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23 changes: 18 additions & 5 deletions README.md
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https://math.stackexchange.com/questions/2956889/how-many-number-of-integer-coordinates-exists-between-a-line-segment-including

no of trees with n labeled vertices is n^(n-2) https://en.wikipedia.org/wiki/Cayley%27s_formula
Number of trees with n labeled vertices = n^(n-2) .
Link - (https://en.wikipedia.org/wiki/Cayley%27s_formula)


https://proofwiki.org/wiki/Sum_of_r%2Bk_Choose_k_up_to_n

Smallest Enclosing Circle https://codeforces.com/blog/entry/23554
Smallest Enclosing Circle. Link - ( https://codeforces.com/blog/entry/23554 )

a+b=a⊕b+2×(a and b)=(a or b)+(a and b)

Dilworth's theorem states that, in any finite partially ordered set, the largest antichain has the same size as the smallest chain decomposition
Dilworth's theorem states that, in any finite partially ordered set, the largest antichain has the same size as the smallest chain decomposition.

Set bits xor pairsum https://atcoder.jp/contests/abc091/submissions/11263481
Set bits xor pairsum . Link - ( https://atcoder.jp/contests/abc091/submissions/11263481 )


Policy Based data structure

OrderedSet

(Use as multiset)

#include <ext/pb_ds/assoc_container.hpp> // Common file
#include <ext/pb_ds/tree_policy.hpp> // Including tree_order_statistics_node_updat

#include <ext/pb_ds/tree_policy.hpp> // Including tree_order_statistics_node_update

using namespace __gnu_pbds;

typedef tree<ll, null_type, less_equal<ll>, rb_tree_tag, tree_order_statistics_node_update> ordered_set;

order_of_key -> find element less than x

find_order_by -> returns iterator to kth largest element counting from 0.

lower bound works as upper bound


Normal set

typedef tree<ll, null_type, less<ll>, rb_tree_tag, tree_order_statistics_node_update> ordered_set;

Fast Hash in cpp

const int RANDOM = chrono::high_resolution_clock::now().time_since_epoch().count();

struct chash { int operator()(int x) const { return x ^ RANDOM; }};

cc_hash_table<int, int, hash<int>> cnt;