köproblem

Köproblem, also known as "cow problem" in English, is a classic problem in computer science and mathematics that involves determining the number of cows that can be bought with a given amount of money, given the prices of cows and the number of cows that can be bought with the money. The problem is often used as an example to illustrate the concept of recursion and dynamic programming.

The problem can be stated as follows: Given a list of prices for cows, where each price is a positive integer, and a budget, determine the maximum number of cows that can be bought with the budget. The budget is also a positive integer. The problem can be solved using a recursive approach, where the function is called with the remaining budget and the number of cows bought so far. The base case is when the budget is zero or negative, in which case the number of cows bought is returned. The recursive case is when the budget is positive, in which case the function is called with the remaining budget after buying a cow at each price, and the maximum number of cows bought is returned.

The problem can also be solved using dynamic programming, where a table is used to store the maximum number of cows that can be bought with each budget. The table is filled using a bottom-up approach, where the maximum number of cows that can be bought with each budget is calculated using the maximum number of cows that can be bought with the remaining budget after buying a cow at each price. The final answer is the maximum number of cows that can be bought with the given budget.

The köproblem is a simple yet powerful example of how recursion and dynamic programming can be used to solve complex problems. It is often used in computer science and mathematics courses to illustrate these concepts and to help students understand the trade-offs between different approaches to problem-solving.