很裸的題目，即求所有點(diǎn)對(duì)之間的最小割。有Gomory-Hu和Gusfield兩種算法，貌似Gomory-Hu的難實(shí)現(xiàn)一點(diǎn)，效率搞一點(diǎn)，Gusfield的容易實(shí)現(xiàn)一點(diǎn)，但是效率沒那么高？
看著網(wǎng)上的偽代碼寫出來的。。具體論文還沒有仔細(xì)看。
貼出論文
Dan Gusfield: Very Simple Methods for All Pairs Network Flow Analysis. SIAM J. Comput. 19(1): 143-155 (1990)#include <iostream>
using namespace std;
#define N 205
#define INF 1 << 28
int g[N][N], mk[N];
int cap[N][N], dis[N], pre[N], cnt[N];
int ISAP(int src, int sink, int n)
{
int maxflow = 0, flow, u = src, v, d;
memset(dis, 0, sizeof(dis));
memset(cnt, 0, sizeof(cnt));
pre[src] = src;
cnt[src] = n;
while(dis[src] < n)
{
if(u == sink)
{
flow = INF;
for(int i = sink; i != src; i = pre[i])
if(cap[pre[i]][i] < flow)
flow = cap[pre[i]][i];
maxflow += flow;
u = src;
for(int i = sink; i != src; i = pre[i])
{
cap[pre[i]][i] -= flow;
cap[i][pre[i]] += flow;
}
}
for(d = n, v = 0; v < n; v++)
{
if(!cap[u][v]) continue;
d = d < dis[v] ? d : dis[v];
if(dis[v] + 1 == dis[u]) break;
}
if(v < n) pre[v] = u, u = v;
else
{
if(!(--cnt[dis[u]])) break;
++cnt[dis[u] = d + 1];
if(u != src) u = pre[u];
}
}
return maxflow;
}
int parent[N], cut[N][N];
void dfs(int u, int n)
{
mk[u] = 1;
for(int i = 0; i < n; i++)
{
if(!mk[i] && cap[u][i])
dfs(i, n);
}
}
void Solve(int n)
{
memset(parent, 0, sizeof(parent));
memset(cut, 127, sizeof(cut));
for(int i = 1; i < n; i++)
{
memset(mk, 0, sizeof(mk));
memcpy(cap, g, sizeof(g));
int mincut = ISAP(i, parent[i], n);
dfs(i, n);
for(int j = i + 1; j < n; j++)
if(mk[j] && parent[j] == parent[i])
{
parent[j] = i;
}
cut[i][parent[i]] = cut[parent[i]][i] = mincut;
for(int j = 0; j < i; j++)
cut[i][j] = cut[j][i] = min(mincut, cut[parent[i]][j]);
}
for(int i = 0; i < n; i++)
{
for(int j = 0; j < n; j++)
{
if(i == j) cut[i][j] = 0;
printf("%d", cut[i][j]);
if(j != n - 1) printf(" ");
}
printf("\n");
}
}
int main()
{
int t, n, cas = 1;
scanf("%d", &t);
while(t--)
{
scanf("%d", &n);
for(int i = 0; i < n; i++)
for(int j = 0; j < n; j++)
scanf("%d", &g[i][j]);
printf("Case #%d:\n", cas++);
Solve(n);
}
return 0;
}