Multiplicative undelta

Question

Let us define the "multiplicative deltas" of values \$[\; a_0, \cdots a_N, \;]\$ as:

$$ [\; a_1 / a_0, \cdots, a_{i+1} / a_i, \cdots, a_N / a_{N-1} \;] $$

The reverse operation - namely "multiplicative undelta" - returns values such that the above operation results in the given values.

Example

Given values \$[\; 1, 5, 3, 2 \;]\$ a general solution to the "multiplicative undelta" operation is:

$$ [\; a_0, \quad \underset{a_1}{\underbrace{a_0 \cdot 1}}, \quad \underset{a_2}{\underbrace{a_1 \cdot 5}}, \quad \underset{a_3}{\underbrace{a_2 \cdot 3}}, \quad \underset{a_4}{\underbrace{a_3 \cdot 2}} \;] $$

A particular solution can be obtained by setting \$a_0\$ to any value other than zero, for example by setting \$a_0 := 1 \$ we would get:

$$ [\; 1, 1, 5, 15, 30 \;] $$

Challenge

Your task for this challenge is to implement the operation "multiplicative undelta" as defined above.

Rules

Inputs are:

• a non-zero value \$a_0\$
• a non-empty list/array/vector/... of non-zero "multiplicative deltas"

Output is a list/array/vector/... of values such that the first element is \$a_0\$ and for which the "multiplicative deltas" are the input.

Note: If your language has no support of negative integers you may replace non-zero by positive.

Test cases

2 [21] -> [2,42]
1 [1,5,3,2] -> [1,1,5,15,30]
-1 [1,5,3,2] -> [-1,-1,-5,-15,-30]
7 [1,-5,3,2] -> [7,7,-35,-105,-210]
2 [-12,3,-17,1311] -> [2,-24,-72,1224,1604664]
-12 [7,-1,-12,4] -> [-12,-84,84,-1008,-4032]
1 [2,2,2,2,2,2,2,2] -> [1,2,4,8,16,32,64,128,256]

Answer 1

Haskell, 8 bytes

scanl(*)

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Answer 2

APL(Dyalog), 3 bytes

×\∊

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If I have to take the number on the left and the array on the right:

-2 thanks to @H.PWiz

7 5 3 bytes

×\,

Answer 3

R, 15 bytes

cumprod(scan())

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Full program. Function is longer (unless we were allowed to "glue" the inputs together, so that built-in cumprod would suffice as a complete answer):

R, 28 bytes

function(i,x)cumprod(c(i,x))

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Answer 4

MATL, 3 bytes

hYp

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            #implicit input, x_0 and A
h           #horizontally concatenate
Yp          #cumulative product
            #implicit output

The hYpe about MATL is real.

Answer 5

JavaScript (ES6), 27 bytes

Takes input as (m)(a).

m=>a=>[m,...a.map(x=>m*=x)]

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Answer 6

Japt, 3 bytes

å*V

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---

Explanation

        :Implicit input of array U and integer V
å       :Cumulatively reduce U
 *      :By multiplication
  V     :With an initial value of V

Answer 7

Python 3, 39 bytes

def f(a,b):
    for x in[1]+b:a*=x;yield a

Alternative approach. Returns a generator.

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Answer 8

Jelly, 3 bytes

;×\

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Answer 9

Wolfram Language (Mathematica), 14 bytes

FoldList@Times

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FoldList[Times, a0, {x1, x2, ..., xn}] produces the desired output. FoldList[Times] is the curried form that produces a pure function still waiting for its a0 and {x1, x2, ..., xn}.

Answer 10

Perl 6, 9 bytes

{[\*] @_}

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Answer 11

Standard ML, 32 bytes

fun f(x::r)a=a::f r(a*x)|f&a=[a]

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Ungolfed:

fun f (x::xr) a = a :: f xr (a*x)
  | f    _    a = [a]

Answer 12

J, 6 5 bytes

-1 byte thanks to Bubbler

*/\@,

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Explanation:

A diadic verb, the left argument is a0, the rigth one - the vector

     @, - append the vector to a0 and 
  */\   - find the running product

Answer 13

Batch, 69 bytes

@set/pa=
@echo %a%
@for %%d in (%*) do @set/aa*=%%d&call echo %%a%%

Takes input of \$a_0\$ on STDIN and the deltas as command-line arguments.

