--- Day 14: Space Stoichiometry ---
As you approach the rings of Saturn, your ship's low fuel indicator turns on. There isn't any fuel here, but the rings have plenty of raw material. Perhaps your ship's Inter-Stellar Refinery Union brand nanofactory can turn these raw materials into fuel.
You ask the nanofactory to produce a list of the reactions it can perform that are relevant to this process (your puzzle input). Every reaction turns some quantities of specific input chemicals into some quantity of an output chemical. 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.
You just need to know how much ORE
you'll need to collect before you can produce one unit of FUEL
.
Each reaction gives specific quantities for its inputs and output; reactions cannot be partially run, so only whole integer multiples of these quantities can be used. (It's okay to have leftover chemicals when you're done, though.) For example, the reaction 1 A, 2 B, 3 C => 2 D
means that exactly 2 units of chemical D
can be produced by consuming exactly 1 A
, 2 B
and 3 C
. You can run the full reaction as many times as necessary; for example, you could produce 10 D
by consuming 5 A
, 10 B
, and 15 C
.
Suppose your nanofactory produces the following list of reactions:
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
The first two reactions use only ORE
as inputs; they indicate that you can produce as much of chemical A
as you want (in increments of 10 units, each 10 costing 10 ORE
) and as much of chemical B
as you want (each costing 1 ORE
). To produce 1 FUEL
, a total of 31 ORE
is required: 1 ORE
to produce 1 B
, then 30 more ORE
to produce the 7 + 7 + 7 + 7 = 28 A
(with 2 extra A
wasted) required in the reactions to convert the B
into C
, C
into D
, D
into E
, and finally E
into FUEL
. (30 A
is produced because its reaction requires that it is created in increments of 10.)
Or, suppose you have the following list of reactions:
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
The above list of reactions requires 165 ORE
to produce 1 FUEL
:
- Consume 45
ORE
to produce 10A
. - Consume 64
ORE
to produce 24B
. - Consume 56
ORE
to produce 40C
. - Consume 6
A
, 8B
to produce 2AB
. - Consume 15
B
, 21C
to produce 3BC
. - Consume 16
C
, 4A
to produce 4CA
. - Consume 2
AB
, 3BC
, 4CA
to produce 1FUEL
.
Here are some larger examples:
13312
ORE
for 1FUEL
:157 ORE => 5 NZVS 165 ORE => 6 DCFZ 44 XJWVT, 5 KHKGT, 1 QDVJ, 29 NZVS, 9 GPVTF, 48 HKGWZ => 1 FUEL 12 HKGWZ, 1 GPVTF, 8 PSHF => 9 QDVJ 179 ORE => 7 PSHF 177 ORE => 5 HKGWZ 7 DCFZ, 7 PSHF => 2 XJWVT 165 ORE => 2 GPVTF 3 DCFZ, 7 NZVS, 5 HKGWZ, 10 PSHF => 8 KHKGT
180697
ORE
for 1FUEL
:2 VPVL, 7 FWMGM, 2 CXFTF, 11 MNCFX => 1 STKFG 17 NVRVD, 3 JNWZP => 8 VPVL 53 STKFG, 6 MNCFX, 46 VJHF, 81 HVMC, 68 CXFTF, 25 GNMV => 1 FUEL 22 VJHF, 37 MNCFX => 5 FWMGM 139 ORE => 4 NVRVD 144 ORE => 7 JNWZP 5 MNCFX, 7 RFSQX, 2 FWMGM, 2 VPVL, 19 CXFTF => 3 HVMC 5 VJHF, 7 MNCFX, 9 VPVL, 37 CXFTF => 6 GNMV 145 ORE => 6 MNCFX 1 NVRVD => 8 CXFTF 1 VJHF, 6 MNCFX => 4 RFSQX 176 ORE => 6 VJHF
2210736
ORE
for 1FUEL
:171 ORE => 8 CNZTR 7 ZLQW, 3 BMBT, 9 XCVML, 26 XMNCP, 1 WPTQ, 2 MZWV, 1 RJRHP => 4 PLWSL 114 ORE => 4 BHXH 14 VRPVC => 6 BMBT 6 BHXH, 18 KTJDG, 12 WPTQ, 7 PLWSL, 31 FHTLT, 37 ZDVW => 1 FUEL 6 WPTQ, 2 BMBT, 8 ZLQW, 18 KTJDG, 1 XMNCP, 6 MZWV, 1 RJRHP => 6 FHTLT 15 XDBXC, 2 LTCX, 1 VRPVC => 6 ZLQW 13 WPTQ, 10 LTCX, 3 RJRHP, 14 XMNCP, 2 MZWV, 1 ZLQW => 1 ZDVW 5 BMBT => 4 WPTQ 189 ORE => 9 KTJDG 1 MZWV, 17 XDBXC, 3 XCVML => 2 XMNCP 12 VRPVC, 27 CNZTR => 2 XDBXC 15 KTJDG, 12 BHXH => 5 XCVML 3 BHXH, 2 VRPVC => 7 MZWV 121 ORE => 7 VRPVC 7 XCVML => 6 RJRHP 5 BHXH, 4 VRPVC => 5 LTCX
Given the list of reactions in your puzzle input, what is the minimum amount of ORE
required to produce exactly 1 FUEL
?