hdu3416(最短路+最大流)

最短路+最大流
用Spfa算出 s到各个点的最短路 t到各个点的最短路
if( dis1[i] + dis2[i] + map[i][j] ==dis1[t] )
满足这种情况说明边在最短路上，所以根据这个方法建边

然后最大流解决

这道题很值得体会体会

/*
* this code is made by LinMeiChen
* Problem: hdu 3416 
* Type of Problem: 网络流 水题
* Thinking:
* Feeling:
*/
#include
#include
#include
#include
#include
#include
#include
#include
#include
#include
using namespace std;
typedef long long lld;
typedef unsigned int ud;
#define oo 0x3f3f3f3f
#define eatline() char chch;while((chch=getchar())!='\n')continue;
#define MemsetMax(a) memset(a,0x3f,sizeof a)
#define MemsetZero(a) memset(a,0,sizeof a)
#define MemsetMin(a) memset(a,-1,sizeof a)
#define MemsetFalse(a) MemsetZero(a)
#define PQ priority_queue
#define Q queue
#define maxn 1008
#define maxm 200008
struct Edge
{
    int v, f, next;
}E[maxm];
int level[maxn], h[maxn];
int stack[maxn];
int head[maxn],mark[maxn];
int dis1[maxn], dis2[maxn];
int map[maxn][maxn];
int c[maxn][maxn];
int q[maxm], front, rear;
int tol, n, m;

void Spfa(int s, int t, int dis[], int f)
{
    fill(dis, dis + maxn, oo);
    memset(mark, 0, sizeof mark);
    front = rear = 0;
    q[rear++] = s;
    dis[s] = 0;
    mark[s] = 1;
    while (front<rear)
    {
        int u = q[front++];
        mark[u] = 0;
        for (int i = 1; i <= n; i++)
        {
            int v = i;
            if (dis[v] > dis[u] + ( f==0 ? map[u][v]:map[v][u]))
            {
                dis[v] = dis[u] + ( f==0 ? map[u][v]:map[v][u]);
                if (!mark[v])
                {
                    q[rear++] = v;
                    mark[v] = 1;
                }
            }
        }
    }
}

void add_edge(int u, int v, int f)
{
    E[tol].v = v;
    E[tol].f = f;
    E[tol].next = head[u];
    head[u] = tol++;

    E[tol].v = u;
    E[tol].f = 0;
    E[tol].next = head[v];
    head[v] = tol++;
}

void Build(int s, int t)
{
    memset(head, -1, sizeof head);
    tol = 0;
    for (int i = 1; i <= n;i++)
    for (int j = 1; j <= n; j++)
    {
        if (dis1[i] + dis2[j] + map[i][j] == dis1[t])
            add_edge(i, j, c[i][j]);
    }
}

bool BFS(int s, int t)
{
    memset(level, 0, sizeof level);
    level[s] = 1;
    front = rear = 0;
    q[rear++] = s;
    while (front < rear)
    {
        int u = q[front++];
        if (u == t)
            return true;
        for (int i = head[u]; i != -1; i = E[i].next)
        {
            int v = E[i].v;
            if (!level[v] && E[i].f>0)
            {
                level[v] = level[u] + 1;
                q[rear++] = v;
            }
        }
    }
    return false;
}

int Dinic(int s, int t)
{
    int maxflow = 0;
    while (BFS(s, t))
    {
        memcpy(h, head, sizeof h);
        int top = 0, u = s;
        while (true)
        {
            if (u == t)
            {
                int minflow = oo, flag;
                for (int i = 0; i < top; i++)
                {
                    if (minflow>E[stack[i]].f)
                    {
                        minflow = E[stack[i]].f;
                        flag = i;
                    }
                }
                for (int i = 0; i < top; i++)
                {
                    E[stack[i]].f -= minflow;
                    E[stack[i] ^ 1].f += minflow;
                }
                top = flag;
                maxflow += minflow;
                u = E[stack[top] ^ 1].v;//反向边的邻接点
            }
            for (int i = h[u]; i != -1; i = h[u] = E[i].next)
            {
                int v = E[i].v;
                if (level[v] == level[u] + 1 && E[i].f)
                    break;
            }
            if (h[u] != -1)
            {
                stack[top++] = h[u];
                u = E[h[u]].v;
            }
            else
            {
                if (top == 0)
                    break;
                level[u] = 0;
                u = E[stack[--top] ^ 1].v;//反向边的邻接点
            }
        }
    }
    return maxflow;
}

int main()
{
    int T;
    int s, t;
    scanf("%d", &T);
    while (T--)
    {
        memset(map, 0x3f, sizeof map);
        memset(c, 0, sizeof c);
        scanf("%d%d", &n, &m);
        for (int i = 1; i <= m; i++)
        {
            int u, v, w;
            scanf("%d%d%d", &u, &v, &w);
            if (map[u][v] > w)
            {
                map[u][v] = w;
                c[u][v] = 1;
            }
            else if (map[u][v] == w)
                c[u][v]++;
        }
        scanf("%d%d", &s, &t);

        Spfa(s, t, dis1,0);
        Spfa(t, s, dis2,1);
        Build(s, t);
        printf("%d\n", Dinic(s, t));
    }
    return 0;
}