Problem 1: Maximum Transfer Time in Server Network
Problem Statement
A server network is represented as a tree of g_nodes servers indexed from 1 to g_nodes and g_nodes - 1 edges where the ith edges connect the servers g_from[i] and g_to[i]. The transfer time between any two connected servers is 1 unit.
Given the graph g, find the maximum time taken to transfer the data between any two servers in the system.
Example
Suppose:
g_nodes = 3
g_from = [1, 2]
g_to = [2, 3]
The maximum time required to transfer data from 1 to 3 that takes 2 units of time. Hence, the answer is:
2
Sample Case 0
Input:
5 4
1 5
1 3
1 2
5 4
Parsed as:
g_nodes = 5
g_from = [1, 1, 1, 5]
g_to = [5, 3, 2, 4]
Output:
3
Sample Case 1
Input:
7
6
4 2
4 7
2 5
1 6
2 3
Parsed as:
g_nodes = 7
g_from = [4, 4, 2, 1, 2]
g_to = [2, 7, 5, 6, 3]
Output:
4
Problem 2: Minimum Time to Execute All Processes
Problem Statement
There are n processes to be executed, and the i-th process has a size of processSize[i], where 1 ≤ i ≤ n. Also, there are m processors of different size capacity. The capacity of the i-th processor is capacity[i] (1 ≤ i ≤ m).
A processor can process a task of size less than or equal to its capacity in 1 second, but it cannot execute processes whose size is greater than its capacity.
A processor can execute multiple processes one after the other, but needs to pause for 1 second after completing its current one. Multiple processors can work on different processes simultaneously.
Find the minimum time to execute all the processes or return -1 if there is no way to execute all the processes.
Example
n = 3
processSize = [2, 5, 3]
m = 3
capacity = [6, 2, 4]
The optimal way to assign processes is to give:
- The first processor the second process
- The second processor the first process
- The third processor the third process
All of them complete their processes in 1 second. Therefore, the minimum time required is:
1
Sample Case 0
Input:
5
1 2 3 4 6
3
4 1 4
6
Parsed as:
n = 5
processSize = [1, 2, 3, 4, 6]
m = 3
capacity = [4, 1, 4]
Output:
3
Explanation: Assign the second and third process to the first processor. It completes the first process in 1 second, then pauses for another second before completing the third process in 1 second.
Sample Case 1
Input:
3
2 5 8
3
6 7 4
Parsed as:
n = 3
processSize = [2, 5, 8]
m = 3
capacity = [6, 7, 4]
Output:
-1
Explanation: No processor has the required capacity to process the third process (size = 8), so there is no way to process them all.
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