From ca1e614f103847f9d54e20635172d21e3352213c Mon Sep 17 00:00:00 2001
From: Aditya Kulkarni <kulkarniaaditya2002@gmail.com>
Date: Thu, 5 Oct 2023 01:40:11 +0530
Subject: [PATCH 1/3] lca added

---
 c++/lca.cpp | 61 +++++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 61 insertions(+)
 create mode 100644 c++/lca.cpp

diff --git a/c++/lca.cpp b/c++/lca.cpp
new file mode 100644
index 0000000..c402bc2
--- /dev/null
+++ b/c++/lca.cpp
@@ -0,0 +1,61 @@
+vector<vector<ll>> g(N), up(N, vector<ll> (100, -1));
+vector<ll> lvl(N);
+
+void dfs(ll node, ll par, ll level){
+	lvl[node] = level;
+
+	for(auto it: g[node]){
+		if(it != par){
+			dfs(it, node, level + 1);
+		}
+	}
+}
+
+
+void binary_lift(ll src, ll par){
+	up[src][0] = par;
+	for(ll i = 1; i < 20; i++){
+		if(up[src][i-1] != -1){
+			up[src][i] = up[up[src][i-1]][i-1];
+		}
+		else up[src][i] = -1;
+	}
+
+	for(auto it: g[src]){
+		if(it != par){
+			binary_lift(it, src);
+		}
+	}
+}
+
+ll lift_node(ll node, ll jump_req){
+
+	for(ll i = 19; i>=0; i--){
+		if(node == -1 or jump_req == 0){
+			break;
+		}
+		if(jump_req >= (1<<i)){
+			jump_req -= (1<<i);
+			node = up[node][i];
+		}
+	}
+	return node;
+}
+
+ll LCA(ll u, ll v){
+	if(lvl[u] < lvl[v]){
+		swap(u,v);
+	}
+
+    // u and v are now at the same level
+	u = lift_node(u, lvl[u] - lvl[v]);
+
+	if(u == v) return u;
+
+	for(ll i = 19; i >=0; i--){
+		if(up[u][i] != up[v][i]){
+			u = up[u][i]; v = up[v][i];
+		}
+	}
+	return lift_node(u,1);
+}
\ No newline at end of file

From 7fbaec6a67737242cf89132f1bd2c02a2bb4ceaa Mon Sep 17 00:00:00 2001
From: Aditya <kulkarniaaditya2002@gmail.com>
Date: Thu, 5 Oct 2023 14:36:42 +0530
Subject: [PATCH 2/3] Added Segment Tree Library

---
 c++/segment_tree.cpp | 116 +++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 116 insertions(+)
 create mode 100644 c++/segment_tree.cpp

