Tips & Tweaks when programming Math !

In this post,I am going to tell you some tips and tricks which you should know & you can implement in your codes if required.You dont need to require long codes for short tasks.

To check if a number is power of 2,just calculate log2(n) and if it is an integer,it is a power of 2 else it is not.

Number of digits in a number is ceil[log(n)]. This formula is used to calculate the number of digits in n!.

nCr denotes the number of ways of choosing ‘r’ objects from ‘n’ objects.
nCr=(n-1)C(r) + (n-1)C(r-1)

To find the gcd/hcf of two numbers,you should use Euclid’s algorithm.
Program in C —

gcd(int a,int b)
{
if(b==0) return a;
else gcd(b,a%b);
}

LCM of two numbers= (a*b)/gcd(a,b)

To find the number which occurs odd number of times in a list given that all other numbers appear even number of times-
XOR all the numbers and the result gives you the element which occurs odd number of times.

To check if the nth bit of a number is on/off.AND the number with 2 to the power i.If the result is 0,then it is OFF.

To find the nth Fibonacci number-

fib(n)
{
if(n==0) return 0;
if(n==1) return 1;
return f(n-1)+f(n-2);
}

Given a list of numbers from 1 to n and a number is missing,you have to find the missing number.
Method 1-
Find the sum of all given numbers and subtract it from n*(n+1)/2,you get the unknown number.
Method 2-
XOR all the numbers from 1 to n.Let the result be A1.
XOR all the given numbers.Let the result be A2.
XOR A1 and A2.The result gives the unknown number.

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