feat: 添加P1967.cpp实现最小生成树算法

实现基于优先队列和并查集的最小生成树算法，用于解决图论中的连通问题。包含边的结构定义、合并操作和结果输出功能。

src/9/2/P1967.cpp

@@ -0,0 +1,78 @@
+#include <cstdint>
+#include <cstdio>
+#include <cstring>
+#include <ios>
+#include <iostream>
+#include <queue>
+#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;
+    }
+};
+
+ll n,m;
+std::vector<std::vector<Edge>> edg;
+std::vector<ll> unf;
+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);
+}
+
+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);
+
+    for(ll i=1;i<=n;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]){
+            char buff[128];
+            memset(buff, 0, sizeof(buff));
+            sprintf(buff,"point %lld to %lld weight %lld\n",u,v,w);
+            std::cout<<buff;
+        }
+    }
+}