Codeforces Ladder(For Beginners)

I've included 400 problems according to rating & solved count. All the problems are very effective to increase your cp knowledge. I've also included possible tags. So that, you can easily understand if the problem can be solved by you or you've study that theory.

Ladder link: https://docs.google.com/spreadsheets/d/1IIgvJyN2Bzu2bsGrJXdiosLOWGb5OzJRCPayRTdK7rw/edit?usp=sharing

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NT Part 6: Sieve of Eratosthenes(Details)

About 2300 years ago from today, famous Greek mathematician Euclid proved that there are an infinite number of prime numbers. Since then people have been searching for these prime numbers. In 1849, one of the greatest mathematician of all time, Carl Fredrick Gauss, had identified almost all of the prime numbers within the first 3 hundred thousand whole numbers. In the age of computers, we can find large prime numbers in the blink of an eye. But to do that, we need to know a bit of programming and a 2000 year old algorithm. By the end of this tutorial, you will be able to figure out a solution on your own to Gauss’s problem. What is a Prime Number? A prime number is an integer number that is divisible by 1 and the number itself only. For example, 7 is divisible by 1 and 7 only. But 6 is not a prime number because 6 is be divisible by 2 and 3 as well. It is worth mentioning that 1 itself is not a prime number. Now if you are asked to determine if a number is a prime number, you can...

Binary Search & The Kahini!

Suppose you are given an array of numbers and you need to find whether the number X is in the array. The straight forward approach to do that would be to run a loop and compare each number in the array with X. This is what the pseudo code would look like: function findNumber ( A , x ) for i = 0 to length of array A if A [ i ] == x return true return false For example, let’s assume you are given this array: [7, 14, 17, 21, 35, 60, 92, 121, 155] And, you were looking for the number 92. The loop would start checking each of the number in the array against 92 and would find after iterating through the array 7 times. The worst case time complexity of this approach would be O(n). However, whenever the array itself is in sorted order (like in this case where the numbers are increasing in value from left to right of the array), you can perform something that is much more efficient: binary search. The prerequisite of binary search is that the array should be sor...

NT Part 3: Playing with Modulars, and Euler Phi Function

Quick stuff first, fast exponentiation in logarithm time. Let us calculate in modular in . It uses binary expansion of , and is very very straightforward. ll exp ( ll x, ll n ) { if ( n == 0 ) return 1 ; if ( n == 1 ) return x ; if ( n % 2 == 0 ) return exp ( ( x * x ) % mod,n / 2 ) ; if ( n % 2 == 1 ) return ( x * exp ( ( x * x ) % mod,n / 2 ) ) % mod ; } Now, let us talk about modular inverses. By using Extended Euclidean Algorithm, we can get the inverse of modulo . #include <iostream> int inv ( int a, int m ) { int temp = m, q, t, u = 0 , v = 1 ; if ( m == 1 ) return 0 ; while ( a > 1 ) { q = a / m ; t = m ; m = a % m ; a = t ; t = u ; u = v - q * u ; v = t ; } if ( v < 0 ) v + = temp ; return v ; } int main ( void ) { int a, m ; std :: cin ...

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