From 2697a4567e78b372ea1615990acd02901c1fd1fc Mon Sep 17 00:00:00 2001
From: Adarsh <46349391+4d4r5h@users.noreply.github.com>
Date: Mon, 10 Oct 2022 20:51:57 +0530
Subject: [PATCH] Create Finding a Centroid.cpp

---
 cses/Finding a Centroid.cpp | 85 +++++++++++++++++++++++++++++++++++++
 1 file changed, 85 insertions(+)
 create mode 100644 cses/Finding a Centroid.cpp

diff --git a/cses/Finding a Centroid.cpp b/cses/Finding a Centroid.cpp
new file mode 100644
index 0000000..ce29adf
--- /dev/null
+++ b/cses/Finding a Centroid.cpp	
@@ -0,0 +1,85 @@
+// Centroid of a tree is a node such that when it is appointed the root of the tree, each subtree has at most floor(n/2) nodes (n = number of nodes in the graph).
+// A vertex is a centroid of a tree only when you cut this vertex (remove it and remove all edges from this vertex),
+// the size of the largest connected component of the remaining graph is the smallest possible (which is at most floor(n/2))
+// A tree may have one centroid or may have two centroids. If it has two centroids, they are always connected.
+
+#include <bits/stdc++.h>
+#define pb(x) push_back(x)
+#define all(x) (x).begin(), (x).end()
+#define rall(x) (x).rbegin(), (x).rend()
+#define F(w,x,y) for(ll w=x; w<y; w++)
+#define endl "\n"
+#define mod 1000000007
+typedef long long ll;
+typedef long double ld;
+using namespace std;
+ 
+ll n;
+vector <ll> adj[200001];
+ll subtreeSize[200001];
+int vis[200001];
+ 
+void dfs(ll node)
+{
+    subtreeSize[node]=1;
+ 
+    for(auto x:adj[node])
+    {
+        if(subtreeSize[x]==-1)
+        {
+            dfs(x);
+            subtreeSize[node]+=subtreeSize[x];
+        }
+    }
+}
+ 
+ll centroid(ll node)
+{
+    vis[node]=1;
+ 
+    for(auto x:adj[node])
+    {
+        if(!vis[x])
+        {
+            if(subtreeSize[x]>(n/2))
+                return centroid(x);
+        }
+    }
+ 
+    return node;
+}
+ 
+void play()
+{
+    memset(subtreeSize,-1,sizeof(subtreeSize));
+    ll a,b;
+    cin>>n;
+    F(i,1,n)
+    {
+        cin>>a>>b;
+        adj[a].pb(b);
+        adj[b].pb(a);
+    }
+ 
+    dfs(1);
+ 
+    cout<<centroid(1);
+}
+ 
+int main()
+{
+    //freopen("milkvisits.in","r",stdin);
+    //freopen("milkvisits.out","w",stdout);
+    ios_base::sync_with_stdio(false);
+    cin.tie(NULL);
+    //pre();
+    ll t;
+    t=1;
+    //cin>>t;
+    F(i,1,t+1)
+    {
+        //cout<<"Case #"<<i<<": ";
+        play();
+    }
+    return 0;
+}