Map IDs to matrix rows in Hadoop/MapReduce - hadoop

Question

I have data about users buying products. I want to create a binary matrix of size |users| x |products| such that the element (i,j) in the matrix is 1 iff user_i has bought product_j, else the value is 0.
Now, my data looks something like
userA, productX
userB, productY
userA, productZ
...
UserIds and productIds are all strings. My problem is, how to map these IDs to row indices (for users) and column indices (for products) in the matrix.
There are over a million unique userIds and roughly 3 million productIds.
To make the problem well defined: given the user1, product1 like input above, how do I convert it to something like
1,1
2,2
1,3
where userA is mapped to row 0 of the matrix, userB is mapped to row 1, productX is mapped to column 0 and so on.
Given the size of data, I would have to use Hadoop Map-Reduce but can't think of a foolproof way of efficiently doing this.
This can be solved if we can do the following:
Dump unique userIds.
Dump unique productIds.
Map each unique userId in (1) to a row index.
Map each unique productId in (2) to a column index.
I can do (1) and (2) easily but having trouble coming up with an efficient approach to solve (3) (4 will be solved if we solve 3).
I have a couple of solutions but they are not foolproof.
Solution 1 (naive) for step 3 above
Map all userIds and emit the same key (say "1") for all map tasks.
Have a long counter initialized to 0 in setup() of the reducer.
In the reduce(), emit the counter value along with the input userId and increment the counter by 1.
This would be very inefficient since all 100 million userIds would be processed by a single reducer.
Solution 2 for step 3 above
While mapping userIds, emit each userId against a key which is an integer uniformly sampled from 1,2,3....N (where N is configurable. N = 100 for example). In a way, we are partitioning the input set.
Within the mapper, use Hadoop counters to count the number of userIds assigned to each of those random partitions.
In the reducer setup, first access the counters in the mapping stage to determine how many IDs were assigned to each partition. Use these counters to determine the start and end values for that partition.
Iterate (while counting) over each userId in reduce and generate matrix rowId as start_of_partition + counter.
context.write(userId, matrix row Id)
This method should work but I am not sure how to handle cases when reducer tasks failed/killed.
I believe there should be ways of doing this which I am not aware of. Can we use hashing/modulo to achieve this? How would we handle collisions at scale?