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Maximum System Memory Capacity

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The developers at Amazon are working on optimising the capacity of their cloud system. In the system, there are n servers where the memory capacity of the i-th server is represented by the array memory[i].

A system always contains an even number of servers. If the system has 2x servers, then x of them will be primary and the other x will be backup servers.

For each primary server P, there exists a backup server B where the memory capacity of B ≥ memory capacity of P. The system's memory capacity is the sum of the memory capacity of all the primary servers.

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Examples

01 · Example 1

memory = [1, 2, 1, 2]
return = 3

Here, we have 4 servers [serverA, serverB, serverC, serverD] having memory sizes as [1, 2, 1, 2]. We can choose serverA and serverB as primary servers, and serverC and serverD as their respective backup. The conditions hold true since memory[serverC] ≥ memory[serverA] and memory[serverD] ≥ memory[serverB]. Hence, the maximum system memory capacity is 3.

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CodePython 3

import heapq
from collections import defaultdict
 
class Solution:
    def solve(self, values, queries):
        # Build the adjacency structure
        n = len(values)
        graph = defaultdict(list)
        for u, v in queries:
            graph[u].append(v)
 
        best = [float("inf")] * n
        heap = [(0, 0)]
        while heap:
            cost, node = heapq.heappop(heap)
            if cost > best[node]:
                continue

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