diff --git a/c++/segment_tree.cpp b/c++/segment_tree.cpp
new file mode 100644
index 0000000..eb6a3a3
--- /dev/null
+++ b/c++/segment_tree.cpp
@@ -0,0 +1,116 @@
+#include<bits/stdc++.h>                                        //  ॐ           
+#include<ext/pb_ds/tree_policy.hpp>                            // Har Har Mahadev                                                    
+#include<ext/pb_ds/assoc_container.hpp>
+                                                                                                                
+using namespace std;
+using namespace __gnu_pbds;
+
+template <typename T>
+using ordered_set = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
+
+
+#define rep(i, zz, n) for (int i = zz; i < (n); ++i)
+#define all(x) x.begin(), x.end()
+#define pb push_back
+#define F first
+#define S second
+#define ll long long
+#define ld long double
+#define pll pair<ll, ll>
+#define PI 3.14159265358979323846
+#define el '\n'
+#define sp " "
+#define vl vector<ll>
+#define dbg(x) cout << #x << ": " << x << " ";
+
+const ll mod = 1e9 + 7;
+const ll inf = 1e18;
+const ll N = 1e6 + 5;
+
+#define     debug(x)    cout << #x << " "; _print(x); cout << '\n';
+#define     _debug(a,b) cout << #a << " [ "; array_debug(a,b); cout << "]\n";
+template <class T, class V> void array_debug(T *a, V n){ rep(i,0,n) cout << a[i] << ' ';}
+template <class T>          void _print(T t) {cout << t;}
+template <class T, class V> void _print(pair <T, V> p) {cout << "{"; _print(p.ff); cout << ","; _print(p.ss); cout << "}";}
+template <class T>          void _print(vector <T> v) {cout << "[ "; for (T i : v) {_print(i); cout << " ";} cout << "]";}
+template <class T>          void _print(set <T> v) {cout << "[ "; for (T i : v) {_print(i); cout << " ";} cout << "]";}
+template <class T>          void _print(multiset <T> v) {cout << "[ "; for (T i : v) {_print(i); cout << " ";} cout << "]";}
+template <class T, class V> void _print(map <T, V> v) {cout << "[ "; for (auto i : v) {_print(i); cout << " ";} cout << "]";}
+
+//greedy/brute force/DP/Graph/binary search/?
+
+template<typename T>
+struct SegmentTree{
+     vector<T> st;
+     void assign(vector<int> &v1) {
+          int n = (v1.size());
+          st = vector<T>(4 * n + 1);
+          build(v1, 1, 0, n - 1);
+     }
+     T combine(T x, T y) {
+          // T z;
+          // return z;
+          return { x.sum + y.sum }; // check which opeartion is to be performed
+     }
+     void build(vector<int>& v1, int v, int tl, int tr) {
+          if (tl == tr) {
+               st[v].sum = v1[tl]; //  check
+          }
+          else{
+               int mid = (tl + tr) / 2;
+               build(v1, 2 * v, tl, mid);
+               build(v1, 2 * v + 1, mid + 1, tr);
+               st[v] = combine(st[2 * v], st[2 * v + 1]);
+          }
+     }
+     // tl, tr   : the current segment/range whose node/vertex is v
+     //  l,  r   : the segment/range on which the 'range query' is to be performed
+     T query(int v, int tl, int tr, int l, int r) {
+          if (tr < l || r < tl) {
+               return { 0 }; // check which opeartion is to be performed
+          }
+          else if (tl == l && tr == r) {
+               return st[v];
+          }
+          int mid = (tl + tr) / 2;
+          return combine(query(2 * v, tl, mid, l, min(r, mid)), query(2 * v + 1, mid + 1, tr, max(l, mid + 1), r));
+     }
+     void update_one(int v, int tl, int tr, int pos, int newVal) {
+          if (tl == tr) {
+               st[v].sum = newVal;
+               // check whether the newVal is added or updated
+               return;
+          }
+          int mid = (tl + tr) / 2;
+          if (pos <= mid) {
+               update_one(2 * v, tl, mid, pos, newVal);
+          }
+          else{
+               update_one(2 * v + 1, mid + 1, tr, pos, newVal);
+          }
+          st[v] = combine(st[2 * v], st[2 * v + 1]);
+     }
+};
+struct Node{
+     int sum;
+};
+SegmentTree<Node> seg;
+
+
+void __roOTs(){          
+               // main code here
+
+}
+signed main(){
+    ios::sync_with_stdio(false);
+    cin.tie(0);
+    cout.tie(0);
+
+    int tt = 1; cin >> tt;
+    for (int i = 1; i <= tt; i++){
+        // cout << "Case #" << i << ": ";
+        __roOTs(); cout << '\n';
+        
+    }
+    return 0;
+}
\ No newline at end of file

From 0a3e1175cb3349aafae1268df96a26a22cbc7a21 Mon Sep 17 00:00:00 2001
From: Aditya <kulkarniaaditya2002@gmail.com>
Date: Thu, 12 Oct 2023 16:35:52 +0530
Subject: [PATCH 3/3] Added Centroid Decomposition Library

---
 c++/centroid_decomposition.cpp | 105 +++++++++++++++++++++++++++++
 c++/lca.cpp                    |  61 -----------------
 c++/segment_tree.cpp           | 116 ---------------------------------
 3 files changed, 105 insertions(+), 177 deletions(-)
 create mode 100644 c++/centroid_decomposition.cpp
 delete mode 100644 c++/lca.cpp
 delete mode 100644 c++/segment_tree.cpp

