标签：网络流
解题思路：
这两道题题目大致相同，都是已知一个矩阵每一行的和和每一列的和，并且每个点的数小于K 还原原矩阵并判断答案是否唯一。建图方式相同，新建一个原点S 和一个汇点T ，S到行连边，容量为该行之和，列到T连边，容量为该列之和， 对于每一个点 i 和 j ，i 行向 j 列连边 ， 容量为K , 求一遍最大流。并且通过判断是否存在环来判断是否唯一。
区别在于 第二道题N 与 M 均扩大，找环需要采用更高效的算法，这里采用Tarjan 算法来找环。
HDOJ 4888
#include <iostream>
#include <cstring>
#include <cstdlib>
#include <cstdio>
#include <algorithm>
#include <cmath>
#include <vector>
#include <queue>
#include <stack>
#define LL long long
using namespace std;
const int maxn = 10000 + 10;
const int INF = 100000000;
struct Edge
{
int from,to,cap,flow;
Edge(int u,int v,int c,int w):from(u),to(v),cap(c),flow(w){ }
};
int n , s , t;
vector<Edge> edges;
vector<int> G[maxn];
bool vis[maxn];
int d[maxn];
int cur[maxn];
void init()
{
for(int i=0;i<=n+1;i++)
G[i].clear();
edges.clear();
}
void AddEdge(int from,int to,int cap)
{
edges.push_back(Edge(from,to,cap,0));
edges.push_back(Edge(to,from,0,0));
int M = edges.size();
G[from].push_back(M-2);
G[to].push_back(M-1);
}
bool BFS()
{
memset(vis,0,sizeof(vis));
queue<int>Q;
Q.push(s);
d[s] = 0;
vis[s] = 1;
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)
{
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[x] + 1 == d[e.to] && (f = DFS(e.to,min(a,e.cap-e.flow))) > 0)
{
e.flow += f;
edges[G[x][i]^1].flow -= f;
flow += f;
a -= f;
if(a == 0) break;
}
}
return flow;
}
int Maxflow()
{
int flow = 0;
while(BFS())
{
memset(cur,0,sizeof(cur));
flow += DFS(s,INF);
}
return flow;
}
int pre[maxn] , lowlink[maxn] ,sccno[maxn] , fa[maxn], dfs_clock , scc_cnt , flag;
stack<int> S;
void dfs(int u)
{
pre[u] = lowlink[u] = ++dfs_clock;
S.push(u);
for(int i=0;i<G[u].size();i++)
{
Edge& e = edges[G[u][i]];
if(e.cap == e.flow) continue;
int v = e.to;
if(!pre[v])
{
fa[v] = u;
dfs(v);
if(!flag) return ;
lowlink[u] = min(lowlink[u] , lowlink[v]);
}
else if(!sccno[v])
{
lowlink[u] = min(lowlink[u] , pre[v]);
if(v != fa[u]) {flag = 0 ; return ;}
}
}
if(lowlink[u] == pre[u])
{
scc_cnt++;
for(;;)
{
int x = S.top(); S.pop();
sccno[x] = scc_cnt;
if(x == u) break;
}
}
}
bool find_scc()
{
dfs_clock = scc_cnt = 0; flag = 1;
memset(pre , 0, sizeof(pre));
memset(lowlink , 0, sizeof(lowlink));
memset(sccno , 0 , sizeof(sccno));
for(int i=0;i<n;i++)
if(!pre[i]) { dfs(i); if(!flag) return 0;}
return 1;
}
int main()
{
int T;
int N , M , K;
while(scanf("%d%d%d",&N,&M,&K)!=EOF)
{
s = 0 , t = N + M + 1;
n = t + 1; init();
int sumr = 0 , sumc = 0;
int x;
for(int i=1;i<=N;i++)
{
scanf("%d",&x);
AddEdge(s , i , x);
sumr += x;
}
for(int i=1;i<=M;i++)
{
scanf("%d",&x);
AddEdge(i + N , t , x);
sumc += x;
}
if (sumr != sumc){ printf("Impossible\n");continue; }
for(int i=1;i<=N;i++)
{
for(int j=1;j<=M;j++)
{
AddEdge(i , j + N , K);
}
}
int ans = Maxflow();
if(ans != sumr) { printf("Impossible\n"); continue; }
if(find_scc())
{
printf("Unique\n");
for(int i=1;i<=N;i++)
{
for(int j=1;j<=M;j++)
{
Edge& e = edges[G[i][j]];
cout<<e.flow;
if(j < M) cout<<' ';
}
cout<<endl;
}
}
else printf("Not Unique\n");
}
return 0;
}HDOJ 4975
<span style="color:#0000ff;">#include <iostream>
#include <cstring>
#include <cstdlib>
#include <cstdio>
#include <algorithm>
#include <cmath>
#include <vector>
#include <queue>
#include <stack>
#define LL long long
</span><strong><span style="color:#0000ff;">using namespace</span></strong> std<strong><span style="color:#ff00ff;">;</span><span style="color:#0000ff;">
const</span><span style="color:blue;"> int</span></strong> maxn<strong><span style="color:#ff00ff;"> =</span></strong><span style="color:#cc3300;"> 10000</span><strong><span style="color:#ff00ff;"> +</span></strong><span style="color:#cc3300;"> 10</span><strong><span style="color:#ff00ff;">;</span><span style="color:#0000ff;">
const</span><span style="color:blue;"> int</span></strong> INF<strong><span style="color:#ff00ff;"> =</span></strong><span style="color:#cc3300;"> 100000000</span><strong><span style="color:#ff00ff;">;</span><span style="color:#0000ff;">
struct</span></strong> Edge<strong><span style="color:#ff00ff;">
{</span><span style="color:blue;">
int</span></strong> from<strong><span style="color:#ff00ff;">,</span></strong>to<strong><span style="color:#ff00ff;">,</span></strong>cap<strong><span style="color:#ff00ff;">,</span></strong>flow<strong><span style="color:#ff00ff;">;</span></strong>
