Hello guys I'm trying to be good at number thery problem

Can anyone recommend some tutorials/problems for me

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Hello guys I'm trying to be good at number thery problem

Can anyone recommend some tutorials/problems for me

Hey Codeforces community! Today, let's dive deep into the fascinating world of Dynamic Programming (DP). Whether you're a beginner looking to grasp the basics or an experienced coder seeking advanced techniques, this guide aims to provide a comprehensive overview of DP concepts and applications.

**What is Dynamic Programming?**

Dynamic Programming is a powerful algorithmic technique used to solve problems by breaking them down into simpler subproblems and storing the solutions to these subproblems to avoid redundant calculations. It's particularly useful for optimization problems where we seek to maximize or minimize certain criteria.

**Basic Concepts**

- Memoization vs. Tabulation: Discuss the two main approaches to implementing DP — memoization (top-down) and tabulation (bottom-up) 2.State Definition: Explain what a "state" means in DP and how to define it based on the problem's constraints.
- Transition Function: Illustrate how to derive the transition function that relates the solution of a larger problem to its subproblems

**Types of Dynamic Programming Problems** 1. **Classic Examples:** - Fibonacci Sequence - Longest Common Subsequence - Knapsack Problem 2. **Optimization vs. Decision Problems:** Differentiate between problems that require optimization (maximizing/minimizing) versus those that are decision-based (yes/no).

**Advanced Techniques** 1. **Bitmask DP** Explore how bitmasking can be used to represent states efficiently, particularly in problems involving subsets or permutations.

**Optimal State Compression:**Discuss strategies for reducing state space to optimize memory usage.**Divide and Conquer Optimization**Introduce techniques like Convex Hull Trick and Li Chao Tree for optimizing DP solutions.

**Implementation Tips**

**Initialization**Explain how to set up initial conditions and base cases for DP arrays.**Iterative Bottom-Up Approach**Walk through the process of building the DP table iteratively.**Space Optimization**Show how to optimize space usage by only storing necessary information in the DP array.

**Challenges and Practice** 1. **Codeforces Problem Set:** Recommend specific DP problems from Codeforces for readers to practice and apply their knowledge.

**Competitive Programming Platforms:**

Highlight other platforms where DP problems can be found, such as AtCoder, LeetCode, and HackerRank.

**Conclusion** Dynamic Programming is a fundamental technique that every competitive programmer should master. By understanding its principles and applying them to diverse problem sets, you'll gain invaluable problem-solving skills that can be applied across various domains.

Keep coding, keep practicing, and enjoy the journey of unraveling the mysteries of Dynamic Programming!

**References** - Competitive Programmer's Handbook by Antti Laaksonen - ntroduction to Algorithms by Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein

**Good luck**

What does Judgement Failed mean?

I got it now in div 2 problem A

To solve this problem, we can apply a simple algorithmic approach. First, we calculate the sum of all the initial prices and divide it by the total number of products to find the average price. Then, we add the tolerance range ±k to the average price to obtain the minimum and maximum possible prices

- Read the number of products n and the tolerance range k.
- Read the prices of the n products and calculate their sum.
- Calculate the average price by dividing the sum by n.
- Calculate the minimum possible price by subtracting k from the average price.
- Calculate the maximum possible price by adding k to the average price

int q;
cin >> q;
for (int i = 0; i < q; ++i) {
int n;
cin >> n;
int sum = 0;
for (int j = 0; j < n; ++j) {
int x;
cin >> x;
sum += x;
}
cout << (sum + n — 1) / n << endl;
}

The Algorithm or Algorithms was named after Muhammad bin Musa Al-Khwarizmi, the Arab mathematician, and what is meant by algorithms in the field of programming are the steps that we use to solve the problems that we meet. And that's it And of course, there is a basis in his book, the algorithm, not anything, and that's it, I can say about it algorithm 1- Simplicity: This is an important thing in writing any algorithm so that I, as a programmer, can turn it into code that I really use. The simpler the steps you use, the easier it is for you to use them later

2 General: And here what is meant by it is that when I create an algorithm, I do it in a way that I can use it on a large scale. I mean, for example, I can’t say 1 + 2 = 3. This is an algorithm because it has a limited scale, which is only these two numbers. But it is possible that x + y = z is an algorithm. So I can use any number and it will do exactly the same job 3- Efficiency: And here we will need to understand the concept of efficiency in programming, and this is in order to be able to measure the efficiency of any algorithm, and the main factor here is the time.

So, do we understand from this statement that there are really existing algorithms that I can use? Oh, of course, there are very many, but we will take simple examples from them, so that it does not prolong you more than that

1- Sort Algorithms or ranking algorithms The arrangement algorithm is one of the most studied and researched algorithms in the field of computer science in general. Its aim is to arrange a large number of elements in a specific order, so that it will be easier for me after that to connect it. Of course, you can write it in any programming language that you use. The most important thing is to understand its principle and one of the most important algorithms. arrangement Merge Sort Quick Sort Heap sort Bubble Sort 2- The Search Algorithms or search algorithms And this is used to search for a specific element in a place, whether it is databases or array objects, for example, and one of the most famous examples of it is binary search or binary search, and this depends on dividing the elements in half each time until we reach the element to look for it Of course, there are many examples of algorithms, but we will suffice with these for now SALAH

**So I work and force myself to reach.** **#### salah**

Night, worries and problems belong to you alone! What does it mean, my good sir! It means the problems of your life, your work, and everything that concerns you, are exactly the same for millions of others. What differentiates one from the other is that each person tries to solve his problems according to his level of awareness and management of matters. One solves problems intelligently and with less losses. And someone solves his problems the hard way, but he reaches in the end. And someone makes impulsive decisions and creates bigger problems and spirals that don't end. Roots of the problem Roots of the problem. etc. The steps to solve any problem in the world begin with realization, then analysis, then developing solutions that suit the situation Each stage is based on the one before it, so if you do well, you will do well for the one that follows it Perception comes with teaching, teaching, patience and calmness And those who are distinguished by these qualities are the smartest in solving problems

The term problem solving has a slightly different meaning depending on the discipline. For instance, it is a mental process in psychology and a computerized process in computer science. There are two different types of problems: ill-defined and well-defined; different approaches are used for each. Well-defined problems have specific end goals and clearly expected solutions, while ill-defined problems do not. Well-defined problems allow for more initial planning than ill-defined problems.[2] Solving problems sometimes involves dealing with pragmatics, the way that context contributes to meaning, and semantics, the interpretation of the problem. The ability to understand what the end goal of the problem is, and what rules could be applied represents the key to solving the problem. Sometimes the problem requires abstract thinking or coming up with a creative solution.

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