Reduce Complexity of This Formula? - optimization

Question

I have a question about optimizing a formula I've been using in Google Sheets:
=ARRAYFORMULA(
IF(
IFERROR(
MATCH($B2 & A2, ($B$1:B1) & ($A$1:A2), 0),
0
) = 0,
1,
0))
The formula works by counting all the unique values in column A (ID) given that it appears in the date range of column B (Date), to give an output in column C (Count).
Notice how the count values are only 0 and 1, and will only show a 1 if it is the ID's first appearance in the date range.
Example data below.
ID Date Count
138 Oct-13 1
138 Oct-13 0
29 Oct-13 1
29 Nov-13 1
138 Nov-13 1
138 Nov-13 0
The issue is once I get over 10000 lines to parse, the formula grinds to a slow pace, and takes upwards of an hour to finish computing. I'm wondering if anyone has a suggestion on how to optimize this formula so I don't need to have it running for so long.
Thanks,

Answer 1

I've been playing around with some formulas, and I think this one works better, but is still becoming quite slow after 10000 lines.
=IF(COUNTIF((FILTER($A$1:$A2, $B$1:$B2 = $B2)),$A2) = 1, 1, 0)
Edit
Here is an additional formula posted on the Google Product Forum which only has to be put in one cell, and autofills down. This is the best answer I've found so far.
=ArrayFormula(IF(LEN(A2:A),--(MATCH(A2:A&B2:B,A2:A&B2:B,0)=ROW(A2:A)-1),))

Answer 2

I wasn't able to find a formula-only solution that I could say outperforms what you have. I did, however, come up with a custom function that runs in linear time, so it ought to perform well. I'd be curious to know how it compares to your final solution.
/**
* Returns 1 for rows in the given range that have not yet occurred in the range,
* or 0 otherwise.
*
* #param {A2:B8} range A range of cells
* #param {2} key_col Relative position of a column to key by, e.g. the sort
* column (optional; may improve performance)
* #return 1 if the values in the row have not yet occurred in the range;
* otherwise 0.
* #customfunction
*/
function COUNT_FIRST_OF_GROUP(range, key_col) {
if (!Array.isArray(range)) {
return 1;
}
const grouped = {};
key_col = typeof key_col === 'undefined' ? 0 : key_col - 1; // convert from 1-based to 0-based
return range.map(function(rowCells) {
const group = groupFor_(grouped, rowCells, key_col);
const rowStr = JSON.stringify(rowCells); // a bit of a hack to identify unique rows, but probably a good compromise
if (rowStr in group) {
return 0;
} else {
group[rowStr] = true;
return 1;
}
});
}
/** #private */
function groupFor_(grouped, row, key_col) {
if (key_col < 0) {
return grouped; // no key column; use one big group for all rows
}
const key = JSON.stringify(row[key_col]);
if (!(key in grouped)) {
grouped[key] = {};
}
return grouped[key];
}
To use it, in Google Sheets go to Tools > Script editor..., paste it into the editor, and click Save. Then, in your spreadsheet, use the function like so:
=COUNT_FIRST_OF_GROUP(A2:B99, 2)
It will autofill for all rows in the range. You can see it in action here.

Answer 3

If certain assumptions are fulfilled, Like, 1. Same ID numbers always occur together(If not, maybe you could SORT them by ID first and then date later), then,
=ARRAYFORMULA(1*(A2:A10000&B2:B10000<>A1:A9999&B1:B9999))
If dates are recognised, I think you could use + instead of & . Again, Various assumptions were made here and there.