Euler Tour & MIsc

Author: zarif98sjs

Algorithm/48 Euler Tour.cpp

@@ -0,0 +1,174 @@
+
+/**
+
+Euler Circuit / Euler Cycle (Undirected graph)
+===========================
+All edges are traversed only once . Starting & Ending Point same.
+
+Condition : All vertices will have EVEN degree .
+
+Euler Path
+==========
+All edges are traversed only once . Starting & Ending Point different.
+
+Condition : All vertices except the 2 endpoints will have EVEN degree .
+
+
+
+Hierholzer's algorithm for finding Euler Circuit
+=================================================
+https://www.wikiwand.com/en/Eulerian_path#/Hierholzer.27s_algorithm
+
+How to modify the same algorithm to find Euler Path ?
+=> Add an edge between the 2 endpoints and find Euler Circuit
+
+**/
+
+/** Which of the favors of your Lord will you deny ? **/
+
+#include<bits/stdc++.h>
+using namespace std;
+
+#define LL long long
+#define PII pair<int,int>
+#define PLL pair<LL,LL>
+#define F first
+#define S second
+
+#define ALL(x) (x).begin(), (x).end()
+#define READ freopen("alu.txt", "r", stdin)
+#define WRITE freopen("vorta.txt", "w", stdout)
+
+#ifndef ONLINE_JUDGE
+#define DBG(x) cout << __LINE__ << " says: " << #x << " = " << (x) << endl
+#else
+#define DBG(x)
+#endif
+
+template<class T1, class T2>
+ostream &operator <<(ostream &os, pair<T1,T2>&p);
+template <class T>
+ostream &operator <<(ostream &os, vector<T>&v);
+template <class T>
+ostream &operator <<(ostream &os, set<T>&v);
+
+inline void optimizeIO()
+{
+ ios_base::sync_with_stdio(false);
+ cin.tie(NULL);
+}
+
+const int nmax = 2e5+7;
+
+vector<set<int>>adj;
+vector<int>deg;
+vector<int>tour;
+
+void eulerDFS(int u)
+{
+ while(!adj[u].empty())
+ {
+ int v = *adj[u].begin();
+
+ adj[u].erase(v);
+ adj[v].erase(u);
+
+ eulerDFS(v);
+ }
+
+ tour.push_back(u);
+}
+
+bool check(int n) /// check if Euler Circuit Exists
+{
+ for(int i=1;i<=n;i++)
+ if(deg[i]&1)
+ return false;
+
+ return true;
+}
+
+int main()
+{
+ optimizeIO();
+
+ int tc;
+ cin>>tc;
+
+ while(tc--)
+ {
+ int n,m;
+ cin>>n>>m;
+
+ adj = vector<set<int>>(n+1);
+ deg = vector<int>(n+1);
+ tour.clear();
+
+ while(m--)
+ {
+ int a , b;
+ cin>>a>>b;
+
+ adj[a].insert(b);
+ adj[b].insert(a);
+
+ deg[a]++;
+ deg[b]++;
+ }
+
+ if(check(n)==false) cout<<"Euler Circuit doesn't exist"<<endl;
+ else
+ {
+ eulerDFS(1);
+
+ reverse(ALL(tour));
+ cout<<"Euler Circuit : "<<tour<<endl;
+ }
+ }
+
+ return 0;
+}
+
+/**
+7 8
+1 4
+1 2
+2 3
+3 7
+3 5
+3 4
+5 6
+6 7
+**/
+
+template<class T1, class T2>
+ostream &operator <<(ostream &os, pair<T1,T2>&p)
+{
+ os<<"{"<<p.first<<", "<<p.second<<"} ";
+ return os;
+}
+template <class T>
+ostream &operator <<(ostream &os, vector<T>&v)
+{
+ os<<"[ ";
+ for(int i=0; i<v.size(); i++)
+ {
+ os<<v[i]<<" " ;
+ }
+ os<<" ]";
+ return os;
+}
+
+template <class T>
+ostream &operator <<(ostream &os, set<T>&v)
+{
+ os<<"[ ";
+ for(T i:v)
+ {
+ os<<i<<" ";
+ }
+ os<<" ]";
+ return os;
+}
+
+

