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😲 Solution
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:
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(if (zero? x) max (/ 1 x))
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I told him (that it’s not (yet) done). (But he wasn’t listening) The function should return false for the following strings:
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:-)
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())(
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]): BooleanThere 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 aList[Char]: e.g. "(just an) example".toList.
😶 Solution
Write a recursive function that counts how many different ways you can make change for an amount, given a list of coin denominations. For example, there are 3 ways to give change for 4 if you have coins with denomination 1 and 2: 1+1+1+1, 1+1+2, 2+2.
Do this exercise by implementing the countChange function inMain.scala. This function takes an amount to change, and a list of unique denominations for the coins. Its signature is as follows:
def countChange(money: Int, coins: List[Int]): IntOnce again, you can make use of functions isEmpty, head and tail on the list of integers coins.
Hint: Think of the degenerate cases. How many ways can you give change for 0 CHF(swiss money)? How many ways can you give change for >0 CHF, if you have no coins?
😣 Solution