Answer 14

MathGolf, 6 5 bytes

\{\o*

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I think this could be 5 bytes (\{\o*) but \ instruction seems a little off when dealing with input. This is now fixed in the latest version.

Explanation:

\       Swap arguments, pushing both to stack
 {      Foreach loop over second argument
  \o    Output counter with newline
    *   Multiply counter by current element
        Implicitly output the last element

Answer 15

Pyth, 6 bytes

*FR._s

Test that one here!

Alternatively, 7 bytes:

.u*NYEQ

Test it here!

The first takes input as a tuple, the second takes input as two separate lines.

Thanks to @Sok for helping me with getting good at mapping and saving 1 byte.

Answer 16

Common Lisp, 67 bytes

(lambda(a l &aux(y 1))(mapcar(lambda(x)(setf y(* y x)))(cons a l)))

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Answer 17

Husk, 2 bytes

G*

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This is equivalent to nimi's answer in Haskell: scanl(*), which means reduce from the left using multiplication, and return all partial results.

Answer 18

05AB1E, 5 3 bytes

šηP

-2 bytes thanks to @BMO.

Try it online or verify all test cases.

Explanation:

š      # Prepend the (implicit) input-integer at the start of the (implicit) input-list
       #  i.e. -12 and [7,-1,-12,4] → ["-12",7,-1,-12,4]
 η     # Prefixes of this new list
       #  i.e. ["-12",7,-1,-12,4]
       #   → [["-12"],["-12",7],["-12",7,-1],["-12",7,-1,-12],["-12",7,-1,-12,4]]
  P    # Take the product of each inner list (and output implicitly)
       #  i.e. [["-12"],["-12",7],["-12",7,-1],["-12",7,-1,-12],["-12",7,-1,-12,4]]
       #   → [-12,-84,84,-1008,-4032]

Answer 19

Python 2, 40 bytes

f=lambda a,b:[a]+(b and f(a*b[0],b[1:]))

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Surprisingly, the move to Python 3 and use of generators there only saves 1 byte over the recursive solution.

Answer 20

PowerShell, 29 bytes

param($a,$b)$a;$b|%{($a*=$_)}

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This assumes just outputting the values is fine.

> .\scratch.ps1 1 (1,5,3,2)
1
1
5
15
30

If that's not fine, this actually builds the list and then pushes it to toString which prints the same way.

param($a,$b)$c=,$a;$b|%{$c+=$_*$c[-1]};$c #41 bytes

Answer 21

Python 2, 47 bytes

lambda n,A:reduce(lambda a,c:a+[a[-1]*c],A,[n])

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Answer 22

Charcoal, 12 bytes

ＩＥ⁺⟦Ｎ⟧ＡΠ⊞Ｏυι

Try it online! Link is to verbose version of code. Explanation:

    Ｎ           Input a₀
   ⟦ ⟧          Wrap in a list
      Ａ         Input deltas as a list
  ⁺              Concatenate lists
 Ｅ              Map over elements
           ι    Current element
          υ     Predefined empty list variable
        ⊞Ｏ      Push and return updated list
       Π        Product
Ｉ               Cast to string
                Implicitly print each value on its own line

Answer 23

K (oK), 9 bytes

{(*\)x,y}

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Joins the first number to the second input as a list, and then returns successive results of multiplication

Test Cases

Enter your input after the function like below and then run, as I'm unsure how to use input properly for this language in TiO

{(*\)x,y}[1;1 5 3 2]

Answer 24

dc, 13 bytes

p[*pz1<A]dsAx

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p[*pz1<A]dsAx
p               # Print the first element
  *p            # Multiply top elements on the stack
 [  z1<A]dsAx   # until only one element is left