans);

}

queue<int> Q;

void bfs()

{

int x;

memset(vis,0,sizeof(vis));

d[T]=1; Q.push(T); vis[T]^=1;

while(!Q.empty())

{

x=Q.front(); Q.pop();

cnt[d[x]]++;

for(int i=fst[x];~i;i=NXT[i])

{

if(vis[TO]||SIZ) continue;

d[TO]=d[x]+1;

Q.push(TO);

vis[TO]^=1;

}

int dis[N],cost;

void init2()

{

int _,__,___,____;

for(int i=0;i<m;i++)

{

_=R[i].a;

__=R[i].b;

____=R[i].d;

add_e(_,__,INF,____);

}

int Augment2()

{

int r=T,c=0,i;

while(r!=S)

{

i=pre[r];

edge[i].flow--; edge[i^1].flow++;

c+=edge[i^1].val;

r=TO;

}

return c;

}

void SPFA()

{

memset(dis,0x7f,sizeof(dis));

memset(vis,false,sizeof(vis));

dis[S]=0; Q.push(S); vis[S]=true;

int x,i;

while(!Q.empty())

{

x=Q.front(); Q.pop(); vis[x]=false;

for(i=fst[x];~i;i=NXT[i])

{

if(!SIZ) continue;

if(dis[TO]<=dis[x]+VAL) continue;

dis[TO]=dis[x]+VAL;

pre[TO]=i^1;

if(vis[TO]) continue;

vis[TO]=true;

Q.push(TO);

}

cost+=Augment2();

}

int main()

{

init1();

bfs();

ISAP();

init2();

for(int i=1;i<=k;i++) SPFA();

printf("%d\n",cost);

return 0;

}

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