efficient algorithms for general tasks with good time complexity.

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bitwise operator not {~} : (a = 10 => 1010 (Binary) => ~a = ~1010 = -(1010 + 1) = -(1011) = -11)

bitwise operator xor {^} : (n^n = 0), (n^0 = n)

bitwise operator rightshift {>>} : (100 >> 2 = 25)

bitwise operator leftshift {<<} : (100 << 2 = 400)

sum of first n numbers:O(1)

defsum_total(n):returnint(n*(n+1)/2)

LCM/GCD:(Euclid's algorithm)

defgcd(a,b):ifa==0:returnbreturngcd(b%a,a)deflcm(a,b):prod=a*bhcf=gcd(a,b)returnprod//hcf

Odd-Even:O(1)

ifn&1==1:print('odd')else:print('even')

Leftshift(multiply) / Rightshift(divide) by 2ⁿ:O(1)

defmultpow(x,y):returnx<<y# x*(2^y)defdivpow(x,y):returnx>>y# x/(2^y)

Check if a number is power of 2:O(1)

defispow(n):ifn<=0:returnFalsex=ny=not(n& (n-1))returnxandy

count 1's in binary representation:O(log(n))

defcntbits(n):cnt=0whilen:cnt+=1n=n& (n-1)returncnt

convert int to binary / binary to int:O(1)

definttobin(n):returnstr(bin(n))[2:]defbintoint(m):returnint(m,2)

check which number occurs once(or odd number of times/doesn't has it's unique identical element) in an array:O(n)

defcheckpair(arr):# n -> araytemp=arr[0]foriinrange(1,len(arr)):temp=temp^arr[i]returntemp