How to get exchange by coins with two denominations? - logic

Question

Develop a method change(amount) that for any integer amount in the range from 24 to 1000 returns a list consisting of numbers 5 and 7 only, such that their sum is equal to amount. For example, change(28) may return [7, 7, 7, 7], while change(49) may return [7, 7, 7, 7, 7, 7, 7] or [5, 5, 5, 5, 5, 5, 5, 7, 7] or [7, 5, 5, 5, 5, 5, 5, 5, 7].
I have written something like this. But it isn't working right.
enter code here
def change (amount):
assert (amount >=24)
if amount == 24:
return [5, 5, 7, 7]
if amount == 29:
return [5, 5, 5, 7, 7]
if amount == 40:
return [5, 5, 5, 5, 5, 5, 5, 5]
coins = change(amount - 5)
coins.append(5)
return coins
for coins in range(24, 1000):
print(coins)

Answer 1

Actually, you should find two numbers:
the number of coins with value 7 (let it be countA) and
the number of coins with value 5 (let it be countB)
As you can see 0 <= countA <= sum/7. Then sum - countA * 7 should be divided by 5 without remainder.
So, the simple implementation in java can be like this:
import java.util.Collections;
// ...
public List<Integer> getExchange(int sum)
{
int coinA = 7;
int coinB = 5;
int maxCountOfCoinA = sum / coinA;
int countA = 0;
int countB = 0;
for (int count = 0; count <= maxCountOfCoinA; count++)
{
int remains = sum - count * coinA;
if (remains % coinB == 0)
{
countA = count;
countB = remains / coinB;
break;
}
}
List<Integer> result = new ArrayList<>();
result.addAll(Collections.nCopies(countA, coinA));
result.addAll(Collections.nCopies(countB, coinB));
return result;
}