Title:

Give a path map of n points to find the secondary short circuit of points 1 to n

Solution:

1. Two shortest paths
d1 [], d2 [, n [] and d1 [] are calculated from 1 and N respectively.
Let the length of secondary short circuit be ans, traverse all sides, and let the current side be w[u,v]
If d1[u]+w[u,v]+d2[v] equals the shortest path from 1 to n, then w[u,v] is skipped on the shortest path.
Otherwise update ans=min(ans,d1[u]+w[u,v]+d2[v])
2. One dijkstra + update the shortest/shortest short circuit length at the same time
Update d1[],d2[] 4 while running dj
But I think there are too many details in the code. I don't like it very much.
Code with detailed comments

Two shortest paths:

#include<iostream>
#include<cstdio>
#include<cstring>
#include<cmath>
#include<queue>
#define set0(a) memset(a,0,sizeof(a))
#define set1(a) memset(a,-1,sizeof(a))
#define setinf(a) memset(a,inf,sizeof(a))
#define ll long long
const int inf=0x3f3f3f3f;
const int inn=0x80808080;
using namespace std;
const int maxm=2e5+5;
int head[maxm],to[maxm],nt[maxm],w[maxm];
int mark[maxm];
int d1[maxm],d2[maxm];
int cnt;
void add(int x,int y,int z){
    cnt++;nt[cnt]=head[x];head[x]=cnt;to[cnt]=y,w[cnt]=z;
    cnt++;nt[cnt]=head[y];head[y]=cnt;to[cnt]=x,w[cnt]=z;
}
void init(){
    set1(head);
    setinf(d1);
    setinf(d2);
    cnt=0;
}
void spfa(int st,int *d){
    queue<int>q;
    q.push(st);
    set0(mark);
    mark[st]=1;
    d[st]=0;
    while(!q.empty()){
        int x=q.front();;
        q.pop();
        mark[x]=0;
        for(int i=head[x];i!=-1;i=nt[i]){
            int v=to[i];
            if(d[v]>d[x]+w[i]){
                d[v]=d[x]+w[i];
                if(!mark[v]){
                    mark[v]=1;
                    q.push(v);
                }
            }
        }
    }
}
int main(){
    init();
    int n,m;
    scanf("%d%d",&n,&m);
    for(int i=1;i<=m;i++){
        int a,b,c;
        scanf("%d%d%d",&a,&b,&c);
        add(a,b,c);
    }
    spfa(1,d1);
    spfa(n,d2);
    int ans=inf;
    for(int x=1;x<=n;x++){
        for(int i=head[x];i!=-1;i=nt[i]){
            int v=to[i];
            int temp=d1[x]+d2[v]+w[i];
            if(temp>d1[n]&&temp<ans){
                ans=temp;
            }
        }
    }
    printf("%d\n",ans);
    return 0;
}

dijkstra:

#include<iostream>
#include<cstdio>
#include<cstring>
#include<cmath>
#include<queue>
#define set0(a) memset(a,0,sizeof(a))
#define set1(a) memset(a,-1,sizeof(a))
#define setinf(a) memset(a,inf,sizeof(a))
#define ll long long
const int inf=0x3f3f3f3f;
const int inn=0x80808080;
using namespace std;
const int maxm=2e5+5;
int head[maxm],to[maxm],nt[maxm],w[maxm];
int d1[maxm],d2[maxm];
int cnt;
void add(int x,int y,int z){
    cnt++;nt[cnt]=head[x];head[x]=cnt;to[cnt]=y,w[cnt]=z;
    cnt++;nt[cnt]=head[y];head[y]=cnt;to[cnt]=x,w[cnt]=z;
}
void init(){
    set1(head);
    setinf(d1);
    setinf(d2);
    cnt=0;
}
void dj(int st){
    priority_queue<pair<int,int>,vector<pair<int,int> >,greater<pair<int,int> > >q;
    d1[st]=0;//Note: This place can only initialize d1[st] and cannot initialize d2[st]
    q.push(make_pair(0,st));
    while(!q.empty()){
        int d=q.top().first;
        int x=q.top().second;
        q.pop();
        if(d>d2[x])continue;//If the distance is longer than the short circuit, it can't be updated.
        for(int i=head[x];i!=-1;i=nt[i]){
            int v=to[i];
            int temp=d+w[i];
            if(temp<d1[v]){
                swap(d1[v],temp);//This place must be an exchange. Update the secondary short circuit with the old one.
                q.push(make_pair(d1[v],v));
            }
            if(d1[v]<temp&&d2[v]>temp){
                d2[v]=temp;
                q.push(make_pair(d2[v],v));
            }
        }
    }
}
int main(){
    init();
    int n,m;
    scanf("%d%d",&n,&m);
    for(int i=1;i<=m;i++){
        int a,b,c;
        scanf("%d%d%d",&a,&b,&c);
        add(a,b,c);
    }
    dj(1);
    printf("%d\n",d2[n]);
    return 0;
}