POJ3114 Countries in War 缩点+SPFA 中等题

//缩点+spfa
/*
*State: POJ3114     Accepted    2908K    375MS    C++    2953B
*题目大意：
*        给定一个有向有权图，然后要求求出图中任意两点间的最短距离。
*        注意图中可能有环，每一个环中的任意两点间的距离为0.
*解题思路：
*        题意看了好久，一开始还以为是lca,后来才发现那个奇怪的特征，
*        原来每个环中的任意两点间的距离为0，就说明要进行缩点了。缩点
*        之后还是要求最短距离，这个时候就想到了spfa.
*        总结就是： 缩点 + spfa
*解题感想：
*        从lca到缩点+spfa,感觉用缩点+spfa比较靠谱，但是估量了下，代码
*        长度可能要200行上下，不过还是稳稳地打了出来，之后经历了两次RE.
*        表示这么长的代码交出了RE是一件非常恐怖的事情。但好在代码里面，我
*        自己给自己留了条路，数组的初始值能赋值为-1的都赋值为-1，经过这条
*        后路查出了是我的tarjan_scc里面一个判断条件，判断son判断成了n.
*        就是缩点缩错了。最终2RE+1wa来到了最后的ac.泪奔~搞了两个钟。
*/

#include <iostream>
#include <vector>
#include <cstdio>
#include <queue>
#include <utility>
#include <stack>
using namespace std;

const int MAXN = 505;
const int inf = 0x3f3f3f3f;

typedef struct _node
{
    int v, w;
}N;

vector<N> vec[MAXN];
stack<int> S;
int scc, dfn[MAXN], low[MAXN], step;
int inS[MAXN], id[MAXN];

//spfa
vector<N> sccvec[MAXN];

void deal_spfa(int n)
{
    N tmp;
    int u, v;
    for(int i = 1; i <= n; i++)
    {
        for(unsigned j = 0; j < vec[i].size(); j++)
        {
            u = i, v = vec[i][j].v;
            if(id[u] == id[v])
                continue;
            else
            {
                tmp.v = id[v]; 
                tmp.w = vec[i][j].w;
                sccvec[id[u]].push_back(tmp);
            }
        }
    }
}

int spfa(int s, int e)
{
    queue<int> Q;
    int dis[MAXN], in[MAXN] = {0};
    for(int i = 0; i < MAXN; i++)
        dis[i] = inf;
    dis[s] = 0;
    in[s] = 1;
    Q.push(s);
    while(!Q.empty())
    {
        int pre = Q.front();
        Q.pop();
        in[pre] = 0;
        for(unsigned i = 0; i < sccvec[pre].size(); i++)
        {
            int son = sccvec[pre][i].v;
            int w = sccvec[pre][i].w;
            if(dis[son] > dis[pre] + w)
            {
                dis[son] = dis[pre] + w;
                if(in[son] == 0)
                {
                    Q.push(son);
                    in[son] = 1;
                }
            }
        }
    }

    return dis[e];
}

void init()
{
    while(!S.empty())
        S.pop();
    step = 0;
    scc = 1;
    for(int i = 0; i < MAXN; i++)
    {
        sccvec[i].clear();
        id[i] = 0;
        inS[i] = 0;
        dfn[i] = low[i] = -1;
        vec[i].clear();
    }
}

void addEdge(int u, int v, int w)
{
    N tmp;
    tmp.v = v, tmp.w = w;
    vec[u].push_back(tmp);
}

void tarjan_scc(int n)
{
    dfn[n] = low[n] = ++step;
    S.push(n);
    inS[n] = 1;
    for(unsigned i = 0; i < vec[n].size(); i++)
    {
        int son = vec[n][i].v;
        if(dfn[son] == -1)
        {
            tarjan_scc(son);
            low[n] = min(low[n], low[son]);
        }
        else if(inS[son] == 1)
        {
            low[n] = min(low[n], dfn[son]);
        }
    }
    if(low[n] == dfn[n] && !S.empty())
    {
        //cout << "--------------" << endl;
        int tmp;
        do
        {
            tmp = S.top();
            //cout << tmp << " ";
            S.pop();
            inS[tmp] = 0;
            id[tmp] = scc;
        }while(!S.empty() && tmp != n);
        //cout << endl;
        scc++;
    }
}

int main(void)
{
#ifndef ONLINE_JUDGE
    //freopen("in.txt", "r", stdin);
#endif
    //cout << inf << endl;
    int n, m, cas_c = 0;
    while(scanf("%d", &n), n)
    {
        scanf("%d", &m);
        if(cas_c++ != 0)
            printf("\n");
        int u, v, w;
        init();
        for(int i = 0; i < m; i++)
        {
            scanf("%d %d %d", &u, &v, &w);
            addEdge(u, v, w);
        }
        for(int i = 1; i <= n; i++)
        {
            if(dfn[i] == -1)
                tarjan_scc(i);
        }

