Python Question

a) Write a generator every_nth(seq, n) that yields a sequence with every nth element from the sequence seq, starting with the first element.

Example: expression every_nth(range(0, 20), 3) returns a sequence with every third elements in range(0,20).

Thus this program:

for x in every_nth(range(0, 20), 3): print(x, end=", ")

prints 0, 3, 6, 9, 12, 15, 18,

b) Write a generator accumulate(seq, fun, val0) that returns the sequence of the values constituting the successive accumulation of elements starting with val0 (the initial value), using the given binary function fun for accumulation.

For illustration, accumulate([a,b,c], f, val0), for some function f and initial value val0 should return sequence val0, f(val0,a), f(f(val0,a), b), f(f(f(val0,a), b), c).

For example, expression accumulate(range(1,6), lambda x,y:x+y, 0) yields sequence 0, 1, 3, 6, 10, 15 since range(1,6) yields sequence 1, 2, 3, 4, 5, actual argument val0 is 0 and the accumulation function is simple addition:

0, (0+1), (2+(0+1)), (3+(2+(0+1))), (4+(3+(2+(0+1)))), (5+(4+(3+(2+(0+1))))).

c) Write an expression using the accumulate generator that displays the sequence of factorials 0!, 1!, 2!, ..., 6!.

d) Write an expression using the accumulate generator and the every_nth generator that displays the sequence of factorials 0!, 2!, 4!, ..., 10!.