On reflection, it was a pretty fun little problem to solve. There wasn't much of a difference between the two parts. I ran into some bugs with my recursion termination conditions, but I got them in the end.
Part 1.
A quick look at the data showed that the input length was short enough to perform an O(2n) search with some early exits. I coded it as a dfs.
Part 2.
Adding concatenation just changes the base from 2 to 3, which, while strictly slower, wasn't much slower for this input.
code
void d7(bool sub) => print(getLines()
.map((l) => l.split(RegExp(r':? ')).map(int.parse).toList())
.fold<int>(
0, (p, ops) => test(ops, ops[0], ops[1], 2, sub) ? ops[0] + p : p));
bool test(List<int> l, int cal, int cur, int i, bool sub) =>
cur == cal && i == l.length ||
(i < l.length && cur <= cal) &&
(test(l, cal, cur + l[i], i + 1, sub) ||
test(l, cal, cur * l[i], i + 1, sub) ||
(sub && test(l, cal, cur.concat(l[i]), i + 1, sub)));
same here, I was dicking around with combinatorics to get all combos of plus and multiply but realized before I got to the end it was gonna take too long. Then I figured that a DFS was the way to go.
I tried to optimize a bit by exiting early if the cumulative result became too large, but for some reason that gave me incorrect (too low) answers. Part 2 runs in around 1 min anyway.
My graph search solves 7-1 and passes the example cases for 7-2, but gives too low a result for the complete puzzle input, and there's no way I'm manually going through every case to find the false negative. On to day 8 I guess.
7-2 Check case by simple graph search that mostly works
// F#
let isLegit ((total: int64), (calibration : int64 array)) =
let rec search (index : int) (acc: int64) =
let currentValue = calibration.[index]
[Add; Times; Concat] // operators - remove 'Concat' to solve for 7-1
|> List.exists (fun op -> // List.exists returns true the first time the lambda returns true, so search stops at first true
match op with // update accumulator
| Add -> acc + currentValue
| Times -> acc * currentValue
| Concat -> int64 (sprintf "%d%d" acc currentValue)
|> function // stop search on current accumulator value (state) exceeding total, or being just right
| state when state > total -> false
| state when state = total && index < (calibration.Length-1) -> false // this was the problem
| state when state = total && index = (calibration.Length-1) -> true
| state -> // stop if index exceeds input length, or continue search
if index+1 = calibration.Length
then false
else search (index+1) state
)
// start search from second element using the first as current sum
search 1 calibration.[0]
EDIT: total && index < (calibration.Length-1) -> false -- i.e. stop if you reach the total before using all numbers, well, also stops you from checking the next operator, So, removing it worked.
Rubber ducking innocent people on the internets works, who knew.
IDK if this is what your issue was, but one thing I ran into was that if you do something like if (current_total >= target) prune(), this can be problematic because if the tail end of the data is 0s and 1s, you exit too early. Basically I would prune strictly when the current total > target.