Advent of Code 2019 Day 14
Task: Solve for X where...
Part 1
X = the minimum amount of ORE required to produce exactly 1 FUEL
Example input
10 ORE => 10 A
1 ORE => 1 B
7 A, 1 B => 1 C
7 A, 1 C => 1 D
7 A, 1 D => 1 E
7 A, 1 E => 1 FUEL
It represents:
 A list of reactions
 Each line denotes one or more input and an output
Part 1
 This feels like Handy Haversack
 Carefully reading the rules
 Attempting to manually evaluate each example input
 Trying to write a recursive algorithm
This feels like Handy Haversack
 The onetomany relationship
 The pairing of labels and quantities
 The pathfinding from a target back to an origin (shiny gold bags)
I'm anxious about whether I can reuse any of the algorithms or data structures I wrote for that puzzle in this one.
Carefully reading the rules
Every reaction turns some quantities of specific input chemicals into some quantity of an output chemical
X INPUT (, Y INPUT?, Z INPUT?) => A OUTPUT
Almost every chemical is produced by exactly one reaction; the only exception, ORE, is the raw material input to the entire process and is not produced by a reaction
Mandatory:
X ORE => A OUTPUT
Won't happen:
X ORE (, Y INPUT?, Z INPUT?) => A OUTPUT
Won't happen:
X INPUT => A ORE
reactions cannot be partially run, so only whole integer multiples of these quantities can be used
XX INPUT => A OUTPUT
...cannot be used as:
X INPUT => 1/2A OUTPUT
It's okay to have leftover chemicals when you're done
XX INPUT => A OUTPUT
But only X was needed? That's ok
You can run the full reaction as many times as necessary
X INPUT, YY INPUT, ZZZ INPUT => A OUTPUT
For AAA OUTPUT:
XXX INPUT, YYYYYY INPUT, ZZZZZZZZZ INPUT
Attempting to manually evaluate each example input
Here is example 1 again:
10 ORE => 10 A
1 ORE => 1 B
7 A, 1 B => 1 C
7 A, 1 C => 1 D
7 A, 1 D => 1 E
7 A, 1 E => 1 FUEL
Evaluating the equation
1 FUEL:
7A + 1E
7A + 7A + 1D
7A + 7A + 7A + 1C
7A + 7A + 7A + 7A + 1B

28A + 1B
??? ORE?
10x + 1x
30 + 1
31 CORRECT
Here is example 2:
9 ORE => 2 A
8 ORE => 3 B
7 ORE => 5 C
3 A, 4 B => 1 AB
5 B, 7 C => 1 BC
4 C, 1 A => 1 CA
2 AB, 3 BC, 4 CA => 1 FUEL
Evaluating the equation
1 FUEL:
2 AB + 3 BC + 4 CA
6 A + 8 B + 15 B + 21 C + 16 C + 4 A
10 A + 23 B + 37 C

????????????? ORE?
2*5A 3*8B 5*8C
5x 8x 8x
9 ORE 8 ORE 7 ORE
9*5 + 8*8 + 7*8
45 + 64 + 56
165 CORRECT
Here is example 3, with labels adjusted for space:
157 ORE => 5 A
165 ORE => 6 B
44 C, 5 D, 1 E, 29 A, 9 F, 48 G => 1 FUEL
12 G, 1 F, 8 H => 9 E
179 ORE => 7 H
177 ORE => 5 G
7 B, 7 H => 2 C
165 ORE => 2 F
3 B, 7 A, 5 G, 10 H => 8 D
Evaluating the equation
1 FUEL:
44 C + 5 D + 1 E + 29 A + 9 F + 48 G
154 B + 154 H + 3 B + 7 A + 5 G + 10 H + 12 G + 1 F + 8 H + 29 A + 9 F + 48 G
157 B + 172 H + 36 A + 65 G + 10 F
6*27 + 7*25 + 5*8 + 5*13 + 2*5
27 25 8 13 5
*165 *179 *157 *177 *165

4455 + 4475 + 1256 + 2301 + 825
13312 CORRECT
Here is example 4, with labels adjusted for space:
2 A, 7 B, 2 C, 11 D => 1 E
17 F, 3 G => 8 A
53 E, 6 D, 46 H, 81 J, 68 C, 25 K => 1 FUEL
22 H, 37 D => 5 B
139 ORE => 4 F
144 ORE => 7 G
5 D, 7 L, 2 B, 2 A, 19 C => 3 J
5 H, 7 D, 9 A, 37 C => 6 K
145 ORE => 6 D
1 F => 8 C
1 H, 6 D => 4 L
176 ORE => 6 H
Evaluating the equation
1 FUEL:
53 E + 6 D + 46 H + 81 J + 68 C + 25 K
106A + 371 B + 106 C + 583 D + 6 D + 46 H + 135 D + 189 L + 54 B + 54 A + 513 C + 72 F + 25 H + 35 D + 45 A + 185 C
238 F + 42 G + 1650 H + 2775 D + 14 F + 583 D + 6 D + 46 H + 135 D + 48 H + 288 D + 242 H + 407 D + 119 F + 21 G + 65 F + 72 F + 25 H + 35 D + 102 F + 18 G + 24 F
F G D H
238 + 14 + 119 + 65 + 72 + 102 + 24 F
42 + 21 + 18 G
2775 + 583 + 6 + 135 + 288 + 407 + 35 D
1650 + 46 + 48 + 242 + 25 H
634 F + 81 G + 4229 D + 2011 H
4*159 + 7*12 + 6*705 + 6*336
159 12 705 336
*139 *144 *145 *176