diff --git a/c++/centroid_decomposition.cpp b/c++/centroid_decomposition.cpp
new file mode 100644
index 0000000..074d3a8
--- /dev/null
+++ b/c++/centroid_decomposition.cpp
@@ -0,0 +1,105 @@
+#include <bits/stdc++.h>
+using namespace std;
+
+#include <ext/pb_ds/assoc_container.hpp>
+#include <ext/pb_ds/tree_policy.hpp>
+using namespace __gnu_pbds;
+template <typename T> using ordered_set = tree<T, null_type,less<T>, rb_tree_tag,tree_order_statistics_node_update>;
+// orderded_set ->  find_by_order(x)<itr, x being 0-indexed>; order_of_key(x)<count, strictly less>
+
+typedef long long       ll;
+typedef long double     lld;
+typedef pair<int, int>  pii;
+typedef pair<ll, ll>    pll;
+#define loop(n)         for(ll i = 0; i < (n); ++i)
+#define rep(i,zz,n)     for(ll i = zz; i < (n); ++i)
+#define repi(i,zz,n)    for(ll i = zz; i >= (n); --i)
+#define all(v)          v.begin(),v.end()
+#define pb              push_back
+#define ff              first
+#define ss              second
+#define sz(x)           (int)x.size()
+#define nline           cout << '\n'
+
+#define     debug(x)    cout << #x << " "; _print(x); cout << '\n';
+#define     _debug(a,b) cout << #a << " [ "; array_debug(a,b); cout << "]\n";
+template <class T, class V> void array_debug(T *a, V n){ rep(i,0,n) cout << a[i] << ' ';}
+template <class T>          void _print(T t) {cout << t;}
+template <class T, class V> void _print(pair <T, V> p) {cout << "{"; _print(p.ff); cout << ","; _print(p.ss); cout << "}";}
+template <class T>          void _print(vector <T> v) {cout << "[ "; for (T i : v) {_print(i); cout << " ";} cout << "]";}
+template <class T>          void _print(set <T> v) {cout << "[ "; for (T i : v) {_print(i); cout << " ";} cout << "]";}
+template <class T>          void _print(multiset <T> v) {cout << "[ "; for (T i : v) {_print(i); cout << " ";} cout << "]";}
+template <class T, class V> void _print(map <T, V> v) {cout << "[ "; for (auto i : v) {_print(i); cout << " ";} cout << "]";}
+
+const lld eps = 1e-9;
+const int mod = 1e9 + 7;
+const ll inf = 1e18;
+const int N1 = 2e5 + 10;
+
+// vector<vector<int>> adj;
+
+template<typename T>
+struct CentroidDecomposition {
+	vector<int> subtr, par_cd;
+	vector<bool> del;
+
+	void assign(int n) {
+		subtr = vector<int>(n);
+		par_cd = vector<int>(n);
+		del = vector<bool>(n);
+
+		decompose_cd(0, 0);
+	}
+
+	int get_subtree_size(int i, int j) {
+		subtr[i] = 1;
+		for (int x : adj[i]) {
+			if (x == j || del[x])  continue;
+			subtr[i] += get_subtree_size(x, i);
+		}
+		return subtr[i];
+	}
+
+	int find_centroid(int i, int j, int n) {
+		for (int x : adj[i]) {
+			if (x != j && !del[x] && subtr[x] * 2 > n) {
+				return find_centroid(x, i, n); 
+			}
+		}
+		return i;
+	}
+
+	void decompose_cd(int i, int j) {
+		int n = get_subtree_size(i, j);
+		int ct = find_centroid(i, j, n);
+		par_cd[ct] = j;     //  parent of centrid-node in centroid-tree
+
+		del[ct] = 1;
+		for (int x : adj[ct]) {
+			if (del[x])  continue;
+			decompose_cd(x, ct);
+		}
+	}
+};
+CentroidDecomposition<int> cd;
+
+int code() {
+
+	// enter main code
+
+	return 0;
+}
+
+int main() {
+	ios::sync_with_stdio(0); cin.tie(0);
+	// freopen("input.txt","r",stdin);
+	// freopen("output.txt","w",stdout);
+
+	int tc = 1;
+	cin >> tc;
+
+	loop(tc)  code();
+	// rep(i, 1, tc + 1)  cout << "Case #" << i << ": ", code();
+
+	return 0;
+}
\ No newline at end of file
diff --git a/c++/lca.cpp b/c++/lca.cpp
deleted file mode 100644
index c402bc2..0000000
--- a/c++/lca.cpp
+++ /dev/null
@@ -1,61 +0,0 @@
-vector<vector<ll>> g(N), up(N, vector<ll> (100, -1));
-vector<ll> lvl(N);
-
-void dfs(ll node, ll par, ll level){
-	lvl[node] = level;
-
-	for(auto it: g[node]){
-		if(it != par){
-			dfs(it, node, level + 1);
-		}
-	}
-}
-
-
-void binary_lift(ll src, ll par){
-	up[src][0] = par;
-	for(ll i = 1; i < 20; i++){
-		if(up[src][i-1] != -1){
-			up[src][i] = up[up[src][i-1]][i-1];
-		}
-		else up[src][i] = -1;
-	}
-
-	for(auto it: g[src]){
-		if(it != par){
-			binary_lift(it, src);
-		}
-	}
-}
-
-ll lift_node(ll node, ll jump_req){
-
-	for(ll i = 19; i>=0; i--){
-		if(node == -1 or jump_req == 0){
-			break;
-		}
-		if(jump_req >= (1<<i)){
-			jump_req -= (1<<i);
-			node = up[node][i];
-		}
-	}
-	return node;
-}
-
-ll LCA(ll u, ll v){
-	if(lvl[u] < lvl[v]){
-		swap(u,v);
-	}
-
-    // u and v are now at the same level
-	u = lift_node(u, lvl[u] - lvl[v]);
-
-	if(u == v) return u;
-
-	for(ll i = 19; i >=0; i--){
