Reducing by steps

DESCRIPTION:

Data: an array of integers, a function f of two variables and an init value.

Example: a = [2, 4, 6, 8, 10, 20], f(x, y) = x + y; init = 0

Output: an array of integers, say r, such that

r = [r[0] = f(init, a[0]), r[1] = f(r[0], a[1]), r[2] = f(r[1], a[2]), ...]

With our example: r = [2, 6, 12, 20, 30, 50]

Task:

Write the following functions of two variables

• som : (x, y) -> x + y
• mini : (x, y) -> min(x, y)
• maxi : (x, y) -> max(x, y)
• lcmu : (x, y) -> lcm(abs(x), abs(y) (see note for lcm)
• gcdi : (x, y) -> gcd(abs(x), abs(y) (see note for gcd)

and

• function oper_array(fct, arr, init) (or operArray or oper-array) where
• fct is the function of two variables to apply to the array arr (fct will be one of som, mini, maxi, lcmu or gcdi)
• init is the initial value

Examples:

a = [18, 69, -90, -78, 65, 40]
oper_array(gcd, a, a[0]) => [18, 3, 3, 3, 1, 1]
oper_array(lcm, a, a[0]) => [18, 414, 2070, 26910, 26910, 107640]
oper_array(sum, a, 0) => [18, 87, -3, -81, -16, 24]
oper_array(min, a, a[0]) => [18, 18, -90, -90, -90, -90]
oper_array(max, a, a[0]) => [18, 69, 69, 69, 69, 69]

Notes:

• The form of the parameter fct in oper_array (or operArray or oper-array) changes according to the language. You can see each form according to the language in "Your test cases".
• AFAIK there are no corner cases, everything is as nice as possible.
• lcm and gcd see: https://en.wikipedia.org/wiki/Least_common_multiple https://en.wikipedia.org/wiki/Greatest_common_divisor
• you could google "reduce function (your language)" to have a general view about the reduce functions.
• In Shell bash, arrays are replaced by strings.
• In OCaml arrays are replaced by lists.

---

def gcdi(x,y):
    if y==0:
        return abs(x)
    else:
        return gcdi(abs(y),abs(x%y))
def lcmu(a, b):
    a=abs(a)
    b=abs(b)
    return (a*b)/gcdi(a,b)
def som(a, b):
    return a+b
def maxi(a, b):
    return max(a,b)
def mini(a, b):
    return min(a,b)
def oper_array(fct, arr, init): 
    alist=[]
    alist.append(fct(arr[0],init))
    for i in range(1,len(arr)):
        alist.append(fct(arr[i],alist[-1]))
    return alist