Algorithm to determine coin combinations

Question

I was recently faced with a prompt for a programming algorithm that I had no idea what to do for. I\'ve never really written an algorithm before, so I\'m kind of a newb at t

Answer 1

An algorithm is a procedure for solving a problem, it doesn't have to be in any particular language.

First work out the inputs:

typedef int CoinValue;

set coinTypes;
int value;

and the outputs:

set< map > results;

Solve for the simplest case you can think of first:

coinTypes = { 1 }; // only one type of coin worth 1 cent
value = 51;

the result should be:

results = { [1 : 51] }; // only one solution, 51 - 1 cent coins

How would you solve the above?

How about this:

coinTypes = { 2 };
value = 51;

results = { }; // there is no solution

what about this?

coinTypes = { 1, 2 };
value = { 4 };

results = { [2: 2], [2: 1, 1: 2], [1: 4] }; // the order I put the solutions in is a hint to how to do the algorithm.