        //cout << "******" << endl;
        deal_spfa(n);
        int q;
        scanf("%d", &q);
        for(int i = 0; i < q; i++)
        {
            scanf("%d %d", &u, &v);
            if(id[u] == id[v])
                printf("0\n");
            else
            {
                int ans = spfa(id[u], id[v]);
                if(ans == inf)
                    printf("Nao e possivel entregar a carta\n");
                else
                    printf("%d\n", ans);
            }
        }
    }
    return 0;
}



第二次优化时间
State: POJ3114    Accepted    3904K    313MS    C++    2878B
#include <iostream>
#include <vector>
#include <cstdio>
#include <queue>
#include <utility>
#include <stack>
using namespace std;

const int MAXN = 505;
const int MAXE = 250005;
const int inf = 0x3f3f3f3f;

typedef struct _node
{
    int v, w;
    int next;
}N;

N edge[MAXE];
int scc, dfn[MAXN], low[MAXN], step, myS[MAXN], top;
int inS[MAXN], id[MAXN], cntEdge, head[MAXN];

//spfa
vector<N> sccvec[MAXN];

void deal_spfa(int n)
{
    N tmp;
    int u, v;
    for(int i = 1; i <= n; i++)
    {
        for(int j = head[i]; j != -1; j = edge[j].next)
        {
            u = i, v = edge[j].v;
            if(id[u] == id[v])
                continue;
            else
            {
                tmp.v = id[v]; 
                tmp.w = edge[j].w;
                sccvec[id[u]].push_back(tmp);
            }
        }
    }
}

int spfa(int s, int e)
{
    queue<int> Q;
    int dis[MAXN], in[MAXN] = {0};
    for(int i = 0; i < MAXN; i++)
        dis[i] = inf;
    dis[s] = 0;
    in[s] = 1;
    Q.push(s);
    while(!Q.empty())
    {
        int pre = Q.front();
        Q.pop();
        in[pre] = 0;
        for(unsigned i = 0; i < sccvec[pre].size(); i++)
        {
            int son = sccvec[pre][i].v;
            int w = sccvec[pre][i].w;
            if(dis[son] > dis[pre] + w)
            {
                dis[son] = dis[pre] + w;
                if(in[son] == 0)
                {
                    Q.push(son);
                    in[son] = 1;
                }
            }
        }
    }

    return dis[e];
}

void init()
{
    step = cntEdge = top = 0;
    scc = 1;
    for(int i = 0; i < MAXN; i++)
    {
        sccvec[i].clear();
        id[i] = 0;
        inS[i] = 0;
        dfn[i] = low[i] = -1;
        head[i] = -1;
    }
}

void addEdge(int u, int v, int w)
{
    edge[cntEdge].v = v;
    edge[cntEdge].w = w;
    edge[cntEdge].next = head[u];
    head[u] = cntEdge++;
}

void tarjan_scc(int n)
{
    dfn[n] = low[n] = ++step;
    myS[top++] = n;
    inS[n] = 1;
    for(int f = head[n]; f != -1; f = edge[f].next)
    {
        int son = edge[f].v;
        if(dfn[son] == -1)
        {
            tarjan_scc(son);
            low[n] = min(low[n], low[son]);
        }
        else if(inS[son] == 1)
        {
            low[n] = min(low[n], dfn[son]);
        }
    }
    if(low[n] == dfn[n] && top != 0)
    {
        int tmp;
        do
        {
            tmp = myS[--top];
            inS[tmp] = 0;
            id[tmp] = scc;
        }while(top != 0 && tmp != n);
        scc++;
    }
}

int main(void)
{
#ifndef ONLINE_JUDGE
    freopen("in.txt", "r", stdin);
#endif
    int n, m, cas_c = 0;
    while(scanf("%d", &n), n)
    {
        scanf("%d", &m);
        if(cas_c++ != 0)
            printf("\n");
        int u, v, w;
        init();
        for(int i = 0; i < m; i++)
        {
            scanf("%d %d %d", &u, &v, &w);
            addEdge(u, v, w);
        }
        for(int i = 1; i <= n; i++)
        {
            if(dfn[i] == -1)
                tarjan_scc(i);
        }

        deal_spfa(n);
        int q;
        scanf("%d", &q);
        for(int i = 0; i < q; i++)
        {
            scanf("%d %d", &u, &v);
            if(id[u] == id[v])
                printf("0\n");
            else
            {
                int ans = spfa(id[u], id[v]);
                if(ans == inf)
                    printf("Nao e possivel entregar a carta\n");
                else
                    printf("%d\n", ans);
            }
        }
    }
    return 0;
}