feat(P3953): 实现基于DFS的路径计数算法替代BFS

用DFS加记忆化搜索替换原有的BFS实现，解决大规模数据下的性能问题
新增距离数组d和动态规划数组dp来优化计算
添加反向图re支持逆向搜索
处理路径计数中的环检测和边界条件

src/11/5/P3953.cpp

@@ -8,8 +8,9 @@
 using ll = int64_t;
 #define sl static inline
 // #define printf
-const ll maxm=2e5+5;
-ll n,m,k,p,nt;
+const ll maxm=2e5+5,inf=1e9+7;
+ll n,m,k,p,nt,d[maxm],dp[maxm][57];
+bool isn,vis[maxm][57];
 struct E{
     ll v,w;
 };
@@ -19,36 +20,78 @@ struct P{
         return step>o.step;
     }
 };
-std::vector<std::vector<E>> edg;
-std::bitset<maxm> vis;
+std::vector<std::vector<E>> edg,re;
 std::deque<P>dq;
 
 sl ll dj(){
-    vis.reset();
+    for(ll i=1;i<=n;i++){
+        d[i]=inf;
+    }
     std::priority_queue<P> pq;
     pq.emplace(1,0);
     while(pq.size()){
         auto[now,step]=pq.top();
+        // printf("dj now=%lld, step=%lld\n",now,step);
         pq.pop();
-        if(now==n)return step;
-        if(vis[now])continue;
-        vis[now]=true;
+        if(step>=d[now])continue;
+        d[now]=step;
         for(auto[v,w]:edg[now]){
             pq.emplace(v,step+w);
         }
     }
-    return -1;
+    
+    printf("d[]:");
+    for(ll i=1;i<=n;i++){
+        printf("%lld ",d[i]);
+    }
+    printf("\n");
+    return d[n]==inf?-1:d[n];
+}
+
+sl ll dfs(ll u,ll k){
+    if(k<0||k>::k)return 0;
+    if(vis[u][k]){
+        isn=true;
+        return 0;
+    }
+    if(u==1)return k==0?1:0;
+    vis[u][k]=true;
+    if(dp[u][k]!=-1){
+        return dp[u][k];
+    }
+    ll nans=0;
+    for(auto[v,w]:re[u]){
+        ll nk=d[u]+k-d[v]-w;
+        if(nk<0||nk>k)continue;
+        nans=(nans+dfs(v, nk))%p;
+        if(isn){
+            return 0;
+        }
+    }
+    vis[u][k]=false;
+    return dp[u][k]=nans;
 }
 
 sl void solve(){
     printf("NT = %lld\n",++nt);
     std::cin>>n>>m>>k>>p;
+    isn=false;
     edg.clear();
     edg.resize(n+1);
+    re.clear();
+    re.resize(n+1);
+    for(ll i=1;i<=n;i++){
+        for(ll j=1;j<=50;j++){
+            dp[i][j]=-1;
+            vis[i][j]=false;
+        }
+    }
+    dp[1][0]=1;
     for(ll i=1;i<=m;i++){
         ll u,v,w;
         std::cin>>u>>v>>w;
         edg[u].emplace_back(v,w);
+        re[v].emplace_back(u,w);
     }
     const ll d = dj();
     printf("found d=%lld\n",d);
@@ -58,27 +101,14 @@ sl void solve(){
     }
     const ll ms=d+k;
     ll ans=0;
-    dq.clear();
-    dq.emplace_back(1,0);
-    ll tick=0;
-    while(dq.size()){
-        tick++;
-        if(tick>1e6){
-            std::cout<<-1<<"\n";
+    for(ll i=0;i<=k;i++){
+        ans=(ans+dfs(n,i))%p;
+        if(isn){
+            std::cout<<"-1\n";
             return;
         }
-        auto[now,step]=dq.front();
-        dq.pop_front();
-        if(now==n){
-            ans++;
-        }
-        for(auto[v,w]:edg[now]){
-            const ll ns=w+step;
-            if(ns>ms)continue;
-            dq.emplace_back(v,ns);
-        }
     }
-    std::cout<<ans%p<<"\n";
+    std::cout<<ans<<"\n";
 }
 
 int main(){