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Get Maximum Stability

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AWS provides a range of servers to meet the deployment needs of its clients. A client wants to choose a set of servers to deploy their application. Each server is associated with an availability factor and a reliability factor.

The client defines the stability of a set of servers as the minimum availability amongst the servers multiplied by the sum of reliabilities of all the servers. Given two arrays of integers, availability, and reliability, where the availability[i] and reliability[i] represent the availability and reliability factors of the ith server, find the maximum possible stability of any subset of servers.

Since the answer can be large, report the answer modulo (109 + 7).

Function Description

Complete the function getMaxStability in the editor below.

getMaxStability has the following parameters:

  1. int reliability[n]: server reliability values
  2. int availability[n]: server availability values

Returns

int: the maximum stability above among all possible non-empty subsets, modulo (10^9+7)

Examples
01 · Example 1
reliability = [1, 2, 2]
availability = [1, 1, 3]
return = 6

Consider the set of servers where reliability = [1, 2, 2] and availability = [1, 1, 3].

The possible subsets of servers are:

  • Indices {0}: Stability = 1*1 = 1
  • Indices {1}: Stability = 1*2 = 2
  • Indices {2}: Stability = 3*2 = 6
  • Indices {0, 1}: Stability = min(1, 1) * (1+ 2) = 3
  • Indices {0, 2}: Stability = min(1, 3) * (1+ 2) = 3
  • Indices {1, 2}: Stability = min(1, 3) * (2+2) = 4
  • Indices {0, 1, 2}: Stability = min(1, 1, 3) * (1+2+2) = 5

So the answer is the maximum stability for the set of index {2}, answer = 6 % 1000000007 = 6.

02 · Example 2
reliability = [75, 104, 72, 72, 8, 125]
availability = [1, 2, 2, 1, 2, 1]
return = 5
Take servers at positions 1, 2, 4, and 6. This will cost 5 and the sum of efficiency values is 376. (This new test case was added on 03-31-2025)
Constraints
  • 1 < n ≤ 10^5
  • 1 <= reliability[i], availability[i] <= 10^6
  • It is guaranteed that lengths of reliability and availability are the same.
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public int getMaxStability(int[] reliability, int[] availability) {
  // write your code here
}
reliability[1, 2, 2]
availability[1, 1, 3]
expected6
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