Edge<strong><span style="color:#ff00ff;">(</span><span style="color:blue;">int</span></strong> u<strong><span style="color:#ff00ff;">,</span><span style="color:blue;">int</span></strong> v<strong><span style="color:#ff00ff;">,</span><span style="color:blue;">int</span></strong> c<strong><span style="color:#ff00ff;">,</span><span style="color:blue;">int</span></strong> w<strong><span style="color:#ff00ff;">):</span></strong>from<strong><span style="color:#ff00ff;">(</span></strong>u<strong><span style="color:#ff00ff;">),</span></strong>to<strong><span style="color:#ff00ff;">(</span></strong>v<strong><span style="color:#ff00ff;">),</span></strong>cap<strong><span style="color:#ff00ff;">(</span></strong>c<strong><span style="color:#ff00ff;">),</span></strong>flow<strong><span style="color:#ff00ff;">(</span></strong>w<strong><span style="color:#ff00ff;">){ }
};</span><span style="color:blue;">
int</span></strong> n<strong><span style="color:#ff00ff;"> ,</span></strong> s<strong><span style="color:#ff00ff;"> ,</span></strong> t<strong><span style="color:#ff00ff;">;</span></strong>
vector<strong><span style="color:#ff00ff;"><</span></strong>Edge<strong><span style="color:#ff00ff;">></span></strong> edges<strong><span style="color:#ff00ff;">;</span></strong>
vector<strong><span style="color:#ff00ff;"><</span><span style="color:blue;">int</span><span style="color:#ff00ff;">></span></strong> G<strong><span style="color:#ff00ff;">[</span></strong>maxn<strong><span style="color:#ff00ff;">];</span><span style="color:blue;">
bool</span></strong> vis<strong><span style="color:#ff00ff;">[</span></strong>maxn<strong><span style="color:#ff00ff;">];</span><span style="color:blue;">
int</span></strong> d<strong><span style="color:#ff00ff;">[</span></strong>maxn<strong><span style="color:#ff00ff;">];</span><span style="color:blue;">
int</span></strong> cur<strong><span style="color:#ff00ff;">[</span></strong>maxn<strong><span style="color:#ff00ff;">];</span><span style="color:blue;">
void</span></strong> init<strong><span style="color:#ff00ff;">()
{</span><span style="color:#0000ff;">
for</span><span style="color:#ff00ff;">(</span><span style="color:blue;">int</span></strong> i<strong><span style="color:#ff00ff;">=</span></strong><span style="color:#cc3300;">0</span><strong><span style="color:#ff00ff;">;</span></strong>i<strong><span style="color:#ff00ff;"><=</span></strong>n<strong><span style="color:#ff00ff;">+</span></strong><span style="color:#cc3300;">1</span><strong><span style="color:#ff00ff;">;</span></strong>i<strong><span style="color:#ff00ff;">++)</span></strong>
G<strong><span style="color:#ff00ff;">[</span></strong>i<strong><span style="color:#ff00ff;">].</span></strong>clear<strong><span style="color:#ff00ff;">();</span></strong>
edges<strong><span style="color:#ff00ff;">.</span></strong>clear<strong><span style="color:#ff00ff;">();
}</span><span style="color:blue;">
void</span></strong> AddEdge<strong><span style="color:#ff00ff;">(</span><span style="color:blue;">int</span></strong> from<strong><span style="color:#ff00ff;">,</span><span style="color:blue;">int</span></strong> to<strong><span style="color:#ff00ff;">,</span><span style="color:blue;">int</span></strong> cap<strong><span style="color:#ff00ff;">)
{</span></strong>
edges<strong><span style="color:#ff00ff;">.</span></strong>push_back<strong><span style="color:#ff00ff;">(</span></strong>Edge<strong><span style="color:#ff00ff;">(</span></strong>from<strong><span style="color:#ff00ff;">,</span></strong>to<strong><span style="color:#ff00ff;">,</span></strong>cap<strong><span style="color:#ff00ff;">,</span></strong><span style="color:#cc3300;">0</span><strong><span style="color:#ff00ff;">));</span></strong>
edges<strong><span style="color:#ff00ff;">.</span></strong>push_back<strong><span style="color:#ff00ff;">(</span></strong>Edge<strong><span style="color:#ff00ff;">(</span></strong>to<strong><span style="color:#ff00ff;">,</span></strong>from<strong><span style="color:#ff00ff;">,</span></strong><span style="color:#cc3300;">0</span><strong><span style="color:#ff00ff;">,</span></strong><span style="color:#cc3300;">0</span><strong><span style="color:#ff00ff;">));</span><span style="color:blue;">
int</span></strong> M<strong><span style="color:#ff00ff;"> =</span></strong> edges<strong><span style="color:#ff00ff;">.</span></strong>size<strong><span style="color:#ff00ff;">();</span></strong>
G<strong><span style="color:#ff00ff;">[</span></strong>from<strong><span style="color:#ff00ff;">].</span></strong>push_back<strong><span style="color:#ff00ff;">(</span></strong>M<strong><span style="color:#ff00ff;">-</span></strong><span style="color:#cc3300;">2</span><strong><span style="color:#ff00ff;">);</span></strong>
