(f) Determine Payment from a "Pocket" of Available Coins

Define a function pay_with_coins_from_pocket( amount, pocket ), where amount is a floating point number with up to two decimal places, and pocket is a list of 8 integers representing the numbers of coins the android has in its pocket, given in the following order (same as for part (e)):

• Number of £2 coins,
• Number of £1 coins,
• Number of 50p coins,
• Number of 20p coins,
• Number of 10p coins,
• Number of 5p coins,
• Number of 2p coins,
• Number of 1p coins.

• If the total value of the coins represented by pocket is less than amount return the boolean value False.
• In all other cases return a list of 9 integers that satisfies the following conditions:
  • The first 8 numbers of the returned list represent coins that should be paid, using the same ordering as the input list, pocket.
  • The last number of the returned list gives the amount of money that the android should get back as change.
    So, if the android can pay the exact money, this will be 0; but if the android has enough money in pocket, but does not have the right coins to pay the exact amount, this will be the amount of change that will be returned. The change should be given as a float, with the whole part being the number of pounds and the part after the decimal being the number of pennies. (If the change is a whole number of pounds, you can represent it either as a float or an integer.)
  • The total of the coins paid must be the exact amount, if it is possible to pay that.
  • If it is not possible to pay the exact amount, the amount paid must be the lowest amount that covers the cost.
    (In other words, the amount of change returned should be as low as possible.)
  • If there are several ways that the android can pay the amount, the payment made should be one that uses the most coins possible. (Even androids don't like carrying a lot of small change.)
  • If there are several ways to pay satisfying all previous conditions, the android should make a payment using the fewest different types of coin. (Will this condition ever make a difference?)

Examples
INPUT 1	INPUT 2	OUPUT	Coins to be paid
0.50	[0,0,0,0,4,1,1,1]	False	Cannot pay (only have 48p)
1.62	[2,1,0,0,0,0,0,0]	[1,0,0,0,0,0,0,0,0.38]	1×£2, Change 38p
3.75	[2,3,4,0,0,0,0,0]	[0,2,4,0,0,0,0,0,0.25]	2×£1, 4×50p, Change 25p
0.05	[0,0,0,0,0,5,3,6]	[0,0,0,0,0,0,0,5,0]	5×1p, Change 0
0.05	[0,0,0,0,0,1,3,0]	[0,0,0,0,0,1,0,0,0]	1×5p, Change 0
0.08	[0,0,0,0,0,1,4,3]	[0,0,0,0,0,0,3,2,0]	3×2p, 2×1p, Change 0

Notes:

• This is quite a difficult programming problem. Don't worry if you cannot write a program that fulfills all the requirements. You can get partial marks if your program only works for the simpler cases, and you can still get a high overall mark for this assignment if you do not do this part.
• A student has pointed out to me that, even with the given constraints on the preferred payment, there are some cases where several options are possible. This was not my intention. It is because I accidentally removed a further constraint thinking it would not be necessary. You do not need to worry about this problem since I will only be marking based on cases where there is a unique solution. For cases where there are multiple solutions, you could return a list of them, or any one of them, or any other value; it will not affect the marking.