zoj How Many Shortest Path

                        How Many Shortest Path

 

题目：

 给出一张图，求解最短路有几条。处理特别BT，还有就是要特别处理map[i][i] = 0，数据有不等于0的情况！

居然脑残到了些错floyd！！！！！！14次wrong！！！！！！！！

 

算法：

  先最短路处理，把在最短路上的边添加上。既是，dist[s][i] + map[i][j] == dist[s][j]表示从起点到i点加上当前边是最短路。把这个加入到网络流边集中，容量为1.然后，建立一个超级源点，容量为INF。

 

#include <iostream>
#include <algorithm>
#include <queue>
#include <vector>
#include <cstdio>
#include <cstring>
using namespace std;

const int INF = 1 << 30;
const int MAXN = 200 + 10;
struct Edge{
int from,to,cap,flow;
Edge(){};
Edge(int _from,int _to,int _cap,int _flow)
:from(_from),to(_to),cap(_cap),flow(_flow){};
};
vector<Edge> edges;
vector<int> G[MAXN];
int cur[MAXN],d[MAXN];
bool vst[MAXN];
int N,M,src,sink;

int mat[MAXN][MAXN],dist[MAXN][MAXN];
int ss,tt;

void init(){
for(int i = 0;i <= N+5;++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 sz = edges.size();
G[from].push_back(sz - 2);
G[to].push_back(sz - 1);
}

void flody(){
memcpy(dist,mat,sizeof(mat));

for(int i = 0;i < N;++i)
for(int j = 0;j < N;++j)
dist[i][j] = (dist[i][j]==-1?INF:dist[i][j]);

for(int k = 0;k < N;++k)
for(int i = 0;i < N;++i)
for(int j = 0;j < N;++j){
//             if(dist[i][k] == INF||dist[k][j] == INF) continue;
if(dist[i][k] < INF && dist[k][j] < INF&&dist[i][j] > dist[i][k] + dist[k][j])
dist[i][j] = dist[i][k] + dist[k][j];
}
}

bool BFS(){
memset(vst,0,sizeof(vst));
queue<int> Q;
Q.push(src);
d[src] = 0;
vst[src] = 1;

while(!Q.empty()){
int u = Q.front(); Q.pop();
for(int i = 0;i < (int)G[u].size();++i){
Edge& e = edges[G[u][i]];
if(!vst[e.to] && e.cap > e.flow){
vst[e.to] = 1;
d[e.to] = d[u] + 1;
Q.push(e.to);
}
}
}

return vst[sink];
}

int DFS(int x,int a){
if(x == sink || a == 0)
return a;

int flow = 0,f;
for(int& i = cur[x];i < (int)G[x].size();++i){
Edge& e = edges[G[x][i]];
if(d[e.to] == d[x] + 1 && (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(src,INF);
}
return flow;
}

int main()
{
//   freopen("Input.txt","r",stdin);

while(~scanf("%d",&N)){
init();
for(int i = 0;i < N;++i)
for(int j = 0;j < N;++j){
scanf("%d",&mat[i][j]);
}

for(int i = 0;i < N;++i)
mat[i][i] = 0;

scanf("%d%d",&ss,&tt);
flody();

if(ss == tt){
printf("inf\n");
continue;
}

src = N + 2; sink = tt;
addEdge(src,ss,INF);
// 建图
for(int i = 0;i < N;++i){
if(dist[ss][i] == INF) continue;
for(int j = 0;j < N;++j){
if(i == j) continue;
if(dist[ss][j] == INF||mat[i][j] == -1) continue;
if(dist[ss][i] + mat[i][j] == dist[ss][j]){   //该边是否在最短路上
addEdge(i,j,1);
}
}
}
printf("%d\n",maxFlow());
}
return 0;
}