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031/main.py

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+# 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))