hdu 3191 次短路的长度和个数

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

求次短路的长度和个数

#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
",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
",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
",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;
}

#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-9const 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 = 0;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 ",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;}