Nested Reduce Functions / Recursion / Functional Programming / Tree Traversal

Question

I keep running into situations where I end up nesting very many reduce functions to drill down into an object. It's hard to pull out the logic because at the bottom I need access to the various keys traversed along the way. Essentially, I'm looking for a better way to achieve the following:

import { curry } from 'lodash/fp'
import { fromJS } from 'immutable'

const reduce = curry((fn, acc, it) => it.reduce(fn, acc))

describe('reduceNested', () => {
  const input = fromJS({
    a1: {
      b1: {
        c1: {
          d1: {
            e1: 'one',
            e2: 'two',
            e3: 'three'
          },
          d2: {
            e1: 'one',
            e2: 'two',
            e3: 'three'
          }
        },
        c2: {
          d1: {
            e1: 'one',
            e2: 'two'
          }
        }
      }
    },
    a2: {
      b1: {
        c1: {
          d1: {
            e1: 'one'
          },
          d2: {
            e1: 'one'
          }
        }
      },
      b2: {
        c1: {
          d1: {
            e1: 'one'
          },
          d2: {
            e1: 'one'
          }
        }
      }
    },
    a3: {
      b1: {
        c1: {}
      }
    }
  })

  const expected = fromJS({
    one: [
      'a1.b1.c1.d1.e1',
      'a1.b1.c1.d2.e1',
      'a1.b1.c2.d1.e1',
      'a2.b1.c1.d1.e1',
      'a2.b1.c1.d2.e1',
      'a2.b2.c1.d1.e1',
      'a2.b2.c1.d2.e1'
    ],
    two: ['a1.b1.c1.d1.e2', 'a1.b1.c1.d2.e2', 'a1.b1.c2.d1.e2'],
    three: ['a1.b1.c1.d1.e3', 'a1.b1.c1.d2.e3']
  })

  const init = fromJS({ one: [], two: [], three: [] })

  test('madness', () => {
    const result = reduce(
      (acc2, val, key) =>
        reduce(
          (acc3, val2, key2) =>
            reduce(
              (acc4, val3, key3) =>
                reduce(
                  (acc5, val4, key4) =>
                    reduce(
                      (acc6, val5, key5) =>
                        acc6.update(val5, i =>
                          i.push(`${key}.${key2}.${key3}.${key4}.${key5}`)
                        ),
                      acc5,
                      val4
                    ),
                  acc4,
                  val3
                ),
              acc3,
              val2
            ),
          acc2,
          val
        ),
      init,
      input
    )

    expect(result).toEqual(expected)
  })

  test('better', () => {
    const result = reduceNested(
      (acc, curr, a, b, c, d, e) =>
        acc.update(curr, i => i.push(`${a}.${b}.${c}.${d}.${e}`)),
      init,
      input
    )

    expect(result).toEqual(expected)
  })
})

I would like to write a function reduceNested that achieves the same result but without all of the nested reduce functions. I don't see something in lodash/fp or similar to address so my thought was to create a new function reduceNested and to add variables to the callback for each key in the tree. I've tried implementing the actual logic but am unfortunately stuck for the time being. I know reduceNested will need to use fn.length to determine how far down into the source to drill, but other than that I'm just stuck.

const reduceNested = curry((fn, acc, iter) => {
  // TODO --> use (fn.length - 2)
})

Answer 1

functional style

You were on the right track with your answer, however recurring based on the user-supplied procedure's length is a misstep. Instead, the variable-length path should be passed as a single, variable-length value – an array

const reduceTree = (proc, state, tree, path = []) =>
  reduce                        // call reduce with:
    ( (acc, [ key, value ]) =>  // reducer
        isObject (value)               // value is an object (another tree):
          ? reduceTree                 //   recur with:
              ( proc                   //     the proc
              , acc                    //     the acc
              , value                  //     this value (the tree)
              , append (path, key)     //     add this key to the path
              )                        // value is NOT an object (non-tree):
          : proc                       //   call the proc with:
              ( acc                    //     the acc
              , value                  //     this value (non-tree, plain value)
              , append (path, key)     //     add this key to the path
              )
    , state                     // initial input state 
    , Object.entries (tree)     // [ key, value ] pairs of input tree
    )

Free values above are defined to use prefix notation, which is more familiar in functional style –

const isObject = x =>
  Object (x) === x

const reduce = (proc, state, arr) =>
  arr .reduce (proc, state)

const append = (xs, x) =>
  xs .concat ([ x ])