G<strong><span style="color:#ff00ff;">[</span></strong>to<strong><span style="color:#ff00ff;">].</span></strong>push_back<strong><span style="color:#ff00ff;">(</span></strong>M<strong><span style="color:#ff00ff;">-</span></strong><span style="color:#cc3300;">1</span><strong><span style="color:#ff00ff;">);
}</span><span style="color:blue;">
bool</span></strong> BFS<strong><span style="color:#ff00ff;">()
{</span></strong>
memset<strong><span style="color:#ff00ff;">(</span></strong>vis<strong><span style="color:#ff00ff;">,</span></strong><span style="color:#cc3300;">0</span><strong><span style="color:#ff00ff;">,</span><span style="color:#0000ff;">sizeof</span><span style="color:#ff00ff;">(</span></strong>vis<strong><span style="color:#ff00ff;">));</span></strong>
queue<strong><span style="color:#ff00ff;"><</span><span style="color:blue;">int</span><span style="color:#ff00ff;">></span></strong>Q<strong><span style="color:#ff00ff;">;</span></strong>
Q<strong><span style="color:#ff00ff;">.</span></strong>push<strong><span style="color:#ff00ff;">(</span></strong>s<strong><span style="color:#ff00ff;">);</span></strong>
d<strong><span style="color:#ff00ff;">[</span></strong>s<strong><span style="color:#ff00ff;">] =</span></strong><span style="color:#cc3300;"> 0</span><strong><span style="color:#ff00ff;">;</span></strong>
vis<strong><span style="color:#ff00ff;">[</span></strong>s<strong><span style="color:#ff00ff;">] =</span></strong><span style="color:#cc3300;"> 1</span><strong><span style="color:#ff00ff;">;</span><span style="color:#0000ff;">
while</span><span style="color:#ff00ff;">(!</span></strong>Q<strong><span style="color:#ff00ff;">.</span></strong>empty<strong><span style="color:#ff00ff;">())
{</span><span style="color:blue;">
int</span></strong> x<strong><span style="color:#ff00ff;"> =</span></strong> Q<strong><span style="color:#ff00ff;">.</span></strong>front<strong><span style="color:#ff00ff;">();</span></strong>Q<strong><span style="color:#ff00ff;">.</span></strong>pop<strong><span style="color:#ff00ff;">();</span><span style="color:#0000ff;">
for</span><span style="color:#ff00ff;">(</span><span style="color:blue;">int</span></strong> i<strong><span style="color:#ff00ff;">=</span></strong><span style="color:#cc3300;">0</span><strong><span style="color:#ff00ff;">;</span></strong>i<strong><span style="color:#ff00ff;"><</span></strong>G<strong><span style="color:#ff00ff;">[</span></strong>x<strong><span style="color:#ff00ff;">].</span></strong>size<strong><span style="color:#ff00ff;">();</span></strong>i<strong><span style="color:#ff00ff;">++)
{</span></strong>
Edge<strong><span style="color:#ff00ff;">&</span></strong> e<strong><span style="color:#ff00ff;"> =</span></strong> edges<strong><span style="color:#ff00ff;">[</span></strong>G<strong><span style="color:#ff00ff;">[</span></strong>x<strong><span style="color:#ff00ff;">][</span></strong>i<strong><span style="color:#ff00ff;">]];</span><span style="color:#0000ff;">
if</span><span style="color:#ff00ff;">(!</span></strong>vis<strong><span style="color:#ff00ff;">[</span></strong>e<strong><span style="color:#ff00ff;">.</span></strong>to<strong><span style="color:#ff00ff;">] &&</span></strong> e<strong><span style="color:#ff00ff;">.</span></strong>cap<strong><span style="color:#ff00ff;"> ></span></strong> e<strong><span style="color:#ff00ff;">.</span></strong>flow<strong><span style="color:#ff00ff;">)
{</span></strong>
vis<strong><span style="color:#ff00ff;">[</span></strong>e<strong><span style="color:#ff00ff;">.</span></strong>to<strong><span style="color:#ff00ff;">] =</span></strong><span style="color:#cc3300;"> 1</span><strong><span style="color:#ff00ff;">;</span></strong>
d<strong><span style="color:#ff00ff;">[</span></strong>e<strong><span style="color:#ff00ff;">.</span></strong>to<strong><span style="color:#ff00ff;">] =</span></strong> d<strong><span style="color:#ff00ff;">[</span></strong>x<strong><span style="color:#ff00ff;">] +</span></strong><span style="color:#cc3300;"> 1</span><strong><span style="color:#ff00ff;">;</span></strong>
Q<strong><span style="color:#ff00ff;">.</span></strong>push<strong><span style="color:#ff00ff;">(</span></strong>e<strong><span style="color:#ff00ff;">.</span></strong>to<strong><span style="color:#ff00ff;">);
}
}
}</span><span style="color:#0000ff;">
return</span></strong> vis<strong><span style="color:#ff00ff;">[</span></strong>t<strong><span style="color:#ff00ff;">];
