poj1459 - Power Network
想看更多的解题报告:http://blog.csdn.net/wangjian8006/article/details/7870410
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题目大意：总共有n个节点，其中有发电站np个、用户nc个和调度器n-np-nc个三种节点，每个发电站有一个最大发电量，每个用户有个最大接受电量，现在有m条有向边，边有一个最大的流量代表，最多可以流出这么多电，现在从发电站发电到用户，问最多可以发多少电
解题思路：将发电站看成源点，用户看成汇点，这样求最大流就可以了，不过因为有多个源点和汇点，所以加一个超级源点指向所有的发电站，流量为无限大，加一个超级汇点让所有的用户指向他，流量也为无限大，这样，从超级源点到超级汇点求最大流即可。
题目比较简单，总结了几种最大流的算法
/*
EdmondsKarp
Memory 320K
Time 1282MS
和没过没什么区别
*/
#include
#include
using namespace std;
#define min(a,b) (aq;
memset(a,0,sizeof(a));
memset(parent,-1,sizeof(parent));
q.push(start);
a[start]=MAXINT;
while(!q.empty()){
v=q.front();q.pop();
for(i=1;i<=vertime;i++){
if(!a[i] && map[v][i].capacity>map[v][i].flow){
q.push(i);
parent[i]=v;
a[i]=min(a[v],map[v][i].capacity-map[v][i].flow);
}
}
if(v==end) break;
}
return a[end];
}
void EdmondsKarp(){
int i,tmp;
maxflow=0;
while(tmp=bfs(sp,fp)){
for(i=fp;i!=sp;i=parent[i]){
map[i][parent[i]].flow-=tmp; //更新反向流
map[parent[i]][i].flow+=tmp; //更新正向流
}
maxflow+=tmp;
}
}
int main(){
int i;
int x,y,z;
char ch;
while(scanf("%d%d%d%d", &vertime, &power_stations,&consumers,&nedges)!= EOF){
//Init
memset(map,0,sizeof(map));
//Read Gragh
for(i=1;i<=nedges;i++){ //设置读图从1开始
cin>>ch>>x>>ch>>y>>ch>>z;
map[x+1][y+1].capacity=z;
}
//Build Gragh
//建立超级源点指向所有的发电站
sp=vertime+1;fp=vertime+2;vertime+=2;
for (i=1; i<=power_stations; i++){
cin>>ch>>x>>ch>>y;
map[sp][x+1].capacity=y;
}
//建立超级汇点，使所有消费者指向它
for (i=1; i<=consumers; i++){
cin>>ch>>x>>ch>>y;
map[x+1][fp].capacity=y;
}
EdmondsKarp();
printf("%d\n",maxflow);
}
return 0;
}
===================================================================================================
/*
dinic
Memory 320K
Time 563MS
*/
#include
#include
using namespace std;
#define min(a,b) (aq;
memset(dis,0,sizeof(dis));
q.push(sp);
dis[sp]=1;
while(!q.empty()){
v=q.front();q.pop();
for(i=1;i<=vertime;i++)
if(!dis[i] && map[v][i].capacity>map[v][i].flow){
q.push(i);
dis[i]=dis[v]+1;
}
if(v==fp) return 1;
}
return 0;
}
int dfs(int cur,int cp){
if(cur==fp) return cp;
int tmp=cp,t;
for(int i=1;i<=vertime;i++)
if(dis[i]==dis[cur]+1 && tmp && map[cur][i].capacity>map[cur][i].flow){
t=dfs(i,min(map[cur][i].capacity-map[cur][i].flow,tmp));
map[cur][i].flow+=t;
map[i][cur].flow-=t;
tmp-=t;
}
return cp-tmp;
}
void dinic(){
maxflow=0;
while(bfs()) maxflow+=dfs(sp,MAXINT);
}
int main(){
int i;
int x,y,z;
char ch;
while(scanf("%d%d%d%d", &vertime, &power_stations,&consumers,&nedges)!= EOF){
//Init
memset(map,0,sizeof(map));
//Read Gragh
for(i=1;i<=nedges;i++){ //设置读图从1开始
cin>>ch>>x>>ch>>y>>ch>>z;
map[x+1][y+1].capacity=z;
}
//Build Gragh
//建立超级源点指向所有的发电站
sp=vertime+1;fp=vertime+2;vertime+=2;
for (i=1; i<=power_stations; i++){
cin>>ch>>x>>ch>>y;
map[sp][x+1].capacity=y;
}
//建立超级汇点，使所有消费者指向它
for (i=1; i<=consumers; i++){
cin>>ch>>x>>ch>>y;
map[x+1][fp].capacity=y;
}
dinic();
printf("%d\n",maxflow);
}
return 0;
}
===========================================================================================
/*
sap
Memory 328K
Time 454MS
*/
#include
#include
using namespace std;
#define MAXV 110
#define INF 1<<29
#define min(a,b) (a>b?b:a)
int n,c[MAXV][MAXV],r[MAXV][MAXV],source,sink;
int dis[MAXV],maxflow;
void bfs(){
int v,i;
queue q;
