perf(P9981): 优化图算法性能并实现快速IO

重构图遍历算法，使用更高效的数据结构和比较逻辑
添加FastIO模块提升输入输出性能

src/9/10/P9981.cpp

@@ -1,107 +1,196 @@
 #include <algorithm>
-#include <cstdint>
 #include <iostream>
-#include <istream>
 #include <queue>
-#include <tuple>
 #include <vector>
-using ll = int64_t;
 
-ll n,m;
+namespace FastIO {
+const int BUF_SIZE = 1 << 20;
+char in_buf[BUF_SIZE], out_buf[BUF_SIZE];
+char *in_ptr = in_buf + BUF_SIZE;
+char *out_ptr = out_buf;
 
-struct Edge{
-    ll to,l;
+char get_char() {
+    if (in_ptr == in_buf + BUF_SIZE) {
+        fread(in_buf, 1, BUF_SIZE, stdin);
+        in_ptr = in_buf;
+    }
+    return *(in_ptr++);
+}
+
+template <typename T> void read(T &x) {
+    x = 0;
+    char c = get_char();
+    bool positive = true;
+    while (!isdigit(c)) {
+        if (c == '-')
+            positive = false;
+        c = get_char();
+    }
+    while (isdigit(c)) {
+        x = x * 10 + (c - '0');
+        c = get_char();
+    }
+    if (!positive)
+        x = -x;
+}
+
+void put_char(char c) {
+    if (out_ptr == out_buf + BUF_SIZE) {
+        fwrite(out_buf, 1, BUF_SIZE, stdout);
+        out_ptr = out_buf;
+    }
+    *(out_ptr++) = c;
+}
+
+template <typename T> void write(T x) {
+    if (x < 0) {
+        put_char('-');
+        x = -x;
+    }
+    if (x == 0) {
+        put_char('0');
+        return;
+    }
+    char buf[20];
+    int len = 0;
+    while (x > 0) {
+        buf[len++] = (x % 10) + '0';
+        x /= 10;
+    }
+    for (int i = len - 1; i >= 0; --i) {
+        put_char(buf[i]);
+    }
+}
+
+struct Flusher {
+    ~Flusher() {
+        if (out_ptr != out_buf) {
+            fwrite(out_buf, 1, out_ptr - out_buf, stdout);
+        }
+    }
+} flusher;
+} // namespace FastIO
+
+using FastIO::put_char;
+using FastIO::read;
+using FastIO::write;
+
+struct Edge {
+    int to;
+    int label;
 };
-std::vector<std::vector<Edge>> edg;
-std::vector<ll> ind;
-std::queue<ll> q;
-std::vector<ll> topo;
-std::vector<ll> len;
-std::vector<std::vector<ll>> lv;
 
-#define p1v(ind)do{\
-        std::cout<<#ind<<"\n";\
-        for(auto& i:ind){\
-            std::cout<<i<<", ";\
-        }\
-        std::cout<<"\n";\
-    }while(0)
+struct Path {
+    long long len = 0;
+    long long sum = 0;
+    int prefix_label = 0;
+    int next_node = 0;
+};
 
-namespace std{
-    static inline bool operator<(const vector<ll>&a,const vector<ll>&b){
-        if((a.size()|b.size()) == 0){
-            return false;
-        }
-        if(a.size()==0 && b.size()!=0){
+bool is_better(const Path &p_cand, const Path &p_best, const std::vector<Path> &dp) {
+    if (p_cand.len > p_best.len)
+        return true;
+    if (p_cand.len < p_best.len)
+        return false;
+
+    if (p_cand.len == 0)
+        return false;
+
+    if (p_cand.prefix_label < p_best.prefix_label)
+        return true;
+    if (p_cand.prefix_label > p_best.prefix_label)
+        return false;
+
+    const Path *ptr1 = &dp[p_cand.next_node];
+    const Path *ptr2 = &dp[p_best.next_node];
+
+    for (int i = 0; i < 110 && ptr1->len > 0 && ptr2->len > 0; ++i) {
+        if (ptr1->prefix_label < ptr2->prefix_label)
             return true;
-        }
-        if(a.size()!=0 && b.size() == 0){
+        if (ptr1->prefix_label > ptr2->prefix_label)
             return false;
-        }
-        for(ll i=0;i<a.size()&&i<b.size()&&i<500;i++){
-            if(a[i]<b[i])return true;
-            else if(a[i]>b[i])return false;
-        }
-        return a.size()<b.size();
+        ptr1 = &dp[ptr1->next_node];
+        ptr2 = &dp[ptr2->next_node];
     }
+
+    return false;
 }
 