}</span><span style="color:blue;">
int</span></strong> DFS<strong><span style="color:#ff00ff;">(</span><span style="color:blue;">int</span></strong> x<strong><span style="color:#ff00ff;">,</span><span style="color:blue;">int</span></strong> a<strong><span style="color:#ff00ff;">)
{</span><span style="color:#0000ff;">
if</span><span style="color:#ff00ff;">(</span></strong>x<strong><span style="color:#ff00ff;"> ==</span></strong> t<strong><span style="color:#ff00ff;"> ||</span></strong> a<strong><span style="color:#ff00ff;"> ==</span></strong><span style="color:#cc3300;"> 0</span><strong><span style="color:#ff00ff;">)</span><span style="color:#0000ff;"> return</span></strong> a<strong><span style="color:#ff00ff;">;</span><span style="color:blue;">
int</span></strong> flow<strong><span style="color:#ff00ff;"> =</span></strong><span style="color:#cc3300;"> 0</span><strong><span style="color:#ff00ff;"> ,</span></strong> f<strong><span style="color:#ff00ff;">;</span><span style="color:#0000ff;">
for</span><span style="color:#ff00ff;">(</span><span style="color:blue;">int</span><span style="color:#ff00ff;"> &</span></strong>i<strong><span style="color:#ff00ff;"> =</span></strong> cur<strong><span style="color:#ff00ff;">[</span></strong>x<strong><span style="color:#ff00ff;">];</span></strong>i<strong><span style="color:#ff00ff;"><</span></strong>G<strong><span style="color:#ff00ff;">[</span></strong>x<strong><span style="color:#ff00ff;">].</span></strong>size<strong><span style="color:#ff00ff;">();</span></strong>i<strong><span style="color:#ff00ff;">++)
{</span></strong>
Edge<strong><span style="color:#ff00ff;">&</span></strong> e<strong><span style="color:#ff00ff;"> =</span></strong> edges<strong><span style="color:#ff00ff;">[</span></strong>G<strong><span style="color:#ff00ff;">[</span></strong>x<strong><span style="color:#ff00ff;">][</span></strong>i<strong><span style="color:#ff00ff;">]];</span><span style="color:#0000ff;">
if</span><span style="color:#ff00ff;">(</span></strong>d<strong><span style="color:#ff00ff;">[</span></strong>x<strong><span style="color:#ff00ff;">] +</span></strong><span style="color:#cc3300;"> 1</span><strong><span style="color:#ff00ff;"> ==</span></strong> d<strong><span style="color:#ff00ff;">[</span></strong>e<strong><span style="color:#ff00ff;">.</span></strong>to<strong><span style="color:#ff00ff;">] && (</span></strong>f<strong><span style="color:#ff00ff;"> =</span></strong> DFS<strong><span style="color:#ff00ff;">(</span></strong>e<strong><span style="color:#ff00ff;">.</span></strong>to<strong><span style="color:#ff00ff;">,</span></strong>min<strong><span style="color:#ff00ff;">(</span></strong>a<strong><span style="color:#ff00ff;">,</span></strong>e<strong><span style="color:#ff00ff;">.</span></strong>cap<strong><span style="color:#ff00ff;">-</span></strong>e<strong><span style="color:#ff00ff;">.</span></strong>flow<strong><span style="color:#ff00ff;">))) ></span></strong><span style="color:#cc3300;"> 0</span><strong><span style="color:#ff00ff;">)
{</span></strong>
e<strong><span style="color:#ff00ff;">.</span></strong>flow<strong><span style="color:#ff00ff;"> +=</span></strong> f<strong><span style="color:#ff00ff;">;</span></strong>
edges<strong><span style="color:#ff00ff;">[</span></strong>G<strong><span style="color:#ff00ff;">[</span></strong>x<strong><span style="color:#ff00ff;">][</span></strong>i<strong><span style="color:#ff00ff;">]^</span></strong><span style="color:#cc3300;">1</span><strong><span style="color:#ff00ff;">].</span></strong>flow<strong><span style="color:#ff00ff;"> -=</span></strong> f<strong><span style="color:#ff00ff;">;</span></strong>
flow<strong><span style="color:#ff00ff;"> +=</span></strong> f<strong><span style="color:#ff00ff;">;</span></strong>
a<strong><span style="color:#ff00ff;"> -=</span></strong> f<strong><span style="color:#ff00ff;">;</span><span style="color:#0000ff;">
if</span><span style="color:#ff00ff;">(</span></strong>a<strong><span style="color:#ff00ff;"> ==</span></strong><span style="color:#cc3300;"> 0</span><strong><span style="color:#ff00ff;">)</span><span style="color:#0000ff;"> break</span><span style="color:#ff00ff;">;
}
}</span><span style="color:#0000ff;">
return</span></strong> flow<strong><span style="color:#ff00ff;">;
}</span><span style="color:blue;">
int</span></strong> Maxflow<strong><span style="color:#ff00ff;">()
{</span><span style="color:blue;">
