You have an unlimited amount of banknotes worth A and B dollars (A not equals to B). You want to pay a total of S dollars using exactly N notes. The task is to find the number of notes worth A dollars you need. If there is no solution return -1.
Input: A = 1, B = 2, S = 7, N = 5
3 * A + 2 * B = S
3 * 1 + 2 * 2 = 7
Input: A = 2, B = 1, S = 7, N = 5
Input: A = 2, B = 1, S = 4, N = 5
Input: A = 2, B = 3, S = 20, N = 8
Approach: Let x be the number of notes of value A required then the rest of the notes i.e. N – x must of value B. Since, their sum is required be S then the following equation must be satisfied:
S = (A * x) + (B * (N – x))
Solving the equation further,
S = (A * x) + (B * N) – (B * x)
S – (B * N) = (A – B) * x
x = (S – (B * N)) / (A – B)
After solving for x, it is the number of notes of value A required
only if the value of x is an integer else the result is not possible.
Below is the implementation of the above approach:
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