22101 + 1728+ 102225 + 59136
185190 WRONG, BUT CLOSE!
Should have been: 180797
Trying to write a recursive algorithm
The regular expression to parse each chemical and amount
For a line like this:
5 VJHF, 7 MNCFX, 9 VPVL, 37 CXFTF => 6 GNMV
I want to extract:
(5, VJHF), (7, MNCFX), (9, VPVL), (37, CXFTF), (6, GNMV)
The simplest regular expression I got to work was:
/(\d+)\s(\w+)/g
Matching:

\d+
several digits 
\s
a space 
\w+
several letters
I recognize I'll have to:
 Run this on each line of input, not the whole input
 Identify the last match as the key to which all other matches must be the linked list
The data structure for storing chemical relations
 I'll use a dictionary/hash/object
 Keys will be each chemical after the
=>
 Values will be a dictionary: a key for the amount, and a key for the list of required chemicals and amounts
An example of this data structure using example 1:
Input:
10 ORE => 10 A
1 ORE => 1 B
7 A, 1 B => 1 C
7 A, 1 C => 1 D
7 A, 1 D => 1 E
7 A, 1 E => 1 FUEL
Planned data structure:
A:
Multiples: 10
Chemicals: ORE: 10
B:
Multiples: 1
Chemicals: ORE: 1
C:
Multiples: 1
Chemicals: A: 7, B: 1
D:
Multiples: 1
Chemicals: A: 7, C: 1
E:
Multiples: 1
Chemicals: A: 7, D: 1
FUEL:
Multiples: 1
Chemicals: A: 7, E: 1
My malfunctioning recursive algorithm
Accept one input  a 2element array:
1. An integer representing the quantity of the chemical produced
2. A string representing the chemical produced
If the array associated with the key specified in item 2 has 'ORE' as its second item:
Return the input array inside an array
Else
Return a mutated list of chemicals associated with the key specified in item 2, such that:
Each integer at location 1 in each chemical's array is updated to reflect the multiple and minimum quantity needed
Then, call this function on each resulting 2element array
 The function is supposed to return a list of 2element arrays that represent each quantity of elements that are directly made from ORE
 I call this function as part of a larger 2step reduction process that generates an object with keys corresponding to each element and integer sums of all quantities...then multiplies each sum by the proper minimum quantity needed based on the multiplier
Running my algorithm on some example inputs
 Example 1: CORRECT
 Example 2: CORRECT
 Example 3: CORRECT
 Example 4: WRONG  Over by 1000+
 Example 5: WRONG  Over by 10000+
 Input: WRONG  Too high, as expected
I'm not sure what I'm missing.
And I suspect I may never know.
UPDATED:
 I returned to Example 4
 I wanted to retry manually calculating the minimum required ORE for one of the base chemicals: NVRVD
 I followed the path from
1 FUEL
down each reaction that included a chemical that includedNVRVD
Here was my path and math:
68 CXFTF:
9 NVRVD : ORE
53 STKFG
53 * 2 = 106 CXFTF :
14 NVRVD : ORE
53 * 2 = 106 VPVL :
136 NVRVD : ORE
81 HVMC
27 * 19 = 513 CXFTF :
65 NVRVD : ORE
27 * 2 = 54 VPVL :
119 NVRVD : ORE
25 GNMV :
37 * 5 = 185 CXFTF :
24 NVRVD : ORE
5 * 9 = VPVL :
119 NVRVD : ORE
486 NVRVD
122 * 139 = 16958 ORE
In my initial attempt, I multiply 139 by 159  nearly 40 greater than in this new round.
I suspect that my algorithm was rounding up too early in each recursive iteration.
I feel a bit better now knowing one instance of where my initial logic was flawed.
I still likely couldn't have written an algorithm to solve this puzzle.
Successes
 I stepped through four examples, confirming the correct answers for 3/4
 I wrote a recursive algorithm that generated the same amount of correct answers...and helped me spot an error in my math for the fourth example
 I returned a few days later to attack one small part of the first example that my algorithm didn't solve correctly, and found a flaw in my logic
Bummer:
 I failed to solve either part
I was really hoping I would at least solve Part 1.
Oh well. Time to move on.
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