Geo Template Added

Cheat Sheet/Game Theory/Nim.md

@@ -0,0 +1,11 @@
+# Nim
+
+## Optimal Strategy
+
+> “If both A and B play optimally (i.e- they don’t make any mistakes), then the player starting first is guaranteed to win if the Nim-Sum at the beginning of the game is non-zero. Otherwise, if the Nim-Sum evaluates to zero, then player A will lose definitely.”
+
+### Reasoning 
+Couple of deductions about bitwise XOR necessary for understanding the Optimal Strategy :
+- If the XOR sum of ‘n’ numbers is already zero then there is no possibility to make the XOR sum zero by single reduction of a number. 
+- If the XOR sum of ‘n’ numbers is non-zero then there is at least a single approach by which if you reduce a number, the XOR sum is zero.
+

Miscellaneous/Problems/Popular/00 Correct Bracket Sequence.cpp → Data Structure/test.cpp

@@ -10,9 +10,10 @@ using namespace std;
 #define MP make_pair
 #define F first
 #define S second
+#define INF INT_MAX
 
 #define ALL(x) (x).begin(), (x).end()
-#define DBG(x) cout << __LINE__ << " says: " << #x << " = " << (x) << endl
+#define DBG(x) cerr << __LINE__ << " says: " << #x << " = " << (x) << endl
 #define READ        freopen("alu.txt", "r", stdin)
 #define WRITE       freopen("vorta.txt", "w", stdout)
 
@@ -62,38 +63,24 @@ string to_str(T x)
 //
 //}
 
-bool isCorrectBracket(string s)
-{
-    vector<char>v;
-
-    for(int i=0;i<(int)s.size();i++)
-    {
-        if(s[i]=='(') v.push_back(s[i]);
-
-        if(v.empty()) return false;
-
-        if(s[i]==')') v.pop_back();
-
-//        cout<<v<<endl;
-    }
-
-    return v.empty();
-}
-
 int main()
 {
+    //freopen("out.txt","w",stdout);
+
     optimizeIO();
 
-    int tc;
-    cin>>tc;
+    multiset<int> a {1, 1 ,3, 7, 10, 10 , 13, 20 , 20 , 20};
+	multiset<int> b {2, 3, 5, 7, 7, 11, 11, 11, 13, 15, 19};
 
-    while(tc--)
-    {
-        string s;
-        cin>>s;
+	vector<int> v;
+	merge(a.begin(), a.end(), b.begin(), b.end(), back_inserter(v));
 
-        cout<<isCorrectBracket(s)<<endl;
-    }
+	multiset<int> m(v.begin(), v.end());
+
+	for(const auto &element : m) {
+		cout << element << " ";
+	}
+	cout << endl;
 
     return 0;
 }
@@ -133,3 +120,4 @@ ostream &operator <<(ostream &os, set<T>&v)
 }
 
 
+

Miscellaneous/Problems/String/06 Make Palindrome adding minimum characters [KMP].cpp → Data Structure/test2.cpp

@@ -1,24 +1,25 @@
 
 /**
 
-KMP
+NOT KNOWING THIS MULTISET VARIENT OF PBDS COST A PROBLEM IN ICPC PRELI 2019 :)
 
-Idea :
+Policy Based Data Structure (MULTI SET)
+===========================
 
-Let , s  = acbabab
-and   rs = bababca (reverse of string s)
+SEE PBDS SET FOR AVAILABLE FUNCTIONS
 
-How can we make Palindrome of shortest length ?
+Implementation 2 : using "pair<,>" in declaration
+--------------------------------------------------
 
- acbabab
- --bababca
+This uses a dummy second variable to use this PBDS as a multiset.
+Works fine with almost all the functions .
 
-So ,  We need to know the Longest Prefix of rs in s .
-We can do that using Prefix Function , KMP .
 
