2014多校联合-第三场

1002：Redraw Beautiful Drawings

最大流。。。。用sap+gap优化的模版过的。。。

1. 源点 -> 每一行相应的点，流量限制为该行的和

2. 每一行相应的点 -> 每一列相应的点。流量限制为 K

3. 每一列相应的点 -> 汇点，流量限制为该列的和

跑一遍最大流。

假设流量小于总权值和，那么说明impossible。

假设等于：

构建残图网络。假设残图网络能够形成一条回路，那么说明有多解。

#include <stdio.h>
#include <iostream>
#include <algorithm>
#include <string.h>
#include<queue>
using namespace std;
#define INF 99999999
const int maxn =810;
const int maxm =2*410*410+410*4;
const int oo = 1<<29;
struct Arclist
{
int cnt, head[maxn], dis[maxn];
int cur[maxn], pre[maxn], gap[maxn], aug[maxn];
int mp[maxn][maxn];
int vis[maxn];
int vis2[maxn];
struct node
{
int u, v, w, next;
}edge[maxm];
void init()
{
cnt = 0;
memset(head,-1,sizeof(head));
}
void add(int u, int v, int w)
{
edge[cnt].u = u;
edge[cnt].v = v;
edge[cnt].w = w;
edge[cnt].next = head[u];
head[u] = cnt++;
edge[cnt].u = v;
edge[cnt].v = u;
edge[cnt].w = 0;
edge[cnt].next = head[v];
head[v] = cnt++;
}
int sap(int s, int e, int n)
{
int max_flow = 0, u = s;
int mindis;
for(int i = 0; i <= n; i++)
{
cur[i] = head[i];
dis[i] = 0;
gap[i] = 0;
}
aug[s] = oo;
pre[s] = -1;
gap[0] = n;
while(dis[s]<n)
{
bool flag = false;
if(u==e)
{
max_flow += aug[e];
for(int v = pre[e]; v != -1; v = pre[v])
{
int id = cur[v];
edge[id].w -= aug[e];
edge[id^1].w += aug[e];
aug[v] -= aug[e];
if(edge[id].w==0) u = v;
}
}
for(int id = cur[u]; id != -1; id = edge[id].next)
{
int v = edge[id].v;
if(edge[id].w>0 && dis[u]==dis[v]+1)
{
flag = true;
pre[v] = u;
cur[u] = id;
aug[v] = std::min(aug[u], edge[id].w);
u = v;
break;
}
}
if(flag==false)
{
if(--gap[dis[u]]==0) break;
mindis = n;
cur[u] = head[u];
for(int id = head[u]; id != -1; id = edge[id].next)
{
int v = edge[id].v;
if(edge[id].w>0 && dis[v]<mindis)
{
mindis = dis[v];
cur[u] = id;
}
}
dis[u] = mindis+1;
++gap[dis[u]];
if(u!=s) u = pre[u];
}
}
return max_flow;
}
int n,m,k;
int sou(int pre,int x,int leap)
{
vis2[x]=1;
if(leap==0)
{
for(int i=n+1;i<=m+n;i++)
{
if(i==pre)continue;
if(mp[x][i]==0)continue;
if(vis2[i])
{
vis2[x]=0;
return 1;
}
if(sou(x,i,1)){
vis2[x]=0;
return 1;
}
}
}
if(leap==1)
{
for(int i=1;i<=n;i++)
{
if(i==pre)continue;
if(mp[x][i]==0)continue;
if(vis2[i]){
vis2[x]=0;
return 1;
}
if(sou(x,i,0)){
vis2[x]=0;
return 1;
}
}
}
vis2[x]=0;
return 0;
}
int dfs()
{
memset(vis,0,sizeof(vis));
memset(vis2,0,sizeof(vis2));
for(int i=1;i<=n;i++)
{
if(vis[i])continue;
if(sou(-1,i,0))return 1;
}
return 0;
}
void pan()
{
memset(mp,0,sizeof(mp));
for(int i=0;i<cnt;i++)
{
int u=edge[i].u;
int v=edge[i].v;
int w=edge[i].w;
if(u>n)continue;
if(v<=n||v>n+m)continue;
mp[u][v]=w;
mp[v][u]=k-w;
}
if(dfs())
{
cout<<"Not Unique"<<endl;
return ;
}
cout<<"Unique"<<endl;
for(int i=1;i<=n;i++)
{
for(int j=1;j<=m;j++)
{
if(j!=1)cout<<" ";
printf("%d",k-mp[i][j+n]);
}
cout<<endl;
}
}
}G;
int a[510];
int b[510];
int main()
{
int m,n,k;
while(~scanf("%d%d%d",&n,&m,&k))
{
int st=n+m+1;
int ed=n+m+2;
G.init();
int ans=0;
for(int i=1;i<=n;i++)
{
scanf("%d",&a[i]);
G.add(st,i,a[i]);
ans+=a[i];
}
for(int i=n+1;i<=n+m;i++)
{
scanf("%d",&b[i]);
G.add(i,ed,b[i]);
}
for(int i=1;i<=n;i++)
{
for(int j=n+1;j<=n+m;j++)
{
G.add(i,j,k);
}
}
int mx;
mx=G.sap(st,ed,n+m+2);
if(mx<ans)cout<<"Impossible"<<endl;
else
{
G.n=n;
G.m=m;
G.k=k;
G.pan();
}
}
return 0;
}

1003：Scary Path Finding Algorithm

由题意可知，直接构造即可。。。

#include <iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>
#include<stdlib.h>
#include<vector>
#include<cmath>
#include<queue>
#include<set>
using namespace std;
void dos()
{
int a[31];
a[0]=1;
for(int i=1; i<=30; i++)
{
a[i]=a[i-1]*2;
}
int n=30*2+1;
int m=30*3-3;
cout<<n<<" "<<m<<endl;
for(int i=1; i<=29; i++)
{
printf("%d %d %d\n",i,i+30,0);
printf("%d %d %d\n",i,i+1,-a[30-i]);
printf("%d %d %d\n",i+30,i+1,-a[30-i+1]);
}
}
long long spfa_slf()
{
int n,m;
cin >> n >> m;

vector<pair<int,int> > edges[111];
for(int i = 0; i < m; i++)
{
int x,y,w;
cin >> x >> y >> w;
edges[x].push_back(make_pair(y,w));
}

deque<int> q;
vector<long long> dist(n+1, ~0ULL>>1);
vector<bool> inQueue(n+1, false);
dist[1] = 0;
q.push_back(1);
inQueue[1] = true;

int doge = 0;
while(!q.empty())
{
int x = q.front();
q.pop_front();
if(doge++ > 23333333)
{
puts("doge");
return 233;
}
for(vector<pair<int,int> >::iterator it = edges[x].begin();
it != edges[x].end(); ++it)
{
int y = it->first;
int w = it->second;
if(dist[y] > dist[x] + w)
{
dist[y] = dist[x] + w;
if(!inQueue[y])
{
inQueue[y] = true;
if(!q.empty() && dist[y] > dist[q.front()])
q.push_back(y);
else
q.push_front(y);
}
}
}
inQueue[x] = false;
}
return dist
;
}
int main()
{
int n;
// freopen("data.in","r",stdin);
while(~scanf("%d",&n))
{
dos();
}
// spfa_slf();
// cout<<"-00"<<endl;
return 0;
}