-static inline ll sum(const std::vector<ll> &v){
-    ll res=0;
-    for(auto i:v){
-        res+=i;
-    }
-    return res;
-}
+int main() {
+    std::ios_base::sync_with_stdio(false);
+    std::cin.tie(NULL);
 
-int main(){
-    std::iostream::sync_with_stdio(false);
-    std::cin.tie(nullptr);
-    // std::cout<<(std::vector<ll>({1,2,2})<std::vector<ll>({1,2,3}))<<"\n";
-    std::cin>>n>>m;
-    edg.resize(n+1);
-    ind.resize(n+1);
-    len.resize(n+1);
-    lv.resize(n+1);
+    int n, m;
+    read(n);
+    read(m);
 
-    for(ll i=1;i<=m;i++){
-        ll a,b,l;
-        std::cin>>b>>a>>l;
-        edg[a].emplace_back(b,l);
-        ind[b]++;
+    std::vector<std::vector<Edge>> adj(n + 1);
+    std::vector<int> in_degree(n + 1, 0);
+
+    for (int i = 0; i < m; ++i) {
+        int u, v, l;
+        read(u);
+        read(v);
+        read(l);
+        adj[u].push_back({v, l});
+        in_degree[v]++;
     }
-    for(ll u=1;u<=n;u++){
-        if(ind[u]==0){
-            q.emplace(u);
+
+    std::queue<int> q;
+    for (int i = 1; i <= n; ++i) {
+        if (in_degree[i] == 0) {
+            q.push(i);
         }
     }
-    while(q.size()){
-        ll top = q.front();
+
+    std::vector<int> topo_order;
+    topo_order.reserve(n);
+    while (!q.empty()) {
+        int u = q.front();
         q.pop();
-        topo.emplace_back(top);
-        for(auto [to,l]:edg[top]){
-            ind[to]--;
-            if(ind[to]==0){
-                q.emplace(to);
-                // len[to]=std::max(len[to],len[top]+1);
-                if(len[top]+1>len[to]){
-                    len[to]=len[top]+1;
-                    lv[to] = lv[top];
-                    lv[to].emplace_back(l);
-                }else if(len[to]==len[top]+1){
-                    std::vector<ll> nlv = lv[top];
-                    nlv.emplace_back(l);
-                    if(lv[to]<nlv){
-                        lv[to]=std::move(nlv);
-                    }
-                }
+        topo_order.push_back(u);
+
+        for (const auto &edge : adj[u]) {
+            int v = edge.to;
+            in_degree[v]--;
+            if (in_degree[v] == 0) {
+                q.push(v);
             }
         }
     }
-    // p1v(topo);
-    // p1v(len);
-    for(ll i=1;i<=n;i++){
-        std::cout<<len[i]<<" "<<sum(lv[i])<<"\n";
+
+    std::vector<Path> dp(n + 1);
+
+    for (int i = n - 1; i >= 0; --i) {
+        int u = topo_order[i];
+
+        std::sort(adj[u].begin(), adj[u].end(), [](const Edge &a, const Edge &b) { return a.label < b.label; });
+
+        Path best_path = {};
+
+        for (const auto &edge : adj[u]) {
+            int v = edge.to;
+            int l = edge.label;
+
+            Path candidate_path;
+            candidate_path.len = 1 + dp[v].len;
+            candidate_path.sum = l + dp[v].sum;
+            candidate_path.prefix_label = l;
+            candidate_path.next_node = v;
+
+            if (is_better(candidate_path, best_path, dp)) {
+                best_path = candidate_path;
+            }
+        }
+        dp[u] = best_path;
     }
 
+    for (int i = 1; i <= n; ++i) {
+        write(dp[i].len);
+        put_char(' ');
+        write(dp[i].sum);
+        put_char('\n');
+    }
+
+    return 0;
 }