Functional Programming Principles in Scala
作业应该做Eclipse里面编辑，使用WorkSheet实时检查。然后使用sbt运行styleCheck，test命令进行测试，run命令来运行main函数，如果没有错误，就可使用submit命令提交作业了。
本周作业不难。 pascal三角需要注意运算过程中尽量不要超出Int的表示范围；我在程序中使用了一个小技巧来做到这一点。 balance程序需要使用多个if else 来控制流程。 countChange则使用迭代的方法实现，如果没有想起来这个方法会比较难。还要注意程序什么条件下终止。
作业要求：
Download the recfun.zip handout archive file and extract it somewhere on your machine.
This assignment counts towards your final grade. Please refer to the Grading Policy for more details.
Do not forget to submit your work using the submit task from SBT. Please refer to the example assignment for instructions.
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
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.
Exercise 3: Counting Change
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 denomiation 1 and 2: 1+1+1+1, 1+1+2, 2+2.
Do this exercise by implementing the countChange function in Main.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]): Int
Once 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? How many ways can you give change for >0 CHF, if you have no coins?
源程序如下：
package recfun
import common._
object Main {
def main(args: Array[String]) {
println("Pascal's Triangle")
for (row <- 0 to 10) {//change to 22 to check pascal if out of Int range
for (col <- 0 to row)
print(pascal(col, row) + " ")
println()
}
}
/**
* Exercise 1
*/
def pascal(c: Int, r: Int): Int = {
//everytime mutiply a little num in case of overflow Int range
def factB(c: Int, r: Int): Int =if (c==0) 1 else factB(c-1,r)*(r-c+1)/c
factB(c,r)
}
/**
* Exercise 2
*/
def balance(chars: List[Char]): Boolean ={
def count(char:Char):Int ={
if (char == '(') 1
else if (char == ')') -1
else 0
}
def isOK(len:Int,chars:List[Char]):Boolean={
if (chars.isEmpty) len==0
else if (len==0 && count(chars.head) == -1) false
else isOK(len+count(chars.head),chars.tail)
}
isOK(0,chars)
}
/**
* Exercise 3
*/
def countChange(money: Int, coins: List[Int]): Int =
if (money==0) 1
else if (coins.isEmpty || money<0) 0
else countChange(money,coins.tail)+countChange(money-coins.head,coins)
}