Average precision@k average recall@k

Question

I have two sets with user sessions. Each set consists two columns:
- id of viewed items in online shop
- id of bought items in online shop

One set have to be used for train (top roducts rating), second set have to be used for test.

all the id's of bought items are different.

I need to do:
1. On test set calculate the frequencies of viewed and bought id (one id can occur several times in viwed items)
2. Realize two algorithms of recommendations:
- sort viewed id's by popularity (frequency occur in viewed items)
- sort viewed id's by buying (frequency occur in bought items)
3. Using this algorithms I need to calculate AverageRecall@1, AveragePrecision@1, AverageRecall@5, AveragePrecision@5

Important:
- Sessions in which the user did not buy anything, rule of quality assessment.
- If the item is not found in the training set, its popularity is 0.
- Need to recommend different items. And its number should be no more than the number of different user-viewed items.
- Recommendations is never greater than the minimum of two numbers: the number of viewed items and the k in recall @ k / precision @ k.

First task (calculate the frequencies) I do using OrderedDict. For second task I use function:

    def apk(viwed, bought, k=1):
            if len(predicted)>k:
                predicted = predicted[:k]

            score = 0.0
            num_hits = 0.0

            for i,p in enumerate(bought):
                if p in actual and p not in bought[:i]:
                    num_hits += 1.0
                    score += num_hits / (i+1.0)

            if not viewed:
                return 0.0

            return score / min(len(viewed), k)

    def mapk(actual, predicted, k=10):
        return np.mean([apk(a,p,k) for a,p in zip(actual, predicted)])

But I dont know how to calculate third task (average recall etc for every k) and what to do with OrderedDict.