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Problem · Array

Find Maximum Pairs

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Problem statement

An AWS client wants to deploy multiple applications and needs two servers, one for their frontend and another for their backend. They have a list of integers representing the quality of servers in terms of availability. The client's preference is that the availability of an application's frontend server must be greater than that of its backend.

Two arrays of same size s, frontend[s] and backend[s] where elements represent the quality of servers, create pairs of elements (frontend[i], backend[i]) such that frontend[i] > backend[i] in each pair. Each element from an array can be picked only once to form a pair. Find the maximum number of pairs that can be formed.

Function

findMaximumPairs(frontend: int[], backend: int[]) → int

Complete the function findMaximumPairs in the editor.

findMaximumPairs has the following parameters:

int frontend[s]: frontend server qualities
int backend[s]: backend server qualities

Returns

int: the maximum number of pairs that can be formed

Examples

Example 1

frontend = [1, 2, 3]backend = [1, 2, 1]return = 2

The possible valid pairs which can be made are: - (frontend[1], backend[0])=(2, 1) and (frontend[2], backend[2])=(3, 1) are valid pairs - (frontend[1], backend[0])=(2, 1) and (frontend[2], backend[1])=(3, 2) are valid pairs It can be seen that a maximum of 2 valid pairs can be made at a time. So the maximum number of pairs that can be formed is 2. Return 2.

Example 2

frontend = [1, 2, 3, 4, 5]backend = [6, 6, 1, 1, 1]return = 3

The valid pairs which we can form are as follows. (According to the given condition of frontend[i] > backend[i]): - (frontend[1], backend[2]) = {2,1}, (frontend[2], backend[3]) = {3,1} and (frontend[3], backend[4]) = {4,1} is one assignment to form pairs. - (frontend[1], backend[2]) = {2,1}, (frontend[2], backend[3]) = {3,1} and (frontend[4], backend[4]) = {5,1} is one assignment to form pairs. - (frontend[1], backend[2]) = {2,1}, (frontend[3], backend[3]) = {4,1} and (frontend[4], backend[4]) = {5,1} is one assignment to form pairs. - (frontend[2], backend[2]) = {3,1}, (frontend[3], backend[3]) = {4,1} and (frontends, backend[4]) = {5,1} is one assignment to form pairs. There are more valid assignment of pairs, but it can be made sure that there is no way we can create more than 3 pairs of assignment as among five elements of backend, two of them are 6 which is greater than the maximum value in frontend array. Hence return 3 as 3 is the maximum number of valid pairs that can be formed.

Constraints

1 ≤ s ≤ 10⁵
1 ≤ frontend[i], backend[i] ≤ 10⁹