Suppose our input data to a map-reduce operation consists of integer values (the keys are not important). The map function takes an integer i and produces the list of pairs (p,i) such that p is a prime divisor of i. For example, map(12) = [(2,12), (3,12)].

The reduce function is addition. That is, reduce(p, [i1, i2, ...,ik]) is (p,i1+i2+...+ik).

Compute the output, if the input is the set of integers 15, 21, 24, 30, 49. Then, identify, in the list below, one of the pairs in the output.

(5,49)
(3,107)
(5,45)
(3,75)

prime no:2,3,5,7,11,..........

15:[3,15],[5,15]
21:[3,21],[7,21]
24:[2,24],[3,24]
30:[2,30],[3,30],[5,30]
49:[7,49]
by combining all common elements part i.e compare left element and add rightmost element of that to get the solution.
[2,(24+30)],[3,(15+21+24+30)],[5,(15+30)],[7,(21+49)]
so, Ans:([2,54],[3,90],[5,45],[7,70])
according to question:Ans is [5,45] .

(3,90)

(3,75)

To compute the output of the map-reduce operation, we need to first apply the map function to each input integer and obtain the list of pairs for each integer. Then, we apply the reduce function to each prime divisor and sum up the corresponding values.

Let's go step by step:

1. Start with the input set of integers: 15, 21, 24, 30, 49.

2. Apply the map function to each integer:
- map(15) = [(3,15), (5,15)]
- map(21) = [(3,21), (7,21)]
- map(24) = [(2,24), (3,24)]
- map(30) = [(2,30), (3,30), (5,30)]
- map(49) = [(7,49)]

3. Combine the pairs with the same prime divisor:
- [(3,15), (3,21), (3,24), (3,30)] --> (3,15+21+24+30) = (3, 90)
- [(5,15), (5,30)] --> (5,15+30) = (5, 45)
- [(7,21), (7,49)] --> (7,21+49) = (7, 70)
- [(2,24), (2,30)] --> (2, 24+30) = (2, 54)

4. Finally, we have the following pairs:
- (3, 90)
- (5, 45)
- (7, 70)
- (2, 54)

Checking the list given in the question, we can see that one of the pairs in the output is (5, 45).