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「HNOI2013」切糕 - 最小割+离散变量模型 | Bill Yang's Blog

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「HNOI2013」切糕 - 最小割+离散变量模型

题目大意


题目分析

离散变量模型模板题。(%%% C_SUNSHINE
切糕选择的高度为离散变量,对离散变量拆点。
用$inf$连边限制两个离散变量可选的值的偏序关系。
如图:

我们这样建模来限制两个离散变量的差$\le D$。


代码

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#include<algorithm>
#include<iostream>
#include<iomanip>
#include<cstring>
#include<cstdlib>
#include<climits>
#include<vector>
#include<cstdio>
#include<cmath>
#include<queue>
using namespace std;

inline const int Get_Int() {
int num=0,bj=1;
char x=getchar();
while(x<'0'||x>'9') {
if(x=='-')bj=-1;
x=getchar();
}
while(x>='0'&&x<='9') {
num=num*10+x-'0';
x=getchar();
}
return num*bj;
}

const int maxn=64005;

struct Edge {
int from,to,cap,flow;
Edge(int x=0,int y=0,int c=0,int f=0):from(x),to(y),cap(c),flow(f) {}
};

struct Dinic {
int n,m,s,t;
vector<Edge>edges;
vector<int>G[maxn];
bool vst[maxn];
int dist[maxn],cur[maxn];
void init(int n) {
this->n=n;
edges.clear();
for(int i=1; i<=n; i++)G[i].clear();
}
void AddEdge(int x,int y,int v) {
edges.push_back(Edge(x,y,v,0));
edges.push_back(Edge(y,x,0,0));
m=edges.size();
G[x].push_back(m-2);
G[y].push_back(m-1);
}
bool bfs() {
memset(vst,0,sizeof(vst));
memset(dist,0,sizeof(dist));
queue<int>Q;
Q.push(t); //反向层次图
vst[t]=1;
while(!Q.empty()) {
int Now=Q.front();
Q.pop();
for(int id:G[Now]) {
Edge& e=edges[id^1];
int Next=e.from;
if(!vst[Next]&&e.cap>e.flow) {
vst[Next]=1;
dist[Next]=dist[Now]+1;
Q.push(Next);
}
}
}
return vst[s];
}
int dfs(int Now,int a) {
if(Now==t||a==0)return a;
int flow=0;
for(int& i=cur[Now]; i<G[Now].size(); i++) {
Edge& e=edges[G[Now][i]];
int Next=e.to;
if(dist[Now]-1!=dist[Next])continue;
int nextflow=dfs(Next,min(a,e.cap-e.flow));
if(nextflow>0) {
e.flow+=nextflow;
edges[G[Now][i]^1].flow-=nextflow;
flow+=nextflow;
a-=nextflow;
if(a==0)break;
}
}
return flow;
}
int maxflow(int s,int t) {
this->s=s;
this->t=t;
int flow=0;
while(bfs()) {
memset(cur,0,sizeof(cur));
flow+=dfs(s,INT_MAX);
}
return flow;
}
} dinic;

const int Dirx[]= {0,1,-1,0,0},Diry[]= {0,0,0,1,-1};
int n,m,h,Delta,S,T;

int id(int x,int y,int z) {
if(z==0)return S;
return (z-1)*n*m+(x-1)*m+y;
}

int main() {
n=Get_Int();
m=Get_Int();
h=Get_Int();
Delta=Get_Int();
S=n*m*h+1,T=n*m*h+2;
for(int x=1; x<=n; x++)
for(int y=1; y<=m; y++)
dinic.AddEdge(S,id(x,y,1),Get_Int());
for(int z=2; z<=h; z++)
for(int x=1; x<=n; x++)
for(int y=1; y<=m; y++) {
dinic.AddEdge(id(x,y,z-1),id(x,y,z),Get_Int());
if(z<=Delta||z==h)continue;
for(int k=1; k<=4; k++) {
int nx=x+Dirx[k],ny=y+Diry[k];
if(nx<1||ny<1||nx>n||ny>m)continue;
dinic.AddEdge(id(x,y,z),id(nx,ny,z-Delta),INT_MAX/2);
}
}
for(int x=1; x<=n; x++)
for(int y=1; y<=m; y++)
dinic.AddEdge(id(x,y,h),T,INT_MAX/2);
printf("%d\n",dinic.maxflow(S,T));
return 0;
}
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