Miscellaneous/04 Square Root Binary Search.cpp

@@ -0,0 +1,101 @@
+
+/** Which of the favors of your Lord will you deny ? **/
+
+#include<bits/stdc++.h>
+using namespace std;
+
+#define LL long long
+#define PII pair<int,int>
+#define PLL pair<LL,LL>
+#define F first
+#define S second
+
+#define ALL(x) (x).begin(), (x).end()
+#define READ freopen("alu.txt", "r", stdin)
+#define WRITE freopen("vorta.txt", "w", stdout)
+
+#ifndef ONLINE_JUDGE
+#define DBG(x) cout << __LINE__ << " says: " << #x << " = " << (x) << endl
+#else
+#define DBG(x)
+#endif
+
+template<class T1, class T2>
+ostream &operator <<(ostream &os, pair<T1,T2>&p);
+template <class T>
+ostream &operator <<(ostream &os, vector<T>&v);
+template <class T>
+ostream &operator <<(ostream &os, set<T>&v);
+
+inline void optimizeIO()
+{
+ ios_base::sync_with_stdio(false);
+ cin.tie(NULL);
+}
+
+const int nmax = 2e5+7;
+
+LL sqroot(LL x)
+{
+ LL l = 0, r = 1e9 + 1;
+ while (l < r - 1)
+ {
+ LL m = (l + r) / 2;
+ if (m * m > x)
+ r = m;
+ else
+ l = m;
+ }
+ return l;
+}
+
+int main()
+{
+ optimizeIO();
+
+ while(1)
+ {
+ LL x;
+ cin>>x;
+
+ cout<<sqroot(x)<<endl;
+ }
+
+ return 0;
+}
+
+/**
+
+**/
+
+template<class T1, class T2>
+ostream &operator <<(ostream &os, pair<T1,T2>&p)
+{
+ os<<"{"<<p.first<<", "<<p.second<<"} ";
+ return os;
+}
+template <class T>
+ostream &operator <<(ostream &os, vector<T>&v)
+{
+ os<<"[ ";
+ for(int i=0; i<v.size(); i++)
+ {
+ os<<v[i]<<" " ;
+ }
+ os<<" ]";
+ return os;
+}
+
+template <class T>
+ostream &operator <<(ostream &os, set<T>&v)
+{
+ os<<"[ ";
+ for(T i:v)
+ {
+ os<<i<<" ";
+ }
+ os<<" ]";
+ return os;
+}
+
+

Miscellaneous/05 Fast Integer Cube and Square Root.cpp

@@ -0,0 +1,65 @@
+
+/**
+
+Code : mochow13
+
+**/
+
+unsigned int fast_sqrt(unsigned int n){
+ unsigned int c, g;
+
+ c = g = 0x8000;
+ for (; ;){
+ if ((g * g) > n) g ^= c;
+ c >>= 1;
+ if (!c) return g;
+ g |= c;
+ }
+}
+
+int fast_cbrt(int n){
+ int x, r = 30, res = 0;
+
+ for (; r >= 0; r -= 3){
+ res <<= 1;
+ x = (3 * res * (res + 1)) + 1;
+ if ((n >> r) >= x){
+ res++;
+ n -= (x << r);
+ }
+ }
+
+ return res;
+}
+
+unsigned long long fast_sqrt(unsigned long long n){
+ unsigned long long c, g;
+
+ c = g = 0x80000000;
+ for (; ;){
+ if ((g * g) > n) g ^= c;
+ c >>= 1;
+ if (!c) return g;
+ g |= c;
+ }
+}
+
+unsigned long long fast_cbrt(unsigned long long n){
+ int r = 63;
+ unsigned long long x, res = 0;
+
+ for (; r >= 0; r -= 3){
+ res <<= 1;
+ x = (res * (res + 1) * 3) + 1;
+ if ((n >> r) >= x){
+ res++;
+ n -= (x << r);
+ }
+ }
+
+ return res;
+}
+
+int main(){
+
+}