Javascript equivalent to Clojure's “reductions” or python's itertools.accumulate

Question

Is there a JavaScript equivalent to Clojure's "reductions" function or Python's itertools.accumulate ? In other words, given an array [x_0, x_1, x_2 ... x_n-1] and a function f(prev, next) , it would return an array of length n with values:

[x_0, f(x_0, x_1), f(f(x_0, x_1), x_2)... f(f(f(...)), x_n)]

I'm simulating the desired behavior below:

function accumsum(prev, next) {
    last = prev[prev.length - 1] || 0;
    prev.push(last + next);
    return prev;
}

var x = [1, 1, 1, 1];
var y = x.reduce(accumsum, []);
var z = y.reduce(accumsum, []);

console.log(x);
console.log(y);
console.log(z);

which displays:

[ 1, 1, 1, 1 ]
[ 1, 2, 3, 4 ]
[ 1, 3, 6, 10 ]

But I'm wondering if there is a way to write something simpler like

[1, 1, 1, 1].reductions(function(prev, next) {return prev + next;});

If not, is there a more idiomatic way to do this in JavaScript than what I wrote?

Answer 1

var a = [1, 1, 1, 1];
var c = 0;
a.map(function(x) { return c += x; })
// => [1, 2, 3, 4]

a.reduce(function(c, a) {
  c.push(c[c.length - 1] + a);
  return c;
}, [0]).slice(1);
// => [1, 2, 3, 4]

I'd use the first one, personally.

EDIT:

Is there a way of doing your first suggestion that doesn't require me to have a random global variable (c in this case) floating around? If I forgot to re-initialize c back to 0, the second time I wrote a.map(...) it would give the wrong answer.

Sure - you can encapsulate it.

function cumulativeReduce(fn, start, array) {
  var c = start;
  return array.map(function(x) {
    return (c = fn(c, x));
  });
}
cumulativeReduce(function(c, a) { return c + a; }, 0, [1, 1, 1, 1]);
// => [1, 2, 3, 4]
c
// => ReferenceError - no dangling global variables

Answer 2

For posterity, if you're in a situation where you're using an older version of JavaScript, or don't have access to Underscore .

It's not difficult to implement from scratch and has some educational value.

Here's one way to do it:

function reduce(a, fn, memo) {
  var i;
  for (i = 0; i < a.length; ++i) {
    if ( typeof memo === 'undefined' && i === 0 ) memo = a[i];
    else memo = fn(memo, a[i]);
  }
  return memo;
}

Also, other higher order functions can be written in terms of reduce, eg "map", shown here:

function map(a, fn) {
  return reduce(a, function(memo, x) {
    return memo.concat(fn(a));
  }, []);
}

for reference the equivalent imperative (and faster) version of map would be:

function map2(a, fn) {
  var newA = [], i;
  for (i = 0; i < a.length; ++i) {
    newA.push(fn(a[i]));
  }
  return newA;
}

Answer 3

I wrote a stateless version

function reductions(coll, reducer, init) {
  if (!coll.length) {
    return [init]
  }
  if (init === undefined) {
    return reductions(_.drop(coll, 1), reducer, _.first(coll))
  }
  return [init].concat(reductions(_.drop(coll, 1), reducer, reducer(init, _.first(coll))))
}