memset(dis,0,sizeof(dis));
q.push(sink);
while(!q.empty()){
v=q.front();q.pop();
for(i=0;i<=sink;i++){
if(!dis[i] && c[i][v]>0){
dis[i] = dis[v] +1;
q.push(i);
}
}
}
}
void sap(){
int top=source,pre[MAXV],i,j,low[MAXV];
bfs(); //分层
memset(low,0,sizeof(low)); //保存路径的最小流量
while(dis[source]0 && dis[top]==dis[i] +1) break;
}
if(i<=sink){ //找到了
low[i]=min(r[top][i],low[top]); //更新最小流量
pre[i]=top;top=i; //记录增广路径
if(top==sink){ //找到一条增广路径更新残量
maxflow += low[sink];
j = top;
while(j != source){
i=pre[j];
r[i][j]-=low[sink];
r[j][i]+=low[sink];
j=i;
}
top=source; //再从头找一条增广路径
memset(low,0,sizeof(low));
}
}
else{ //找不到这样一条允许弧更新距离数组
int mindis=INF;
for(j=0;j <=sink;j++){
if(r[top][j]>0 && mindis>dis[j] +1)
mindis=dis[j] +1;
}
dis[top]=mindis;
if(top!=source) top=pre[top];
}
}
}
int main(){
int i,nedges,power_stations,consumers;
int x,y,z;
char ch;
while(scanf("%d%d%d%d", &n, &power_stations,&consumers,&nedges)!= EOF){
//Init
memset(r,0,sizeof(r));
memset(c,0,sizeof(c));
source=0;sink=n+1;n+=2;maxflow=0;
//Read Gragh
for(i=1;i<=nedges;i++){ //设置读图从1开始
cin>>ch>>x>>ch>>y>>ch>>z;
c[x+1][y+1]=r[x+1][y+1]=z;
}
//Build Gragh
//建立超级源点指向所有的发电站
for (i=1;i<=power_stations;i++){
cin>>ch>>x>>ch>>y;
c[source][x+1]=r[source][x+1]=y;
}
//建立超级汇点，使所有消费者指向它
for (i=1;i<=consumers;i++){
cin>>ch>>x>>ch>>y;
c[x+1][sink]=r[x+1][sink]=y;
}
sap();
printf("%d\n",maxflow);
}
return 0;
}
=======================================================================================================
/*
sap+分层+gap优化
Memory 328K
Time 438MS
*/
#include
#include
using namespace std;
#define MAXV 110
#define INF 1<<29
#define min(a,b) (a>b?b:a)
int n,c[MAXV][MAXV],r[MAXV][MAXV],source,sink;
int dis[MAXV],maxflow,gap[MAXV];
void bfs(){
int v,i;
queue q;
memset(dis,0,sizeof(dis));
memset(gap,0,sizeof(gap));
gap[0]++;
q.push(sink);
while(!q.empty()){
v=q.front();q.pop();
for(i=0;i<=sink;i++){
if(!dis[i] && c[i][v]>0){
dis[i] = dis[v] +1;
gap[dis[i]]++;
q.push(i);
}
}
}
}
void sap(){
int top=source,pre[MAXV],i,j,low[MAXV];
bfs(); //分层
memset(low,0,sizeof(low)); //保存路径的最小流量
while(dis[source]0 && dis[top]==dis[i]+1 && dis[i]>=0) break;
}
if(i<=sink){ //找到了
low[i]=min(r[top][i],low[top]); //更新最小流量
pre[i]=top;top=i; //记录增广路径
if(top==sink){ //找到一条增广路径更新残量
maxflow += low[sink];
j = top;
while(j != source){
i=pre[j];
r[i][j]-=low[sink];
r[j][i]+=low[sink];
j=i;
}
top=source; //再从头找一条增广路径
memset(low,0,sizeof(low));
}
}
else{ //找不到这样一条允许弧更新距离数组
int mindis=INF;
for(j=0;j <=sink;j++){
if(r[top][j]>0 && mindis>dis[j] +1 && dis[j]>=0)
mindis=dis[j] +1;
}
gap[dis[top]]--;
if (gap[dis[top]] ==0) break;
gap[mindis]++;
dis[top]=mindis;
if(top!=source) top=pre[top];
}
}
}
int main(){
int i,nedges,power_stations,consumers;
int x,y,z;
char ch;
while(scanf("%d%d%d%d", &n, &power_stations,&consumers,&nedges)!= EOF){
//Init
memset(r,0,sizeof(r));
memset(c,0,sizeof(c));
source=0;sink=n+1;n+=2;maxflow=0;
//Read Gragh
for(i=1;i<=nedges;i++){ //设置读图从1开始
cin>>ch>>x>>ch>>y>>ch>>z;
c[x+1][y+1]=r[x+1][y+1]=z;
}
//Build Gragh
//建立超级源点指向所有的发电站
for (i=1;i<=power_stations;i++){
cin>>ch>>x>>ch>>y;
c[source][x+1]=r[source][x+1]=y;
}
//建立超级汇点，使所有消费者指向它
for (i=1;i<=consumers;i++){
cin>>ch>>x>>ch>>y;
c[x+1][sink]=r[x+1][sink]=y;
}
sap();
printf("%d\n",maxflow);
}
return 0;
}