http://acm.hdu.edu.cn/showproblem.php?pid=3191

求次短路的长度和个数

相关分析在这里http://blog.csdn.net/u012774187/article/details/40681515

#pragma comment(linker, "/STACK:36777216")

#pragma GCC optimize ("O2")

#include <cstdio>

#include <cstdlib>

#include <cmath>

#include <cstring>

#include <string>

#include <queue>

#include <map>

#include <iostream>

#include <algorithm>

using namespace std;

#define RD(x) scanf("%d",&x)

#define RD2(x,y) scanf("%d%d",&x,&y)

#define RD3(x,y,z) scanf("%d%d%d",&x,&y,&z)

#define clr0(x) memset(x,0,sizeof(x))

#define clr1(x) memset(x,-1,sizeof(x))

#define eps 1e-9

const double pi = acos(-1.0);

typedef long long LL;

typedef unsigned long long ULL;

const int modo = 1e9 + 7;

const int INF = 0x3f3f3f3f;

const int inf = 0x3fffffff;

const LL _inf = 1e18;

const int maxn = 55,maxm = 10005;

struct edge{

    int v,w,next;

    edge(){};

    edge(int vv,int ww,int nnext):v(vv),w(ww),next(nnext){};

}e[maxn*maxn*2];

int head[maxn],inq[maxn][2],dist[maxn][2],cnt[maxn][2];//0最短1次短

int n,m,ecnt;

void init()

{

    clr1(head);

    ecnt = 0;

    for(int i = 1;i <= maxn;++i)

        dist[i][0] = dist[i][1] = inf;

    //fill(dist,dist+maxn*2,inf);

    clr0(inq),clr0(cnt);

}

void add(int u,int v,int w)

{

    e[ecnt] = edge(v,w,head[u]);

    head[u] = ecnt++;

//    e[ecnt] = edge(u,w,head[v]);

//    head[v] = ecnt++;

}

typedef pair<int,int> p2;

struct cmp {

     bool operator() (const p2 &a, const p2 &b)

     {

        if(dist[a.first][a.second] != dist[b.first][b.second])

            return dist[a.first][a.second] > dist[b.first][b.second];

        else

            return a.first > b.first;

     }

};

void spfa(int src,int dst)

{

    priority_queue<p2 , vector<p2> , cmp> q;

    q.push(make_pair(src,0));

    dist[src][0] = 0,cnt[src][0] = 1;

    while(!q.empty()){

        int u = q.top().first,flag = q.top().second;

        q.pop();

        if(inq[u][flag])    continue;

        inq[u][flag] = 1;

        for(int i = head[u];i != -1;i = e[i].next){

            int v = e[i].v,w = e[i].w;

            if(!inq[v][0] && dist[v][0] > dist[u][flag] + e[i].w){

                if(dist[v][0] != inf){

                    dist[v][1] = dist[v][0];

                    cnt[v][1] = cnt[v][0];

                    q.push(make_pair(v,1));

                }

                dist[v][0] = dist[u][flag] + e[i].w;

                cnt[v][0] = cnt[u][flag];

                q.push(make_pair(v,0));

            }else if(!inq[v][0] && dist[v][0] == dist[u][flag] + e[i].w){

                cnt[v][0] += cnt[u][flag];

            }else if(!inq[v][1] && dist[v][1] > dist[u][flag] + e[i].w){

                dist[v][1] = dist[u][flag] + e[i].w;

                cnt[v][1] = cnt[u][flag];

                q.push(make_pair(v,1));

            }else if(!inq[v][1] && dist[v][1] == dist[u][flag] + e[i].w){

                cnt[v][1] += cnt[u][flag];

            }

        }

    }

    printf("%d %d\n",dist[dst][1],cnt[dst][1]);

}

int main(){

    int u,v,w,s,t;

    while(~RD2(n,m)){

        RD2(s,t);s++,t++;

        init();

        while(m--){

            RD3(u,v,w);u++,v++;

            add(u,v,w);

        }

        spfa(s,t);

    }

    return 0;

}

上面是错误代码

经过筛查，发现是

if(dist[a.first][a.second] != dist[b.first][b.second])

            return dist[a.first][a.second] > dist[b.first][b.second];

有问题，因为不同的路径到达同一个点的同一个状态的值不一样，所有比较和更新穿插在一起就会出错了

可是每次更新dist数组都是向小了更新，所以不应该有影响啊..?