 **/
 
-/** Which of the favors of your Lord will you deny ? **/
+/**Which of the favors of your Lord will you deny ?**/
+
+//#undef _GLIBCXX_DEBUG
 
 #include<bits/stdc++.h>
 using namespace std;
@@ -29,17 +30,21 @@ using namespace std;
 #define MP make_pair
 #define F first
 #define S second
+#define INF INT_MAX
 
 #define ALL(x) (x).begin(), (x).end()
-#define DBG(x) cout << __LINE__ << " says: " << #x << " = " << (x) << endl
+#define DBG(x) cerr << __LINE__ << " says: " << #x << " = " << (x) << endl
 #define READ        freopen("alu.txt", "r", stdin)
 #define WRITE       freopen("vorta.txt", "w", stdout)
 
 #include <ext/pb_ds/assoc_container.hpp>
 #include <ext/pb_ds/tree_policy.hpp>
 using namespace __gnu_pbds;
 
-template<class TIn>using indexed_set = tree<TIn, null_type, less<TIn>,rb_tree_tag, tree_order_statistics_node_update>;
+template<class TIn>
+using indexed_multiset = tree<
+                    pair<TIn,TIn>, null_type, less< pair<TIn,TIn> >,
+                    rb_tree_tag, tree_order_statistics_node_update>;
 
 /**
 
@@ -59,13 +64,14 @@ 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;
+const int nmax = 1e6+7;
 const LL LINF = 1e17;
 
 template <class T>
@@ -76,64 +82,69 @@ string to_str(T x)
     return ss.str();
 }
 
-//bool cmp(const PII &A,const PII &B)
-//{
-//
-//}
-
-vector<int> prefix_function(string s) {
-    int n = (int)s.length();
-    vector<int> pi(n);
-    for (int i = 1; i < n; i++) {
-        int j = pi[i-1];
-        while (j > 0 && s[i] != s[j])
-            j = pi[j-1];
-        if (s[i] == s[j])
-            j++;
-        pi[i] = j;
-    }
-    return pi;
-}
+indexed_multiset<int> MS;
+indexed_multiset<int> MS2;
 
-int minimumPalindromeLength(string s)
+template <class T>
+void erase_all_occurrence(T val) /** O(n) **/
 {
-    int sz = s.size();
-    string rs = s;
-    reverse(ALL(rs));
-
-    vector<int>pi = prefix_function(rs+"#"+s);
-    int psz = pi.size();
+    while((*MS.lower_bound({val,0})).F==val)
+        MS.erase(MS.lower_bound({val,0}));
+}
 
-    int maximum_match = pi[psz-1];
+template <class T>
+void erase_one_occurrence(T val) /** O(logN) **/
+{
+    MS.erase(MS.lower_bound({val,0}));
+}
 
-    int ans = sz + (sz-maximum_match);
-    return ans;
+void printMS()
+{
+    for(auto x:MS)
+        cout<<x<<" ";
+    cout<<endl;
 }
 
 int main()
 {
     optimizeIO();
 
-    int tc;
-    cin>>tc;
+    MS.clear();
 
-    for(int qq=1;qq<=tc;qq++)
+    int n;
+    cin>>n;
+
+    for(int i=1;i<=n;i++)
     {
-        string s;
-        cin>>s;
+        int x;
+        cin>>x;
 
-        int ans = minimumPalindromeLength(s);
+        MS.insert({x,i}); /** insert **/
+        MS2.insert({x,i}); /** insert **/
+    }
+
+    printMS();
+
+    vector<int> v;
+	merge(MS.begin(), MS.end(), MS2.begin(), MS2.end(), back_inserter(v));
+
+	multiset<int> m(v.begin(), v.end());
+
+	for(const auto &element : m) {
+		cout << element << " ";
+	}
+	cout << endl;
 
-        cout<<"Case "<<qq<<": ";
-        cout<<ans<<endl;
 
-    }
 
-    return 0;
 }
 
+
 /**
 
+8
+30 10 20 10 40 30 20 20
+
 **/
 
 template<class T1, class T2>
@@ -165,5 +176,3 @@ ostream &operator <<(ostream &os, set<T>&v)
     os<<" ]";
     return os;
 }
-
-