Coin Change Problem hackerrank

coin_change.py

def getWays(n, c):
    # Complete this function
    m = len(c)
    
    # table will contains "cache"
    # table[i, j] ~  change number i by first j coins (coins array should be sorted firstly)
    table = [ [0 for j in range(m)] for i in range(n + 1) ]
    for i in range(n+1):
        for j in range(m):
            if i == 0:
                # change 0 with any coins --> 1
                table[i][j] = 1
            elif j == 0:
                # only one coin
                if i % c[j]:
                    # no way to change if the number is not multiple of current (sole) coin
                    table[i][j] = 0
                else:
                    # only one way if the number if the multiple of current coin
                    table[i][j] = 1
            elif i < c[j]:
                # the number to change is smaller than current coin, no luck for it :)
                # it gets the ways with only coins smaller than it
                table[i][j] = table[i][j - 1]
            else:
                # others = summary of number of ways to change without a coin and number of ways to change with a least one of that coin
                table[i][j] = table[i - c[j]][j] + table[i][j - 1]
    
    return table[n][m - 1]