2) v zabaleném projektu recfun.zip implementujte metodu pro vypočet prvků pascalova trojúhelníku
Exercise 1: Pascal’s Triangle

The following pattern of numbers is called Pascal’s triangle.

    1
   1 1
  1 2 1
 1 3 3 1
1 4 6 4 1
   ...
The numbers at the edge of the triangle are all 1, and each number inside the triangle is the sum of the two numbers above it. Write a function that computes the elements of Pascal’s triangle by means of a recursive process.

Do this exercise by implementing the pascal function in Main.scala, which takes a column c and a row r, counting from 0 and returns the number at that spot in the triangle. For example, pascal(0,2)=1, pascal(1,2)=2 and pascal(1,3)=3.

def pascal(c: Int, r: Int): Int

3) v zabaleném projektu recfun.zip implementujte metodu, která bude kontrolovat uzavření všech kulatých závorek v daném výrazu
Exercise 2: Parentheses Balancing

Write a recursive function which verifies the balancing of parentheses in a string, which we represent as a List[Char] not a String. For example, the function should return true for the following strings:
·         (if (zero? x) max (/ 1 x))
·         I told him (that it’s not (yet) done). (But he wasn’t listening)
The function should return false for the following strings:
·         :-)
·         ())(
The last example shows that it’s not enough to verify that a string contains the same number of opening and closing parentheses.
Do this exercise by implementing the balance function in Main.scala. Its signature is as follows:
def balance(chars: List[Char]): Boolean

There are three methods on List[Char] that are useful for this exercise:
·         chars.isEmpty: Boolean returns whether a list is empty
·         chars.head: Char returns the first element of the list
·         chars.tail: List[Char] returns the list without the first element
Hint: you can define an inner function if you need to pass extra parameters to your function.
Testing: You can use the toList method to convert from a String to a List[Char]: e.g. "(just an) example".toList.