-		if(up[u][i] != up[v][i]){
-			u = up[u][i]; v = up[v][i];
-		}
-	}
-	return lift_node(u,1);
-}
\ No newline at end of file
diff --git a/c++/segment_tree.cpp b/c++/segment_tree.cpp
deleted file mode 100644
index eb6a3a3..0000000
--- a/c++/segment_tree.cpp
+++ /dev/null
@@ -1,116 +0,0 @@
-#include<bits/stdc++.h>                                        //  ॐ           
-#include<ext/pb_ds/tree_policy.hpp>                            // Har Har Mahadev                                                    
-#include<ext/pb_ds/assoc_container.hpp>
-                                                                                                                
-using namespace std;
-using namespace __gnu_pbds;
-
-template <typename T>
-using ordered_set = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
-
-
-#define rep(i, zz, n) for (int i = zz; i < (n); ++i)
-#define all(x) x.begin(), x.end()
-#define pb push_back
-#define F first
-#define S second
-#define ll long long
-#define ld long double
-#define pll pair<ll, ll>
-#define PI 3.14159265358979323846
-#define el '\n'
-#define sp " "
-#define vl vector<ll>
-#define dbg(x) cout << #x << ": " << x << " ";
-
-const ll mod = 1e9 + 7;
-const ll inf = 1e18;
-const ll N = 1e6 + 5;
-
-#define     debug(x)    cout << #x << " "; _print(x); cout << '\n';
-#define     _debug(a,b) cout << #a << " [ "; array_debug(a,b); cout << "]\n";
-template <class T, class V> void array_debug(T *a, V n){ rep(i,0,n) cout << a[i] << ' ';}
-template <class T>          void _print(T t) {cout << t;}
-template <class T, class V> void _print(pair <T, V> p) {cout << "{"; _print(p.ff); cout << ","; _print(p.ss); cout << "}";}
-template <class T>          void _print(vector <T> v) {cout << "[ "; for (T i : v) {_print(i); cout << " ";} cout << "]";}
-template <class T>          void _print(set <T> v) {cout << "[ "; for (T i : v) {_print(i); cout << " ";} cout << "]";}
-template <class T>          void _print(multiset <T> v) {cout << "[ "; for (T i : v) {_print(i); cout << " ";} cout << "]";}
-template <class T, class V> void _print(map <T, V> v) {cout << "[ "; for (auto i : v) {_print(i); cout << " ";} cout << "]";}
-
-//greedy/brute force/DP/Graph/binary search/?
-
-template<typename T>
-struct SegmentTree{
-     vector<T> st;
-     void assign(vector<int> &v1) {
-          int n = (v1.size());
-          st = vector<T>(4 * n + 1);
-          build(v1, 1, 0, n - 1);
-     }
-     T combine(T x, T y) {
-          // T z;
-          // return z;
-          return { x.sum + y.sum }; // check which opeartion is to be performed
-     }
-     void build(vector<int>& v1, int v, int tl, int tr) {
-          if (tl == tr) {
-               st[v].sum = v1[tl]; //  check
-          }
-          else{
-               int mid = (tl + tr) / 2;
-               build(v1, 2 * v, tl, mid);
-               build(v1, 2 * v + 1, mid + 1, tr);
-               st[v] = combine(st[2 * v], st[2 * v + 1]);
-          }
-     }
-     // tl, tr   : the current segment/range whose node/vertex is v
-     //  l,  r   : the segment/range on which the 'range query' is to be performed
-     T query(int v, int tl, int tr, int l, int r) {
-          if (tr < l || r < tl) {
-               return { 0 }; // check which opeartion is to be performed
-          }
-          else if (tl == l && tr == r) {
-               return st[v];
-          }
-          int mid = (tl + tr) / 2;
-          return combine(query(2 * v, tl, mid, l, min(r, mid)), query(2 * v + 1, mid + 1, tr, max(l, mid + 1), r));
-     }
-     void update_one(int v, int tl, int tr, int pos, int newVal) {
-          if (tl == tr) {
-               st[v].sum = newVal;
-               // check whether the newVal is added or updated
-               return;
-          }
-          int mid = (tl + tr) / 2;
-          if (pos <= mid) {
-               update_one(2 * v, tl, mid, pos, newVal);
-          }
-          else{
-               update_one(2 * v + 1, mid + 1, tr, pos, newVal);
-          }
-          st[v] = combine(st[2 * v], st[2 * v + 1]);
-     }
-};
-struct Node{
-     int sum;
-};
-SegmentTree<Node> seg;
-
-
-void __roOTs(){          
-               // main code here
-
-}
-signed main(){
-    ios::sync_with_stdio(false);
-    cin.tie(0);
-    cout.tie(0);
-
-    int tt = 1; cin >> tt;
-    for (int i = 1; i <= tt; i++){
-        // cout << "Case #" << i << ": ";
-        __roOTs(); cout << '\n';
-        
-    }
-    return 0;
-}
\ No newline at end of file