# Coin sums

# You have coins for 1p, 2p, 5p, 10p, 20p, 50p, 100p and 200p
# Find out how many ways there are to pay 200p

def count(S, n, N):

	if N == 0:
		return 1

	if N < 0 or n < 0:
		return 0

	# Case 1. include current coin S[n] in solution and recur
	# with remaining change (N - S[n]) with same number of coins
	incl = count(S, n, N - S[n])

	# Case 2. exclude current coin S[n] from solution and recur
	# for remaining coins (n - 1)
	excl = count(S, n - 1, N)

	# return total ways by including or excluding current coin
	return incl + excl


if __name__ == '__main__':

	S = [1, 2, 5, 10, 20, 50, 100, 200]

	N = 200

	print("Total number of ways to get desired change is", count(S, len(S) - 1, N))