以下是AC代码，谁能清楚一点地告诉为啥上面的程序就不对呢？

#pragma comment(linker, "/STACK:36777216")

#pragma GCC optimize ("O2")

#include <cstdio>

#include <cstdlib>

#include <cmath>

#include <cstring>

#include <string>

#include <queue>

#include <map>

#include <iostream>

#include <algorithm>

using namespace std;

#define RD(x) scanf("%d",&x)

#define RD2(x,y) scanf("%d%d",&x,&y)

#define RD3(x,y,z) scanf("%d%d%d",&x,&y,&z)

#define clr0(x) memset(x,0,sizeof(x))

#define clr1(x) memset(x,-1,sizeof(x))

#define eps 1e-9

const double pi = acos(-1.0);

typedef long long LL;

typedef unsigned long long ULL;

const int modo = 1e9 + 7;

const int INF = 0x3f3f3f3f;

const int inf = 0x3fffffff;

const LL _inf = 1e18;

const int maxn = 55,maxm = 10005;

struct edge{

    int v,w,next;

    edge(){};

    edge(int vv,int ww,int nnext):v(vv),w(ww),next(nnext){};

}e[maxn*maxn*2];

int head[maxn],inq[maxn][2],dist[maxn][2],cnt[maxn][2];//0最短1次短

int n,m,ecnt;

struct node{

    int v,flag,dis;

    node(int a,int b,int c):v(a),flag(b),dis(c){};

    bool operator < (const node & a) const{

        if(a.dis == dis)

            return a.v < v;

        return a.dis < dis;

    }

};

void init()

{

    clr1(head);

    ecnt = 0;

    for(int i = 0;i <= n;++i)

        dist[i][0] = dist[i][1] = inf;

    //fill(dist,dist+maxn*2,inf);

    clr0(inq),clr0(cnt);

}

void add(int u,int v,int w)

{

    e[ecnt] = edge(v,w,head[u]);

    head[u] = ecnt++;

//    e[ecnt] = edge(u,w,head[v]);

//    head[v] = ecnt++;

}

void spfa(int src,int dst)

{

    priority_queue<node> q;

    q.push(node(src,0,0));

    dist[src][0] = 0,cnt[src][0] = 1;

    while(!q.empty()){

        int u = q.top().v,flag = q.top().flag,dis = q.top().dis;

        q.pop();

        if(inq[u][flag])    continue;

        inq[u][flag] = 1;

        for(int i = head[u];i != -1;i = e[i].next){

            int v = e[i].v,w = e[i].w;

            if(!inq[v][0] && dist[v][0] > dis + e[i].w){

                if(dist[v][0] != inf){

                    dist[v][1] = dist[v][0];

                    cnt[v][1] = cnt[v][0];

                    q.push(node(v,1,dist[v][1]));

                }

                dist[v][0] = dis + e[i].w;

                cnt[v][0] = cnt[u][flag];

                q.push(node(v,0,dist[v][0]));

            }else if(!inq[v][0] && dist[v][0] == dis + e[i].w){

                cnt[v][0] += cnt[u][flag];

            }else if(!inq[v][1] && dist[v][1] > dis + e[i].w){

                dist[v][1] = dis + e[i].w;

                cnt[v][1] = cnt[u][flag];

                q.push(node(v,1,dist[v][1]));

            }else if(!inq[v][1] && dist[v][1] == dis+ e[i].w){

                cnt[v][1] += cnt[u][flag];

            }

        }

    }

    printf("%d %d\n",dist[dst][1],cnt[dst][1]);

