## GCD Property for competitive programming -

properties of modulo or modulo property play important role in competitive programming. Some of the Problems of competitive programming is directly asked based on properties of modulo or modulo property. So here are some most important Modulo Properties That you should know.

What is modulo operation:
The remainder obtained after the division operation on two operands is known as modulo operation. Operator for doing modulus operation is ‘%’. For ex: a % b = c which means, when a is divided by b it gives the remainder c, 7%2 = 1, 17%3 = 2.

### Important properties of modulo-

1. ( a + b) % c = ( ( a % c ) + ( b % c ) ) % c
2. ( a * b) % c = ( ( a % c ) * ( b % c ) ) % c
3. ( a – b) % c = ( ( a % c ) – ( b % c ) ) % c
4. ( a / b ) % c = ( ( a % c ) / ( b % c ) ) % c
Basic Euclidean Algorithm for GCD-
• If we subtract smaller number from larger (we reduce larger number), GCD doesn’t change. So if we keep subtracting repeatedly the larger of two, we end up with GCD.
• Now instead of subtraction, if we divide a smaller number, the algorithm stops when we find remainder 0.
GCD calculation is a recursive approach and modulo expression also used while calculating GCD of two numbers.

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

What is the concept of taking modulo by 1000000007?
This is done to avoid calculations involving very large numbers.
If you take mod after the final (actual) answer it would defeat the very purpose of using the mod operator in the question.

Code discussion It's a community where you people helps each other.

### codeforces rating system | Codeforces rating Newbie to Legendary Grandmaster

Codeforces rating system | Codeforces rating Newbie to Legendary Grandmaster- Codeforces is one of the most popular platforms for competitive programmers and  codeforces rating matters a lot  .  Competitive Programming  teaches you to find the easiest solution in the quickest possible way. CP enhances your problem-solving and debugging skills giving you real-time fun. It's brain-sport. As you start solving harder and harder problems in live-contests your analytical and rational thinking intensifies. To have a good codeforces profile makes a good impression on the interviewer. If you have a good  codeforces profile so it is very easy to get a referral for product base company like amazon, google , facebook etc.So in this blog I have explained everything about codeforces rating system. What are different titles on codeforces- based on rating codeforces divide rating into 10 part. Newbie Pupil Specialist Expert Candidate Codemaster Master International Master Grandmaster Internat

### Apple Division CSES Problem Set Solution | CSES Problem Set Solution Apple division with code

Apple Division CSES Problem Set Solution | CSES Problem Set Solution Apple division with code - Apple Division CSES Problem Solution Easy Explanation. Apple division is problem is taken form cses introductory problem set.Let's Read Problem statement first. Problem Statement- Time limit:  1.00 s   Memory limit:  512 MB There are  n n  apples with known weights. Your task is to divide the apples into two groups so that the difference between the weights of the groups is minimal. Input The first input line has an integer  n n : the number of apples. The next line has  n n  integers  p 1 , p 2 , … , p n p 1 , p 2 , … , p n : the weight of each apple. Output Print one integer: the minimum difference between the weights of the groups. Constraints 1 ≤ n ≤ 20 1 ≤ n ≤ 20 1 ≤ p i ≤ 10 9 1 ≤ p i ≤ 10 9 Example Input: 5 3 2 7 4 1 Output: 1 Explanation: Group 1 has weights 2, 3 and 4 (total weight 9), and group 2 has weights 1 and 7 (total weight 8). Join Telegram channel for code discussi

### Movie Festival CSES problem set solution

Movie Festival CSES problem set solution - Problem statement-  Time limit:  1.00 s   Memory limit:  512 MB In a movie festival  n n  movies will be shown. You know the starting and ending time of each movie. What is the maximum number of movies you can watch entirely? Input The first input line has an integer  n n : the number of movies. After this, there are  n n  lines that describe the movies. Each line has two integers  a a  and  b b : the starting and ending times of a movie. Output Print one integer: the maximum number of movies. Constraints 1 ≤ n ≤ 2 ⋅ 10 5 1 ≤ n ≤ 2 ⋅ 10 5 1 ≤ a < b ≤ 10 9 1 ≤ a < b ≤ 10 9 Example Input: 3 3 5 4 9 5 8 Output: 2 Solution - Step -1 take input in a vector as a pair first element is ending time ans second element is starting time Step -2 sort the vector in increasing order because we will watch that movie which is ending first. Step -3 iterate over vector and calculate ans .           follow code below-