SPFA+Dinic HDOJ 3416 Marriage Match IV

题目传送门

题意:求A到B不同最短路的条数(即边不能重复走, 点可以多次走)

分析:先从A跑最短路,再从B跑最短路,如果d(A -> u) + w (u, v) + d (B -> v) == shortest path,那么这条边就是有用边(在最短路中),利用这个性质重新建最大流的图,然后增广路算法Dinic求出最多有多少条最短路.SPFA + Dinic 组合已经见过一次了

#include <bits/stdc++.h>
using namespace std;
 
const int N = 1e3 + 5;
const int M = 1e5 + 5;
const int INF = 0x3f3f3f3f;
struct	Edge	{
	int u, v, w, nex;
	Edge()	{}
	Edge(int u, int v, int w, int nex) : u (u), v (v), w (w), nex (nex) {}
}edge[2][M];
struct Flow	{
	int v, cap, rev;
	Flow()	{}
	Flow(int v, int cap, int rev) : v (v), cap (cap), rev (rev) {}
};
vector<Flow> F[N];
int it[N];
int lv[N];
int head[2][N];
int d[2][N];
bool vis[N];
int n, m, e[2];
int a, b, sp;
 
void init(int id)	{
	memset (head[id], -1, sizeof (head[id]));
	e[id] = 0;
}
 
void add_edge(int u, int v, int w, int id)	{
	edge[id][e[id]] = Edge (u, v, w, head[id][u]);
	head[id][u] = e[id]++;
}
 
void re_edge(void)	{
	init (1);
	for (int i=0; i<e[0]; ++i)	{
		add_edge (edge[0][i].v, edge[0][i].u, edge[0][i].w, 1);
	}
}
 
void add_flow_edge(int u, int v, int cap)	{
	F[u].push_back (Flow (v, cap, (int) F[v].size ()));
	F[v].push_back (Flow (u, 0, (int) F[u].size ()-1));
}
 
void BFS(int s)	{
	memset (lv, -1, sizeof (lv));
	queue<int> que;	que.push (s);	lv[s] = 0;
	while (!que.empty ())	{
		int u = que.front ();	que.pop ();
		for (int i=0; i<F[u].size (); ++i)	{
			Flow &e = F[u][i];
			if (e.cap > 0 && lv[e.v] < 0)	{
				lv[e.v] = lv[u] + 1;
				que.push (e.v);
			}
		}
	}
}
 
int DFS(int u, int t, int f)	{
	if (u == t)	return f;
	for (int &i=it[u]; i<F[u].size (); ++i)	{
		Flow &e = F[u][i];
		if (e.cap > 0 && lv[u] < lv[e.v])	{
			int d = DFS (e.v, t, min (f, e.cap));
			if (d > 0)	{
				e.cap -= d;	F[e.v][e.rev].cap += d;
				return d;
			}
		}
	}
	return 0;
}
 
//最大流算法
int Dinic(int s, int t)	{
	int flow = 0, f;
	for (; ;)	{
		BFS (s);
		if (lv[t]< 0)	return flow;
		memset (it, 0, sizeof (it));
		while ((f = DFS (s, t, INF)) > 0)	flow += f;
	}
}
 
void build_max_flow_graph(void)	{
	for (int i=1; i<=n; ++i)	F[i].clear ();
	for (int i=0; i<m; ++i)	{
		Edge &e = edge[0][i];
		if (d[0][e.u] + e.w + d[1][e.v] == sp)	{
			add_flow_edge (e.u, e.v, 1);
			add_flow_edge (e.v, e.u, 0);
		}
	}
}
 
void SPFA(int s, int id)	{
	memset (d[id], INF, sizeof (d[id]));
	memset (vis, false, sizeof (vis));
	d[id][s] = 0;	vis[s] = true;
	queue<int> que;	que.push (s);
	while (!que.empty ())	{
		int u = que.front ();	que.pop ();
		vis[u] = false;
		for (int i=head[id][u]; ~i; i=edge[id][i].nex)	{
			int v = edge[id][i].v, w = edge[id][i].w;
			if (d[id][v] > d[id][u] + w)	{
				d[id][v] = d[id][u] + w;
				if (!vis[v])	{
					vis[v] = true;	que.push (v);
				}
			}
		}
	}
}
 
int run(void)	{
	SPFA (a, 0);
	sp = d[0][b];
	if (sp == INF)	return 0;
	re_edge ();
	SPFA (b, 1);
	build_max_flow_graph ();
	return Dinic (a, b);
}
 
int main(void)	{
	int T;	scanf ("%d", &T);
	while (T--)	{
		init (0);
		scanf ("%d%d", &n, &m);
		for (int u, v, w, i=1; i<=m; ++i)	{
			scanf ("%d%d%d", &u, &v, &w);
			add_edge (u, v, w, 0);
		}
		scanf ("%d%d", &a, &b);
		printf ("%d\n", run ());
	}
 
	return 0;
}