The input is a number of periods (N), a constant amount (A) that has to be paid each period to a creditor and an initial balance in your bank account (B). For each time period, you need to write a cheque for an amount . given the following rules: • You cannot owe money to your creditor: • Your balance cannot be negative (but you can assume that your account gets credited by an amount equal to A every time period). • At the end of the N periods you paid the creditor exactly the amount owed. • The cheque amount has to be positive. An amount of 0 as payment is allowed, but the cost is 0 as it does not require writing a cheque. For example:
- If N=3, A=100, B=0. The only way to pay is to write a cheque for 100 every time period
We associate to writing each cheque a cost C[x] equal to the number of characters taken to write the amount x on the cheque. You are asked to write a program that finds a payment schedule that satisfies the constraints above and it is optimal:
- If N=2, A=100, B=0; the optimal schedule cost is 20: writing twice “one hundred”
- If N=2, A= 100, B=100; the optimal schedule cost is 10:(writing one cheque for “two hundred”). Note that a payment schedule of (200,0) is valid.
- If N=3, A=97, B=6; the optimal schedule is 28 for the schedule (99,96,96) corresponding to writing: “ninety nine” and twice “ninety six”. Another valid schedule might be (97,97,97) but its cost is higher at
I have implemented only main logic by taking hardcode value from file. Input file is for reference.