Findall possible ways €2 can be split using coins 1p, 2p, 5p, 10p, 20p, 50p, €1 (100p) and €2 (200p)

coin_change.py

final_target = 200
possibilities = [0] * (final_target + 1)
possibilities[0] = 1
# keeping the coins sorted is the key here
# we want to compute possibilities for lower coins first.
# This helps us to fix one particular coin and 
# then find the other possibilites of the change needed
coins = [1, 2, 5, 10, 20, 50, 100, 200]
for coin in coins:
  for current_target in range(coin, final_target + 1):
    # possibilities[current_target - coin] --> possibilies of giving the 
    # remaining change keeping the coin fixed.
    # also sum this up with previously computed possibilities of coins 
    # of lesser value then the current one
    possibilities[current_target] += possibilities[current_target - coin]       
print(possibilities[final_target])