int</span></strong> flow<strong><span style="color:#ff00ff;"> =</span></strong><span style="color:#cc3300;"> 0</span><strong><span style="color:#ff00ff;">;</span><span style="color:#0000ff;">
while</span><span style="color:#ff00ff;">(</span></strong>BFS<strong><span style="color:#ff00ff;">())
{</span></strong>
memset<strong><span style="color:#ff00ff;">(</span></strong>cur<strong><span style="color:#ff00ff;">,</span></strong><span style="color:#cc3300;">0</span><strong><span style="color:#ff00ff;">,</span><span style="color:#0000ff;">sizeof</span><span style="color:#ff00ff;">(</span></strong>cur<strong><span style="color:#ff00ff;">));</span></strong>
flow<strong><span style="color:#ff00ff;"> +=</span></strong> DFS<strong><span style="color:#ff00ff;">(</span></strong>s<strong><span style="color:#ff00ff;">,</span></strong>INF<strong><span style="color:#ff00ff;">);
}</span><span style="color:#0000ff;">
return</span></strong> flow<strong><span style="color:#ff00ff;">;
}</span><span style="color:blue;">
int</span></strong> pre<strong><span style="color:#ff00ff;">[</span></strong>maxn<strong><span style="color:#ff00ff;">] ,</span></strong> lowlink<strong><span style="color:#ff00ff;">[</span></strong>maxn<strong><span style="color:#ff00ff;">] ,</span></strong>sccno<strong><span style="color:#ff00ff;">[</span></strong>maxn<strong><span style="color:#ff00ff;">] ,</span></strong> fa<strong><span style="color:#ff00ff;">[</span></strong>maxn<strong><span style="color:#ff00ff;">],</span></strong> dfs_clock<strong><span style="color:#ff00ff;"> ,</span></strong> scc_cnt<strong><span style="color:#ff00ff;"> ,</span></strong> flag<strong><span style="color:#ff00ff;">;</span></strong>
stack<strong><span style="color:#ff00ff;"><</span><span style="color:blue;">int</span><span style="color:#ff00ff;">></span></strong> S<strong><span style="color:#ff00ff;">;</span><span style="color:blue;">
void</span></strong> dfs<strong><span style="color:#ff00ff;">(</span><span style="color:blue;">int</span></strong> u<strong><span style="color:#ff00ff;">)
{</span></strong>
pre<strong><span style="color:#ff00ff;">[</span></strong>u<strong><span style="color:#ff00ff;">] =</span></strong> lowlink<strong><span style="color:#ff00ff;">[</span></strong>u<strong><span style="color:#ff00ff;">] = ++</span></strong>dfs_clock<strong><span style="color:#ff00ff;">;</span></strong>
S<strong><span style="color:#ff00ff;">.</span></strong>push<strong><span style="color:#ff00ff;">(</span></strong>u<strong><span style="color:#ff00ff;">);</span><span style="color:#0000ff;">
for</span><span style="color:#ff00ff;">(</span><span style="color:blue;">int</span></strong> i<strong><span style="color:#ff00ff;">=</span></strong><span style="color:#cc3300;">0</span><strong><span style="color:#ff00ff;">;</span></strong>i<strong><span style="color:#ff00ff;"><</span></strong>G<strong><span style="color:#ff00ff;">[</span></strong>u<strong><span style="color:#ff00ff;">].</span></strong>size<strong><span style="color:#ff00ff;">();</span></strong>i<strong><span style="color:#ff00ff;">++)
{</span></strong>
Edge<strong><span style="color:#ff00ff;">&</span></strong> e<strong><span style="color:#ff00ff;"> =</span></strong> edges<strong><span style="color:#ff00ff;">[</span></strong>G<strong><span style="color:#ff00ff;">[</span></strong>u<strong><span style="color:#ff00ff;">][</span></strong>i<strong><span style="color:#ff00ff;">]];</span><span style="color:#0000ff;">
if</span><span style="color:#ff00ff;">(</span></strong>e<strong><span style="color:#ff00ff;">.</span></strong>cap<strong><span style="color:#ff00ff;"> ==</span></strong> e<strong><span style="color:#ff00ff;">.</span></strong>flow<strong><span style="color:#ff00ff;">)</span><span style="color:#0000ff;"> continue</span><span style="color:#ff00ff;">;</span><span style="color:blue;">
int</span></strong> v<strong><span style="color:#ff00ff;"> =</span></strong> e<strong><span style="color:#ff00ff;">.</span></strong>to<strong><span style="color:#ff00ff;">;</span><span style="color:#0000ff;">
if</span><span style="color:#ff00ff;">(!</span></strong>pre<strong><span style="color:#ff00ff;">[</span></strong>v<strong><span style="color:#ff00ff;">])
{</span></strong>
fa<strong><span style="color:#ff00ff;">[</span></strong>v<strong><span style="color:#ff00ff;">] =</span></strong> u<strong><span style="color:#ff00ff;">;</span></strong>
dfs<strong><span style="color:#ff00ff;">(</span></strong>v<strong><span style="color:#ff00ff;">);</span><span style="color:#0000ff;">