Now we have a generic reduceTree function –

const result =
  reduceTree
    ( (acc, value, path) =>           // reducer
        [ ...acc, { path, value } ] 
    , []                              // initial state
    , input                           // input tree
    )

console.log (result)
// [ { path: [ 'a1', 'b1', 'c1', 'd1', 'e1' ], value: 'one' }
// , { path: [ 'a1', 'b1', 'c1', 'd1', 'e2' ], value: 'two' }
// , { path: [ 'a1', 'b1', 'c1', 'd1', 'e3' ], value: 'three' }
// , { path: [ 'a1', 'b1', 'c1', 'd2', 'e1' ], value: 'one' }
// , { path: [ 'a1', 'b1', 'c1', 'd2', 'e2' ], value: 'two' }
// , { path: [ 'a1', 'b1', 'c1', 'd2', 'e3' ], value: 'three' }
// , { path: [ 'a1', 'b1', 'c2', 'd1', 'e1' ], value: 'one' }
// , { path: [ 'a1', 'b1', 'c2', 'd1', 'e2' ], value: 'two' }
// , { path: [ 'a2', 'b1', 'c1', 'd1', 'e1' ], value: 'one' }
// , { path: [ 'a2', 'b1', 'c1', 'd2', 'e1' ], value: 'one' }
// , { path: [ 'a2', 'b2', 'c1', 'd1', 'e1' ], value: 'one' }
// , { path: [ 'a2', 'b2', 'c1', 'd2', 'e1' ], value: 'one' } 
// ]

We can shape the output of the result however we like –

const result =
  reduceTree
    ( (acc, value, path) =>                        // reducer
        ({ ...acc, [ path .join ('.') ]: value })
    , {}                                           // initial state
    , input                                        // input tree
    )

console.log (result)
// { 'a1.b1.c1.d1.e1': 'one'
// , 'a1.b1.c1.d1.e2': 'two'
// , 'a1.b1.c1.d1.e3': 'three'
// , 'a1.b1.c1.d2.e1': 'one'
// , 'a1.b1.c1.d2.e2': 'two'
// , 'a1.b1.c1.d2.e3': 'three'
// , 'a1.b1.c2.d1.e1': 'one'
// , 'a1.b1.c2.d1.e2': 'two'
// , 'a2.b1.c1.d1.e1': 'one'
// , 'a2.b1.c1.d2.e1': 'one'
// , 'a2.b2.c1.d1.e1': 'one'
// , 'a2.b2.c1.d2.e1': 'one'
// }

The input for our test should demonstrate that reduceTree works for various levels of nesting –

test ('better', () => {
  const input =
    { a: { b: { c: 1, d: 2 } }, e: 3 }

  const expected =
    { 'a.b.c': 1, 'a.b.d': 2, e: 3 }

  const result =
    reduceTree
      ( (acc, value, path) =>
          ({ ...acc, [ path .join ('.') ]: value })
      , {}
      , input 
      )

  expect(result).toEqual(expected)
})

Lastly, verify the program works in your browser below –

const isObject = x =>
  Object (x) === x

const reduce = (proc, state, arr) =>
  arr .reduce (proc, state)

const append = (xs, x) =>
  xs .concat ([ x ])

const reduceTree = (proc, state, tree, path = []) =>
  reduce
    ( (acc, [ key, value ]) =>
        isObject (value)
          ? reduceTree
              ( proc
              , acc
              , value
              , append (path, key)
              )
          : proc
              ( acc
              , value
              , append (path, key)
              )
    , state
    , Object.entries (tree)
    )

const input =
  { a: { b: { c: 1, d: 2 } }, e: 3 }

const result =
  reduceTree
    ( (acc, value, path) =>
        [ ...acc, { path, value } ]
    , []
    , input
    )

console.log (result)
// { 'a.b.c': 1, 'a.b.d': 2, e: 3 }

---

… with the help of some friends

Imperative-style generators make light work of this kind of task while offering an intuitive language to describe the intended process. Below we add traverse which generates [ path, value ] pairs for a nested tree (object) –

const traverse = function* (tree = {}, path = [])
{ for (const [ key, value ] of Object.entries (tree))
    if (isObject (value))
      yield* traverse (value, append (path, key))
    else
      yield [ append (path, key), value ]
}

Using Array.from we can plug the generator directly into our existing functional reduce; reduceTree is now just a specialization –

const reduceTree = (proc, state, tree) =>
  reduce
    ( (acc, [ path, value ]) =>
        proc (acc, value, path)
    , state
    , Array.from (traverse (tree))
    )

The call site is the same –

const input =
  { a: { b: { c: 1, d: 2 } }, e: 3 }

const result =
  reduceTree
    ( (acc, value, path) =>
        ({ ...acc, [ path .join ('.') ]: value })
    , {}
    , input
    )

console.log (result)
// { 'a.b.c': 1, 'a.b.d': 2, e: 3 }

Verify the result in your browser below –

const isObject = x =>
  Object (x) === x

const reduce = (proc, state, arr) =>
  arr .reduce (proc, state)

const append = (xs, x) =>
  xs .concat ([ x ])

const traverse = function* (tree = {}, path = [])
{ for (const [ key, value ] of Object.entries (tree))
    if (isObject (value))
      yield* traverse (value, append (path, key))
    else
      yield [ append (path, key), value ]
}

const reduceTree = (proc, state, tree) =>
  reduce
    ( (acc, [ path, value ]) =>
        proc (acc, value, path)
    , state
    , Array.from (traverse (tree))
    )

const input =
  { a: { b: { c: 1, d: 2 } }, e: 3 }

const result =
  reduceTree
    ( (acc, value, path) =>
        ({ ...acc, [ path .join ('.') ]: value })
    , {}
    , input
    )

console.log (result)
// { 'a.b.c': 1, 'a.b.d': 2, e: 3 }