This is a Python solution for all general cases. Any suggestions at all would be appreciated; in my opinion it's already quite good! [Here's a link to the problem.][1]

from timeit import default_timer as timer

def count_coins(target, operands):
    ways_to_make = [1] # list of ways to make x at index x
    for o in range(0, len(operands)):
        for t in range(target + 1):
            # initialise undefined target
            if len(ways_to_make) <= t:
                ways_to_make.append(0)
            # add ways to make number recursively
            if t >= operands[o]:
                ways_to_make[t] += ways_to_make[t - operands[o]]
                
    return ways_to_make[target]

start = timer()
ans = count_coins(200, [1, 2, 5, 10, 20, 50, 100, 200])
elapsed_time = (timer() - start) * 1000 # s --> ms

print "Found %d in %r ms." % (ans, elapsed_time)


  [1]: http://projecteuler.net/problem=31

This is a Python solution for all general cases. Any suggestions at all would be appreciated; in my opinion it's already quite good! Here's a link to the problem.

from timeit import default_timer as timer

def count_coins(target, operands):
    ways_to_make = [1] # list of ways to make x at index x
    for o in range(0, len(operands)):
        for t in range(target + 1):
            # initialise undefined target
            if len(ways_to_make) <= t:
                ways_to_make.append(0)
            # add ways to make number recursively
            if t >= operands[o]:
                ways_to_make[t] += ways_to_make[t - operands[o]]
                
    return ways_to_make[target]

start = timer()
ans = count_coins(200, [1, 2, 5, 10, 20, 50, 100, 200])
elapsed_time = (timer() - start) * 1000 # s --> ms

print "Found %d in %r ms." % (ans, elapsed_time)