if</span><span style="color:#ff00ff;">(!</span></strong>flag<strong><span style="color:#ff00ff;">)</span><span style="color:#0000ff;"> return</span><span style="color:#ff00ff;"> ;</span></strong>
lowlink<strong><span style="color:#ff00ff;">[</span></strong>u<strong><span style="color:#ff00ff;">] =</span></strong> min<strong><span style="color:#ff00ff;">(</span></strong>lowlink<strong><span style="color:#ff00ff;">[</span></strong>u<strong><span style="color:#ff00ff;">] ,</span></strong> lowlink<strong><span style="color:#ff00ff;">[</span></strong>v<strong><span style="color:#ff00ff;">]);
}</span><span style="color:#0000ff;">
else if</span><span style="color:#ff00ff;">(!</span></strong>sccno<strong><span style="color:#ff00ff;">[</span></strong>v<strong><span style="color:#ff00ff;">])
{</span></strong>
lowlink<strong><span style="color:#ff00ff;">[</span></strong>u<strong><span style="color:#ff00ff;">] =</span></strong> min<strong><span style="color:#ff00ff;">(</span></strong>lowlink<strong><span style="color:#ff00ff;">[</span></strong>u<strong><span style="color:#ff00ff;">] ,</span></strong> pre<strong><span style="color:#ff00ff;">[</span></strong>v<strong><span style="color:#ff00ff;">]);</span><span style="color:#0000ff;">
if</span><span style="color:#ff00ff;">(</span></strong>v<strong><span style="color:#ff00ff;"> !=</span></strong> fa<strong><span style="color:#ff00ff;">[</span></strong>u<strong><span style="color:#ff00ff;">]) {</span></strong>flag<strong><span style="color:#ff00ff;"> =</span></strong><span style="color:#cc3300;"> 0</span><strong><span style="color:#ff00ff;"> ;</span><span style="color:#0000ff;"> return</span><span style="color:#ff00ff;"> ;}
}
}</span><span style="color:#0000ff;">
if</span><span style="color:#ff00ff;">(</span></strong>lowlink<strong><span style="color:#ff00ff;">[</span></strong>u<strong><span style="color:#ff00ff;">] ==</span></strong> pre<strong><span style="color:#ff00ff;">[</span></strong>u<strong><span style="color:#ff00ff;">])
{</span></strong>
scc_cnt<strong><span style="color:#ff00ff;">++;</span><span style="color:#0000ff;">
for</span><span style="color:#ff00ff;">(;;)
{</span><span style="color:blue;">
int</span></strong> x<strong><span style="color:#ff00ff;"> =</span></strong> S<strong><span style="color:#ff00ff;">.</span></strong>top<strong><span style="color:#ff00ff;">();</span></strong> S<strong><span style="color:#ff00ff;">.</span></strong>pop<strong><span style="color:#ff00ff;">();</span></strong>
sccno<strong><span style="color:#ff00ff;">[</span></strong>x<strong><span style="color:#ff00ff;">] =</span></strong> scc_cnt<strong><span style="color:#ff00ff;">;</span><span style="color:#0000ff;">
if</span><span style="color:#ff00ff;">(</span></strong>x<strong><span style="color:#ff00ff;"> ==</span></strong> u<strong><span style="color:#ff00ff;">)</span><span style="color:#0000ff;"> break</span><span style="color:#ff00ff;">;
}
}
}</span><span style="color:blue;">
bool</span></strong> find_scc<strong><span style="color:#ff00ff;">()
{</span></strong>
dfs_clock<strong><span style="color:#ff00ff;"> =</span></strong> scc_cnt<strong><span style="color:#ff00ff;"> =</span></strong><span style="color:#cc3300;"> 0</span><strong><span style="color:#ff00ff;">;</span></strong> flag<strong><span style="color:#ff00ff;"> =</span></strong><span style="color:#cc3300;"> 1</span><strong><span style="color:#ff00ff;">;</span></strong>
memset<strong><span style="color:#ff00ff;">(</span></strong>pre<strong><span style="color:#ff00ff;"> ,</span></strong><span style="color:#cc3300;"> 0</span><strong><span style="color:#ff00ff;">,</span><span style="color:#0000ff;"> sizeof</span><span style="color:#ff00ff;">(</span></strong>pre<strong><span style="color:#ff00ff;">));</span></strong>
memset<strong><span style="color:#ff00ff;">(</span></strong>lowlink<strong><span style="color:#ff00ff;"> ,</span></strong><span style="color:#cc3300;"> 0</span><strong><span style="color:#ff00ff;">,</span><span style="color:#0000ff;"> sizeof</span><span style="color:#ff00ff;">(</span></strong>lowlink<strong><span style="color:#ff00ff;">));</span></strong>
memset<strong><span style="color:#ff00ff;">(</span></strong>sccno<strong><span style="color:#ff00ff;"> ,</span></strong><span style="color:#cc3300;"> 0</span><strong><span style="color:#ff00ff;"> ,</span><span style="color:#0000ff;"> sizeof</span><span style="color:#ff00ff;">(</span></strong>sccno<strong><span style="color:#ff00ff;">));</span><span style="color:#0000ff;">
