Find the least number of coins required that can make any change from 1 to 99 cents

Question

Recently I challenged my co-worker to write an algorithm to solve this problem:

Find the least number of coins required that can make any change from

Answer 1

Came across this one today, while studying https://www.coursera.org/course/bioinformatics

DPCHANGE(money, coins)
 MinNumCoins(0) ← 0
 for m ← 1 to money
        MinNumCoins(m) ← ∞
        for i ← 1 to |coins|
            if m ≥ coini
                if MinNumCoins(m - coini) + 1 < MinNumCoins(m)
                    MinNumCoins(m) ← MinNumCoins(m - coini) + 1
    output MinNumCoins(money)

Takes a comma-separated string of denominations available, and the target amount.

C# implementation:

    public static void DPCHANGE(int val, string denoms)
    {
        int[] idenoms = Array.ConvertAll(denoms.Split(','), int.Parse);
        Array.Sort(idenoms);
        int[] minNumCoins = new int[val + 1];

        minNumCoins[0] = 0;
        for (int m = 1; m <= val; m++)
        {
            minNumCoins[m] = Int32.MaxValue - 1;
            for (int i = 1; i <= idenoms.Count() - 1; i++)
            {
                if (m >= idenoms[i])
                {
                    if (minNumCoins[m - idenoms[i]] + 1 < minNumCoins[m])
                    {
                        minNumCoins[m] = minNumCoins[m - idenoms[i]] + 1;
                    }
                }
            }
        }
    }