}

int main(){

    int u,v,w,s,t;

    while(~RD2(n,m)){

        RD2(s,t);s++,t++;

        init();

        while(m--){

            RD3(u,v,w);u++,v++;

            add(u,v,w);

        }

        spfa(s,t);

    }

    return 0;

}

AC代码2

#pragma comment(linker, "/STACK:36777216")

#pragma GCC optimize ("O2")

#include <cstdio>

#include <cstdlib>

#include <cmath>

#include <cstring>

#include <string>

#include <queue>

#include <map>

#include <iostream>

#include <algorithm>

using namespace std;

#define RD(x) scanf("%d",&x)

#define RD2(x,y) scanf("%d%d",&x,&y)

#define RD3(x,y,z) scanf("%d%d%d",&x,&y,&z)

#define clr0(x) memset(x,0,sizeof(x))

#define clr1(x) memset(x,-1,sizeof(x))

#define eps 1e-9

const double pi = acos(-1.0);

typedef long long LL;

typedef unsigned long long ULL;

const int modo = 1e9 + 7;

const int INF = 0x3f3f3f3f;

const int inf = 0x3fffffff;

const LL _inf = 1e18;

const int maxn = 55,maxm = 10005;

struct edge{

    int v,w,next;

    edge(){};

    edge(int vv,int ww,int nnext):v(vv),w(ww),next(nnext){};

}e[maxn*maxn*2];

int head[maxn],inq[maxn][2],dist[maxn][2],cnt[maxn][2];//0最短1次短

int n,m,ecnt;

struct node{

    int v,flag,dis;

    node(int a,int b,int c):v(a),flag(b),dis(c){};

    bool operator < (const node & a) const{

        if(a.dis == dis)

            return a.v < v;

        return a.dis < dis;

    }

};

void init()

{

    clr1(head);

    ecnt = 0;

    for(int i = 0;i <= n;++i)

        dist[i][0] = dist[i][1] = inf;

    //fill(dist,dist+maxn*2,inf);

    clr0(inq),clr0(cnt);

}

void add(int u,int v,int w)

{

    e[ecnt] = edge(v,w,head[u]);

    head[u] = ecnt++;

//    e[ecnt] = edge(u,w,head[v]);

//    head[v] = ecnt++;

}

void spfa(int src,int dst)

{

    priority_queue<node> q;

    q.push(node(src,0,0));

    dist[src][0] = 0,cnt[src][0] = 1;

    while(!q.empty()){

        int u = q.top().v,flag = q.top().flag;//dis = q.top().dis;

        q.pop();

        if(inq[u][flag])    continue;

        inq[u][flag] = 1;

        for(int i = head[u];i != -1;i = e[i].next){

            int v = e[i].v,w = e[i].w;

            if(!inq[v][0] && dist[v][0] > dist[u][flag] + e[i].w){

                if(dist[v][0] != inf){

                    dist[v][1] = dist[v][0];

                    cnt[v][1] = cnt[v][0];

                    q.push(node(v,1,dist[v][1]));

                }

                dist[v][0] = dist[u][flag] + e[i].w;

                cnt[v][0] = cnt[u][flag];

                q.push(node(v,0,dist[v][0]));

            }else if(!inq[v][0] && dist[v][0] == dist[u][flag] + e[i].w){

                cnt[v][0] += cnt[u][flag];

            }else if(!inq[v][1] && dist[v][1] > dist[u][flag] + e[i].w){

                dist[v][1] = dist[u][flag] + e[i].w;

                cnt[v][1] = cnt[u][flag];

                q.push(node(v,1,dist[v][1]));

            }else if(!inq[v][1] && dist[v][1] == dist[u][flag] + e[i].w){

                cnt[v][1] += cnt[u][flag];

            }

        }

    }

    printf("%d %d\n",dist[dst][1],cnt[dst][1]);

}

int main(){

    int u,v,w,s,t;

    while(~RD2(n,m)){

        RD2(s,t);s++,t++;

        init();

        while(m--){

            RD3(u,v,w);u++,v++;

            add(u,v,w);

        }

        spfa(s,t);

    }

    return 0;

}