for</span><span style="color:#ff00ff;">(</span><span style="color:blue;">int</span></strong> i<strong><span style="color:#ff00ff;">=</span></strong><span style="color:#cc3300;">0</span><strong><span style="color:#ff00ff;">;</span></strong>i<strong><span style="color:#ff00ff;"><</span></strong>n<strong><span style="color:#ff00ff;">;</span></strong>i<strong><span style="color:#ff00ff;">++)</span><span style="color:#0000ff;">
if</span><span style="color:#ff00ff;">(!</span></strong>pre<strong><span style="color:#ff00ff;">[</span></strong>i<strong><span style="color:#ff00ff;">]) {</span></strong> dfs<strong><span style="color:#ff00ff;">(</span></strong>i<strong><span style="color:#ff00ff;">);</span><span style="color:#0000ff;"> if</span><span style="color:#ff00ff;">(!</span></strong>flag<strong><span style="color:#ff00ff;">)</span><span style="color:#0000ff;"> return</span></strong><span style="color:#cc3300;"> 0</span><strong><span style="color:#ff00ff;">;}</span><span style="color:#0000ff;">
return</span></strong><span style="color:#cc3300;"> 1</span><strong><span style="color:#ff00ff;">;
}</span><span style="color:blue;">
int</span><span style="color:#0000ff;"> main</span><span style="color:#ff00ff;">()
{</span><span style="color:blue;">
int</span></strong> T<strong><span style="color:#ff00ff;"> ,</span></strong> kcase<strong><span style="color:#ff00ff;"> =</span></strong><span style="color:#cc3300;"> 1</span><strong><span style="color:#ff00ff;">;</span><span style="color:blue;">
int</span></strong> N<strong><span style="color:#ff00ff;"> ,</span></strong> M<strong><span style="color:#ff00ff;"> ,</span></strong> K<strong><span style="color:#ff00ff;">;</span></strong>
scanf<strong><span style="color:#ff00ff;">(</span></strong><span style="color:green;">"%d"</span><strong><span style="color:#ff00ff;">,&</span></strong>T<strong><span style="color:#ff00ff;">);</span><span style="color:#0000ff;">
while</span><span style="color:#ff00ff;">(</span></strong>T<strong><span style="color:#ff00ff;">--)
{</span></strong>
scanf<strong><span style="color:#ff00ff;">(</span></strong><span style="color:green;">"%d%d"</span><strong><span style="color:#ff00ff;">,&</span></strong>N<strong><span style="color:#ff00ff;">,&</span></strong>M<strong><span style="color:#ff00ff;">);</span></strong>
K<strong><span style="color:#ff00ff;"> =</span></strong><span style="color:#cc3300;"> 9</span><strong><span style="color:#ff00ff;">;</span></strong>s<strong><span style="color:#ff00ff;"> =</span></strong><span style="color:#cc3300;"> 0</span><strong><span style="color:#ff00ff;"> ,</span></strong> t<strong><span style="color:#ff00ff;"> =</span></strong> N<strong><span style="color:#ff00ff;"> +</span></strong> M<strong><span style="color:#ff00ff;"> +</span></strong><span style="color:#cc3300;"> 1</span><strong><span style="color:#ff00ff;">;</span></strong>
n<strong><span style="color:#ff00ff;"> =</span></strong> t<strong><span style="color:#ff00ff;"> +</span></strong><span style="color:#cc3300;"> 1</span><strong><span style="color:#ff00ff;">;</span></strong> init<strong><span style="color:#ff00ff;">();</span><span style="color:blue;">
int</span></strong> sumr<strong><span style="color:#ff00ff;"> =</span></strong><span style="color:#cc3300;"> 0</span><strong><span style="color:#ff00ff;"> ,</span></strong> sumc<strong><span style="color:#ff00ff;"> =</span></strong><span style="color:#cc3300;"> 0</span><strong><span style="color:#ff00ff;">;</span><span style="color:blue;">
int</span></strong> x<strong><span style="color:#ff00ff;">;</span><span style="color:#0000ff;">
for</span><span style="color:#ff00ff;">(</span><span style="color:blue;">int</span></strong> i<strong><span style="color:#ff00ff;">=</span></strong><span style="color:#cc3300;">1</span><strong><span style="color:#ff00ff;">;</span></strong>i<strong><span style="color:#ff00ff;"><=</span></strong>N<strong><span style="color:#ff00ff;">;</span></strong>i<strong><span style="color:#ff00ff;">++)
{</span></strong>
scanf<strong><span style="color:#ff00ff;">(</span></strong><span style="color:green;">"%d"</span><strong><span style="color:#ff00ff;">,&</span></strong>x<strong><span style="color:#ff00ff;">);</span></strong>
AddEdge<strong><span style="color:#ff00ff;">(</span></strong>s<strong><span style="color:#ff00ff;"> ,</span></strong> i<strong><span style="color:#ff00ff;"> ,</span></strong> x<strong><span style="color:#ff00ff;">);</span></strong>
