Today’s exercise provides two questions involving selection from a stream. Both require a solution that takes O(n) time and O(1) space.

First: Given a stream of unknown length, select a random item from the stream, with all items selected with equal probability. For instance, given the stream {A, D, F, A, G} the selection would return A with probability 40% and D, F or G with probability 20%.

Second: Given a stream of unknown length, each item in the stream paired with a weight, select a random item from the stream with all items selected with probability according to their weights. For instance, given the stream {1 A, 2 D, 5 F, 3 A, 9 G} the selection would return A with probability 20%, D with probability 10%, F with probability 25%, and G with probability 45%.

Your task is to write the two programs that select items from streams. When you are finished, you are welcome to read or run a suggested solution, or to post your own solution or discuss the exercise in the comments below.

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