target = 200
coins = [1,2,5,10,20,50,100,200]
ways = [1]+[0]*target
for coin in coins:
    for i in range(coin,target+1):
        ways[i]+=ways[i-coin]
print(ways[target])

ways[i]+=ways[i-coin]

ways = [1]+[0]*target

coinsOptions = [1, 2, 3]
def numberOfWays(target):
    if (target < 0):
        return 0
    elif(target == 0):
        return 1
    else:
        return sum([numberOfWays(target - coin) for coin in coinsOptions])
print numberOfWays(5)

target = 5
coins = [1,2,3]
ways = [1]+[0]*target
for coin in coins:
    for i in range(coin, target+1):
        ways[i]+=ways[i-coin]
print ways[target]

/// <summary>
    /// We are going to fill the biggest coins one by one.
    /// </summary>
    /// <param name="n"> the amount of money </param>
    public static void MakeChange (int n)
    {
        int n1, n2, n3; // residual of amount after each coin
        int quarter, dime, nickel; // These are number of 25c, 10c, 5c, 1c
        for (quarter = n/25; quarter >= 0; quarter--)
        {
            n1 = n - 25 * quarter;
            for (dime = n1/10; dime >= 0; dime--)
            {
                n2 = n1 - 10 * dime;
                for (nickel = n2/5; nickel >= 0 && (n2 - 5*nickel) >= 0; nickel--)
                {
                    n3 = n2 - 5 * nickel;
                    Console.WriteLine("{0},{1},{2},{3}", quarter, dime, nickel, n3); // n3 becomes the number of cent.
                }
            }
        }
    }