docs: 更新README并清理测试代码

更新README添加超时优化方法，同时清理test.cpp中未使用的代码

README.md

@@ -14,3 +14,8 @@
 1. 编辑距离 i-1,j i,j-1
 2. 合并石子 1~k,k+1~i
 3. 网捉蛇 1~k用j-1, k+1~i用1
+
+## 超时优化的三种方法
+1. 预处理(排序最常用)
+2. 二分
+3. 数学方法

src/9/2/P1967.cpp

@@ -0,0 +1,138 @@
+#include <algorithm>
+#include <cstdint>
+#include <cstring>
+#include <ios>
+#include <iostream>
+#include <queue>
+#include <utility>
+#include <vector>
+
+using ll = int64_t;
+
+struct Edge{
+    ll to{};
+    ll w{};
+    inline bool operator<(const Edge&r){
+        return w<r.w;
+    }
+};
+
+struct XYZ{
+    ll x{},y{},z{};
+    inline bool operator<(const XYZ&r)const{
+        return z<r.z;
+    }
+};
+
+const ll maxlog = 15, inf=1e9;
+ll n,m,q;
+std::vector<std::vector<Edge>> edg;
+std::vector<ll> unf, dpth;
+std::vector<std::vector<ll>> fth,cost;
+std::priority_queue<XYZ> pq;
+ll mergednum = 0;
+
+static inline ll find(ll idx){
+    if(idx==unf[idx])return idx;
+    return unf[idx]=find(unf[idx]);
+}
+
+static inline void merge(ll a,ll b){
+    unf[find(a)]=find(b);
+}
+
+static inline bool ismerged(ll a,ll b){
+    return find(a)==find(b);
+}
+
+static inline void dfs(ll f,ll cur){
+    dpth[cur]=dpth[f]+1;
+    fth[cur][0]=f;
+    for(ll i=1;i<=maxlog;i++){
+        fth[cur][i]=fth[fth[cur][i-1]][i-1];
+        cost[cur][i]=std::min(cost[fth[cur][i-1]][i-1],cost[cur][i-1]);
+    }
+    for(auto nxt:edg[cur]){
+        if(nxt.to==f)continue;
+        cost[nxt.to][0]=nxt.w;
+        dfs(cur,nxt.to);
+    }
+}
+
+static inline ll lca(ll a,ll b){
+    if(dpth[a]>dpth[b])std::swap(a,b);
+    // ll tmp = dpth[b]-dpth[1],ans=0;错误
+    ll tmp = dpth[b]-dpth[a],ans=inf;
+    for(ll j=0;tmp;j++,tmp>>=1){
+        if(tmp&1){
+            ans=std::min(ans,cost[b][j]);
+            b=fth[b][j]; // 注意在if里面
+        }
+    }
+    if(a==b)return ans;
+    for(ll j=maxlog;j>=0 && a!=b;j--){
+        if(fth[a][j]!=fth[b][j]){
+            ans=std::min({ans,cost[a][j],cost[b][j]});
+            a=fth[a][j];
+            b=fth[b][j];
+        }
+    }
+    ans=std::min({ans,cost[a][0],cost[b][0]});
+    return ans;
+}   
+
+int main(){
+    std::ios_base::sync_with_stdio(false);
+    std::cin.tie(nullptr);
+
+    std::cin>>n>>m;
+
+    edg.resize(n+1);
+    unf.resize(n+1);
+    fth.resize(n+1,std::vector<ll>(maxlog+1));
+    cost.resize(n+1,std::vector<ll>(maxlog+1,inf));
+    dpth.resize(n+1);
+
+    for(ll i=1;i<=n;i++){
+        unf[i]=i;
+    }
+
+    for(ll i=1;i<=m;i++){
+        ll x,y,z;
+        std::cin>>x>>y>>z;
+        pq.emplace(x,y,z);
+    }
+
+    while(pq.size() && mergednum < n-1){
+        auto[x,y,z] = pq.top();
+        pq.pop();
+        if(ismerged(x, y))continue;
+        edg[x].emplace_back(y,z);
+        edg[y].emplace_back(x,z);
+        merge(x, y);
+        mergednum++;
+    }
+
+    // for(ll u=1;u<=n;u++){
+    //     for(auto [v,w]:edg[u]){
+    //         printf("point %lld to %lld weight %lld\n",u,v,w);
+    //     }
+    // }
+
+    for(ll i=1;i<=n;i++){
+        if(dpth[i]==0){
+            dpth[0]=0;
+            dfs(0,i);
+        }
+    }
+    std::cin>>q;
+    for(ll i=1;i<=q;i++){
+        ll a,b;
+        std::cin>>a>>b;
+        if (!ismerged(a, b)) {
+            std::cout<<"-1\n";
+            continue;
+        }
+        std::cout<<lca(a,b)<<'\n';
+    }
+}

src/test.cpp

@@ -1,19 +1,3 @@
-#include <cmath>
-#include <iostream>
-#include <set>
-#include <stdexcept>
-#include <string>
 int main(){
-    int n;
-    std::cin>>n;
-    std::set<int> s;
-    std::cout<<n<<"\n";
-    for(int i=1;i<=n;i++){
-        int tmp;
-        std::cin>>tmp;
-        if(s.find(tmp)==s.end()){
-            throw std::runtime_error(std::to_string(tmp));
-        }
-        s.insert(tmp);
-    }
+    
 }