poj 2175 Evacuation Plan 最小费用流判定,消圈算法

时间:2021-11-10 11:59:25

题目链接

题意:一个城市有n座行政楼和m座避难所,现发生核战,要求将避难所中的人员全部安置到避难所中,每个人转移的费用为两座楼之间的曼哈顿距离+1,题目给了一种方案,问是否为最优方案,即是否全部的人员转移费用之和最小?若不是,输出SUBOPTIMAL,之后输出转移矩阵Ei,j.即第i座行政楼中Ei,j个人转移到第j座避难所;输出的不必是最优转移方案,只要比题解的sum小即可;

思路:直接建一个残量网络,即按照开始建的原图跑完最小费用流之后剩下的网络,行政楼和避难所之间的原图连边正向容量为inf,反向为0。之后反向从汇点t跑最短路,看是否存在一个负圈,若存在负圈则说明题目解的并不是最优解,这时找到圈中一点,把圈中权值为正(正向边)的流量-1,为负的流量加1即可;

负圈:圈中所有边的流量为正(跑spfa时可行),并且总的权值之和为负(不断地更新dist,直到有一点的序号超过总点数);

注:从spfa中跳出的点并不是就是圈中的点,可能开始时就弄进去负边权,导致之后出圈了序号才大于点数;

ps: sb地竟然是一直MLE...,但是返回WA,图中的边数为n*n(没算源汇连边)..

#include<iostream>
#include
<cstdio>
#include
<cstring>
#include
<string.h>
#include
<algorithm>
#include
<vector>
#include
<cmath>
#include
<stdlib.h>
#include
<time.h>
#include
<stack>
#include
<set>
#include
<map>
#include
<queue>
using namespace std;
#define rep0(i,l,r) for(int i = (l);i < (r);i++)
#define rep1(i,l,r) for(int i = (l);i <= (r);i++)
#define rep_0(i,r,l) for(int i = (r);i > (l);i--)
#define rep_1(i,r,l) for(int i = (r);i >= (l);i--)
#define MS0(a) memset(a,0,sizeof(a))
#define MS1(a) memset(a,-1,sizeof(a))
#define MSi(a) memset(a,0x3f,sizeof(a))
#define inf 0x3f3f3f3f
#define lson l, m, rt << 1
#define rson m+1, r, rt << 1|1
typedef
long long ll;
#define A first
#define B second
#define MK make_pair
typedef __int64 ll;
template
<typename T>
void read1(T &m)
{
T x
=0,f=1;char ch=getchar();
while(ch<'0'||ch>'9'){if(ch=='-')f=-1;ch=getchar();}
while(ch>='0'&&ch<='9'){x=x*10+ch-'0';ch=getchar();}
m
= x*f;
}
template
<typename T>
void read2(T &a,T &b){read1(a);read1(b);}
template
<typename T>
void read3(T &a,T &b,T &c){read1(a);read1(b);read1(c);}
template
<typename T>
void out(T a)
{
if(a>9) out(a/10);
putchar(a
%10+'0');
}
int T,kase = 1,i,j,k,n,m,s,t;
const int M = 25007;
const int N = 207;
int head[M],tot;
struct Edge{
int from,to,cap,Next,w;
Edge(){}
Edge(
int f,int to,int cap,int w,int Next):from(f),to(to),cap(cap),Next(Next),w(w){}
}e[M
<<1];
inline
void ins(int u,int v,int cap,int w)
{
e[
++tot] = Edge{u,v,cap,w,head[u]};
head[u]
= tot;
}
int dist[N][N];
struct data{int x,y,c;}X[N],Y[N];
void calc()
{
rep1(i,
1,n)
rep1(j,
1,m) //这和之后的建图并不一样;
dist[i][j] = abs(X[i].x - Y[j].x) + abs(X[i].y - Y[j].y) + 1;
}
int sum[N],ans[N][N];
int inq[N],d[N],num[N],p[N];
queue
<int> Q;
int spfa()
{
while(!Q.empty()) Q.pop();
MSi(d);MS0(inq);MS0(num);
Q.push(t);
inq[t]
= 1;d[t] = 0;num[t] = 1;
while(!Q.empty()){
int u = Q.front();Q.pop();
inq[u]
= 0;
for(int id = head[u];id;id = e[id].Next){
int v = e[id].to;
if(d[v] > d[u] + e[id].w && e[id].cap){ //负圈的判定,所有圈中的边费用均为正,费用之和为负;
d[v] = d[u] + e[id].w;
p[v]
= u;
if(!inq[v]){
num[v]
= num[u] + 1;
if(num[v] > n+m+2) return v;
Q.push(v);inq[v]
= 1;
}
}
}
}
return -1;
}
int solve()
{
int st = spfa(),u,v;
if(st == -1){return puts("OPTIMAL"),0;}
puts(
"SUBOPTIMAL");
MS0(inq);
while(1){
if(!inq[st]) inq[st] = 1,st = p[st];
else{ v = st;break;}
}
do{
u
= p[v];
if(u > n) ans[v][u-n]--;//正向边的费用为正,所以--将费用减少;
else ans[u][v-n]++;
v
= u;
}
while(v != st);
rep1(i,
1,n){
printf(
"%d",ans[i][1]);
rep1(j,
2,m) printf(" %d",ans[i][j]);
puts(
"");
}
}
int main()
{
while(scanf("%d%d",&n,&m) == 2){
MS0(head);tot
= 1;
rep1(i,
1,n) read3(X[i].x,X[i].y,X[i].c);
rep1(i,
1,m) read3(Y[i].x,Y[i].y,Y[i].c);
calc();
s
= 0, t = n + m + 1;
int w;
rep1(i,
1,n)
rep1(j,
1,m){
read1(w);
ans[i][j]
= w;
ins(i,n
+j,inf - w,dist[i][j]);//残余网络,但是边的权值没变
ins(n+j,i,w,-dist[i][j]);//原图中房子之间容量为inf和0;
sum[j] += w;
}
rep1(i,
1,n) ins(s,i,0,0), ins(i,s,X[i].c,0);
rep1(j,
1,m) ins(j+n,t,Y[j].c-sum[j],0), ins(t,j+n,sum[j],0);
solve();
}
return 0;
}