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hdu 1565 方格取数(神奇的最小割,模板题)

2017-10-12 12:24 323 查看
题目:http://acm.split.hdu.edu.cn/showproblem.php?pid=1565

思路:

最大流最小割:最大和=所有数之和—最小割(网络流)

建图:奇数点连源点,然后以inf为容量连周围偶数点,偶数点连汇点。

#include<cstdio>
#include<cstring>
#include<algorithm>
#include<vector>
#include<queue>
#include<iostream>
#define mem(a,x) memset(a,x,sizeof(a))
using namespace std;
const int inf =  0x3f3f3f3f;
const int maxn = 50 + 5;
const int maxs = maxn*maxn + 5;
int n,m,source,sink;
int mp[maxn][maxn];

struct Edge{
int from,to,cap,flow;
};

struct Dicnic{
int n,m,s,t;
int d[maxs],cur[maxs],vis[maxs];
vector<int>G[maxs];
vector<Edge>edges;
void AddEdge(int from,int to,int cap){
Edge e1 = {from,to,cap,0};
Edge e2 = {to,from,0,0};
edges.push_back(e1);
edges.push_back(e2);
int m = edges.size();
G[from].push_back(m-2);
G[to].push_back(m-1);
}
void init(int n){
this -> n = n;
for(int i = 0;i<=n;i++){
G[i].clear();
}
edges.clear();
}
bool BFS(){     //就是用BFS分了个层而已,一看代码便知
mem(vis,0);
queue<int>Q;
Q.push(s);
vis[s] = 1;
d[s] = 0;
//mem(d,0);
while(!Q.empty()){
int x = Q.front();      Q.pop();
for(int i=0;i<G[x].size();i++){
Edge &e = edges[G[x][i]];
if(!vis[e.to]&&e.cap>e.flow){
vis[e.to] = 1;
d[e.to] = d[x] + 1;
Q.push(e.to);
}
}
}
return vis[t];
}
int DFS(int x ,int a){  //就是顺着层次dfs而已
if(x==t||a==0)      return a;
int flow = 0 , f;
for(int &i = cur[x];i<G[x].size();i++){
Edge &e = edges[G[x][i]];
if(d[e.to]==d[x]+1&&(f = DFS(e.to,min(a,e.cap-e.flow)))>0){  //a是路径上的最小残存容量
e.flow += f;
edges[G[x][i]^1].flow -= f;  //反向边
flow += f;
a -= f;
if(a==0) break;   //a等于0及时退出,再从s那找一遍,因为从哪断的不知道
}
}
return flow;
}
int MaxFlow(int s,int t){
this -> s = s;      this ->t  = t;
int flow = 0;
while(BFS()){
mem(cur,0);
flow += DFS(s,inf);
}
return flow;
}
}g;
int drx[] = {0,1,0,-1};
int dry[] = {1,0,-1,0};
bool valid(int x,int y){
if(x<1||x>n||y<1||y>m)
return false;
else
return true;
}
int id(int x,int y){
return (x-1)*m + y;
}
int main(){
while(scanf("%d",&n)!=EOF){
m=n;
g.init(n*m + 1);
for(int i=1;i<=n;i++)
for(int j=1;j<=m;j++)
scanf("%d",&mp[i][j]);
source = 0 ; sink = n * m + 1;
int sum=0;
for(int i=1;i<=n;i++)
for(int j=1;j<=m;j++){
if((i+j)%2==1){
g.AddEdge(source,id(i,j),mp[i][j]);
for(int k = 0;k<4;k++){
int nx = i + drx[k];
int ny = j + dry[k];
if(valid(nx,ny))
g.AddEdge(id(i,j),id(nx,ny),inf);
}
}
else{
g.AddEdge(id(i,j),sink,mp[i][j]);
}
sum+=mp[i][j];
}
int ans = g.MaxFlow(source,sink);
printf("%d\n",sum-ans);
}
return 0;
}
/*
6
0 31 1231 12 1 21
13 135 1321 1 3 21
132 132 5 15 3 12
13 453 321 45 0 0
35 534 4 531 124 12
13 135 1321 1 3 21
*/
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