C++ program to give minimum amount of change doesn't work for lowest denominations

Question

The aim of this is to give an amount of change in the minimum number of notes/coins. So far, my code works fine for all values except those that include 2p or 1p coins, eg. 12.33 gives 1 £10, 1 £2, 1 20p, 1 10p, and 1 2p, but no 1p. I also tried just 2p which gives 1 1p and 1p gives 0 coins at all. I can't figure out what is wrong for these specific values, since the code is identical for each denomination.

#include <iostream>

using namespace std;

int main()
{
  float change;
  int fifty = 0;
  int twenty = 0;
  int ten = 0;
  int five = 0;
  int two = 0;
  int one = 0;
  int fiftyp = 0;
  int twentyp = 0;
  int tenp = 0;
  int fivep = 0;
  int twop = 0;
  int onep = 0;

  cout << "Please enter the amount of change given:\n";
  cin >> change;

  while ( change >= 50)
    {
      fifty++;
      change -= 50;
    }


  while ( change >= 20)
    {
      twenty++;
      change -= 20;
    }


  while ( change >= 10)
    {
      ten++;
      change -= 10;
    }


  while ( change >= 5)
    {
      five++;
      change -= 5;
    }


  while ( change >= 2)
    {
      two++;
      change -= 2;
    }


  while ( change >= 1)
    {
      one++;
      change -= 1;
    }


  while ( change >= 0.5)
    {
      fiftyp++;
      change -= 0.5;
    }


  while ( change >= 0.2)
    {
      twentyp++;
      change -= 0.2;
    }


  while ( change >= 0.1)
    {
      tenp++;
      change -= 0.1;
    }


  while ( change >= 0.05)
    {
      fivep++;
      change -= 0.05;
    }


  while ( change >= 0.02)
    {
      twop++;
      change -= 0.02;
    }


  while ( change >= 0.01)
    {
      onep++;
      change -= 0.01;
    }


    cout << "Give " << fifty << " £50 notes.\n"; 
    cout << "Give " << twenty << " £20 notes.\n";
    cout << "Give " << ten << " £10 notes.\n";
    cout << "Give " << five << " £5 notes.\n";
    cout << "Give " << two << " £2 coins.\n";
    cout << "Give " << one << " £1 coins.\n";
    cout << "Give " << fiftyp << " 50p coins.\n";
    cout << "Give " << twentyp << " 20p coins.\n";
    cout << "Give " << tenp << " 10p coins.\n";
    cout << "Give " << fivep << " 5p coins.\n";
    cout << "Give " << twop << " 2p coins.\n";
    cout << "Give " << onep << " 1p coins.\n";

    return 0;
}

Answer 1

The problem is floating point maths. Consider adding the following line at the end of your program:

cout << "Change left: " << change << '\n';

Running your program with 12.33 as input results in:

Change left: 0.00999992

Clearly this is less than 0.01. Although you can try to add fudge factors to handle "small" deviations from perfect numbers, it is generally best to use integers for money, such that 1 equals 1 cent. You should do this conversion with the proper rounding:

long int cents = lrintf(change * 100.0);

Then replace your while loops like this:

while (cents >= 5000) {
  fifty++;
  cents -= 5000;
}

Et cetera.

Answer 2

The problem is that float can't represent all decimal numbers, and 0.02 is actually slightly less than 0.02 (and 0.01 is less than 0.01).

The remedy is to do the calculations on integers representing your smallest denomination (that is, one penny).

Either let the user input the amount in pence, or read a string that you parse.
The latter method is both more complicated and user-friendly, but it's probably a good idea to get a working program using the former method first.
(Both methods let you ignore nonsense amounts like 3.14159265.)

I also recommend that you read about loops and arrays in your fine C++ book.

Answer 3

Answers below/above solves the question you're actually asking
But imo, i don't think you're actually asking yourself the right question
Here is another simpler way to make your program using arrays:

int main(){
    double change;
    double coins[12]{ 50,20,10,5,2,1,0.5,0.2,0.1,0.05,0.02,0.01 }; //All coins that can be given
    int coinsChanged[12]{0,0,0,0,0,0,0,0,0,0,0,0}; //All coins that are going to be given

    std::cout << "Please enter the amount of change given:\n";
    std::cin >> change;

    while (change >= 0.01) { //If the amount gets below the minimum coin you can give, the progrm stops
        for (int i = 0; i < 12; ++i) //Checks all available coins one by one
            while (change >= coins[i]) { 
                coinsChanged[i]++;
                change -= coins[i]; //Add the coin to the "giving" array
            }
    }

    for (int i = 0; i < 12; ++i)
        std::cout << "Give : " << coinsChanged[i] << "  £" << coins[i] << " notes" << std::endl; // Prints everything

    return 0;
}

If you want to change the amount/value of coins at any time, consider using vectors instead of arrays