POJ 1815 Friendship

最小割

参考

网络流建模汇总

教程：最大流-最小割定理

http://blog.csdn.net/lenleaves/article/details/7887217

#include <cstdio>
#include <iostream>
#include <algorithm>
#include <cstring>
#include <vector>
#include <sstream>
using namespace std;
#define ll long long
const int MAXN = 505;
const int MAXM = 400010;
const int INF = 0x3f3f3f3f;
struct Edge{
int from,to,next,cap,flow;
}edge[MAXM];
int tol;
int head[MAXN<<1];
int gap[MAXN<<1],dep[MAXN<<1],cur[MAXN<<1];
void init(){
tol = 0;
memset(head,-1,sizeof(head));
}
void addedge(int u,int v,int w,int rw = 0){
edge[tol].from = u, edge[tol].to = v; edge[tol].cap = w; edge[tol].flow = 0;
edge[tol].next = head[u]; head[u] = tol++;

edge[tol].from = v, edge[tol].to = u; edge[tol].cap = rw; edge[tol].flow = 0;
edge[tol].next = head[v]; head[v] = tol++;
}
int Q[MAXN];
void BFS(int start,int end)
{
memset(dep,-1,sizeof(dep));
memset(gap,0,sizeof(gap));
gap[0] = 1;
int front = 0, rear = 0;
dep[end] = 0;
Q[rear++] = end;
while(front != rear){
int u = Q[front++];
for(int i = head[u]; i != -1; i = edge[i].next){
int v = edge[i].to;
if(dep[v] != -1)continue;
Q[rear++] = v;
dep[v] = dep[u] + 1;
gap[dep[v]]++;
}
}
}

int S[MAXN];
int isap(int start,int end,int N){
BFS(start,end);
memcpy(cur,head,sizeof(head));
int top = 0;
int u = start;
int ans = 0;
while(dep[start] < N){
if(u == end){
int Min = INF;
int inser;
for(int i = 0;i < top;i++)
if(Min > edge[S[i]].cap - edge[S[i]].flow){
Min = edge[S[i]].cap - edge[S[i]].flow;
inser = i;
}
for(int i = 0;i < top;i++){
edge[S[i]].flow += Min;
edge[S[i]^1].flow -= Min;
}
ans += Min;
top = inser;
u = edge[S[top]^1].to;
continue;
}
bool flag = false;
int v;
for(int i = cur[u]; i != -1; i = edge[i].next){
v = edge[i].to;
if(edge[i].cap - edge[i].flow && dep[v]+1 == dep[u]){
flag = true;
cur[u] = i;
break;
}
}
if(flag){
S[top++] = cur[u];
u = v;
continue;
}
int Min = N;
for(int i = head[u]; i != -1; i = edge[i].next)
if(edge[i].cap - edge[i].flow && dep[edge[i].to] < Min){
Min = dep[edge[i].to];
cur[u] = i;
}
gap[dep[u]]--;
if(!gap[dep[u]])return ans;
dep[u] = Min + 1;
gap[dep[u]]++;
if(u != start)u = edge[S[--top]^1].to;
}
return ans;
}

int s, en, n, m, a, t;
int g[205][205];
bool del[205];
vector<int> vec;
void build(){
init();
for(int i = 1; i <= n; i++){
if(del[i])continue;
if(i != s && i != t)addedge(i, i+n, 1);
for(int j = 1; j <= n; j++){
if(del[j])continue;
if(i == j )continue;
if(!g[i][j])continue;
if(s == i)addedge(s, j, INF);
else if(t == i)addedge(j+n, t, INF);
else if(j != s && j != t)addedge(i+n, j, INF);
}
}
}
int main(){
while(~scanf("%d%d%d", &n, &s, &t)) {
vec.clear();
for(int i = 1; i <= n; i++){
for(int j = 1; j <= n; j++){
scanf("%d",&g[i][j]);
}
}
if(g[s][t]){
puts("NO ANSWER!");
continue;
}
memset(del,false,sizeof(del));
build();
int ans = isap(s,t,2*n);
printf("%d\n",ans);
if(!ans)continue;
int temp = ans;
for(int i = 1; i <= n; i++){
if(i == s || i == t)continue;
del[i] = true;
build();
int k = isap(s,t,2*n);
if(k < temp){
vec.push_back(i);
temp = k;
}
else del[i] = false;
}
int sz = vec.size();
for(int i = 0; i < sz-1; i++){
printf("%d ",vec[i]);
}
printf("%d\n",vec[sz-1]);
}
return 0;
}