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Daily Coding Problem 5

Daily Coding Problem 5

This problem was asked by Jane Street.

cons(a, b) constructs a pair, and car(pair) and cdr(pair) returns the first and last element of that pair. For example, car(cons(3, 4)) returns 3, and cdr(cons(3, 4)) returns 4.

Given this implementation of cons:

def cons(a, b):
def pair(f):
return f(a, b)
return pair


Implement car and cdr.

Solution

This is not a difficult problem, but requires that the person understand how to use functions as first-class members of the language. Admittedly, python is not a language I use often. I personally prefer statically typed languages and the compile-time goodness that comes along with them.

Regardless, the solution is quite simple. The key is that cons returns a function that expects a function as an argument. That argument is what must, in turn, return the correct value from the pair.

First, let's put the cons function into scope.

In :
def cons(a, b):
def pair(f):
return f(a, b)
return pair


Implementation of car

As the problem states, car needs to return the first element of the pair.

In :
def car(cns):
# Returns the first parameter passed to the function.
def fst(x, y):
return x
return cns(fst)


Implementation of cdr

cdr needs to return the second element of the pair.

In :
def cdr(cns):
# Returns the second parameter passed to the function.
def snd(x, y):
return y
return cns(snd)


Testing

We can perform some basic test to ensure that these implementation work correctly. Since the problem did not specify any test cases, i made some up using different types.

In :
a = cons(1, 2)
b = cons('a', 'b')
c = cons(5.0, 6.0)
d = cons(True, False)

In :
print ('a: ', car(a), ',', cdr(a))
print ('b: ', car(b), ',', cdr(b))
print ('c: ', car(c), ',', cdr(c))
print ('d: ', car(d), ',', cdr(d))

a:  1 , 2
b:  a , b
c:  5.0 , 6.0
d:  True , False


Conclusion

While this wasn't a difficult problem by any means, it was a fun little exercise that demonstrates the use of functions as first class citizens of a language.