sumr<strong><span style="color:#ff00ff;"> +=</span></strong> x<strong><span style="color:#ff00ff;">;
}</span><span style="color:#0000ff;">
for</span><span style="color:#ff00ff;">(</span><span style="color:blue;">int</span></strong> i<strong><span style="color:#ff00ff;">=</span></strong><span style="color:#cc3300;">1</span><strong><span style="color:#ff00ff;">;</span></strong>i<strong><span style="color:#ff00ff;"><=</span></strong>M<strong><span style="color:#ff00ff;">;</span></strong>i<strong><span style="color:#ff00ff;">++)
{</span></strong>
scanf<strong><span style="color:#ff00ff;">(</span></strong><span style="color:green;">"%d"</span><strong><span style="color:#ff00ff;">,&</span></strong>x<strong><span style="color:#ff00ff;">);</span></strong>
AddEdge<strong><span style="color:#ff00ff;">(</span></strong>i<strong><span style="color:#ff00ff;"> +</span></strong> N<strong><span style="color:#ff00ff;"> ,</span></strong> t<strong><span style="color:#ff00ff;"> ,</span></strong> x<strong><span style="color:#ff00ff;">);</span></strong>
sumc<strong><span style="color:#ff00ff;"> +=</span></strong> x<strong><span style="color:#ff00ff;">;
}</span></strong>
printf<strong><span style="color:#ff00ff;">(</span></strong><span style="color:green;">"Case #%d: "</span><strong><span style="color:#ff00ff;">,</span></strong>kcase<strong><span style="color:#ff00ff;">++);</span><span style="color:#0000ff;">
if</span><span style="color:#ff00ff;"> (</span></strong>sumr<strong><span style="color:#ff00ff;"> !=</span></strong> sumc<strong><span style="color:#ff00ff;">){</span></strong> printf<strong><span style="color:#ff00ff;">(</span></strong><span style="color:green;">"So naive!\n"</span><strong><span style="color:#ff00ff;">);</span><span style="color:#0000ff;">continue</span><span style="color:#ff00ff;">; }</span><span style="color:#0000ff;">
for</span><span style="color:#ff00ff;">(</span><span style="color:blue;">int</span></strong> i<strong><span style="color:#ff00ff;">=</span></strong><span style="color:#cc3300;">1</span><strong><span style="color:#ff00ff;">;</span></strong>i<strong><span style="color:#ff00ff;"><=</span></strong>N<strong><span style="color:#ff00ff;">;</span></strong>i<strong><span style="color:#ff00ff;">++)
{</span><span style="color:#0000ff;">
for</span><span style="color:#ff00ff;">(</span><span style="color:blue;">int</span></strong> j<strong><span style="color:#ff00ff;">=</span></strong><span style="color:#cc3300;">1</span><strong><span style="color:#ff00ff;">;</span></strong>j<strong><span style="color:#ff00ff;"><=</span></strong>M<strong><span style="color:#ff00ff;">;</span></strong>j<strong><span style="color:#ff00ff;">++)
{</span></strong>
AddEdge<strong><span style="color:#ff00ff;">(</span></strong>i<strong><span style="color:#ff00ff;"> ,</span></strong> j<strong><span style="color:#ff00ff;"> +</span></strong> N<strong><span style="color:#ff00ff;"> ,</span></strong> K<strong><span style="color:#ff00ff;">);
}
}</span><span style="color:blue;">
int</span></strong> ans<strong><span style="color:#ff00ff;"> =</span></strong> Maxflow<strong><span style="color:#ff00ff;">();</span><span style="color:#0000ff;">
if</span><span style="color:#ff00ff;">(</span></strong>ans<strong><span style="color:#ff00ff;"> !=</span></strong> sumr<strong><span style="color:#ff00ff;">) {</span></strong> printf<strong><span style="color:#ff00ff;">(</span></strong><span style="color:green;">"So naive!\n"</span><strong><span style="color:#ff00ff;">);</span><span style="color:#0000ff;"> continue</span><span style="color:#ff00ff;">; }</span><span style="color:#0000ff;">
if</span><span style="color:#ff00ff;">(</span></strong>find_scc<strong><span style="color:#ff00ff;">())</span></strong> printf<strong><span style="color:#ff00ff;">(</span></strong><span style="color:green;">"So simple!\n"</span><strong><span style="color:#ff00ff;">);</span><span style="color:#0000ff;">
else</span></strong> printf<strong><span style="color:#ff00ff;">(</span></strong><span style="color:green;">"So young!\n"</span><strong><span style="color:#ff00ff;">);
}</span><span style="color:#0000ff;">
return</span></strong><span style="color:#cc3300;"> 0</span><strong><span style="color:#ff00ff;">;
}</span></strong>
HDOJ 4888 Redraw Beautiful Drawings && HDOJ 4975 A simple Gaussian elimination problem
标签：网络流
原文地址：http://blog.csdn.net/moguxiaozhe/article/details/38756229
