Asked in: SALESFORCE
Image of the Question
All Testcases Passed ✔
Solution
def minRequestTime(requested_server, transition_time):
total = len(transition_time)-1
def helper(arr):
prefix = []
// ... rest of solution available after purchaseExplanation
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To solve this problem, you need to carefully analyze the nature of the circular network of servers and how to calculate the minimum transition time between requested servers in a given sequence. The servers are arranged in a circle, so the key challenge is finding the shortest path along this circle from the current server position to the next requested server, considering the transition times along the edges.
Step 1: Understanding the Circular Structure and Transition Times
The m servers form a circular linked structure, where server 1 is adjacent to server 2 and server m, creating a closed loop. Between every pair of adjacent servers i and i+1 (with server m adjacent to server 1), there is a transition time given by transitionTime[i]. Note that transitionTime array is 1-indexed conceptually: transitionTime[i] is the time to move from server i to the next server (i+1 modulo m). Since the circle is closed, moving from server m to 1 also has a corresponding transition time, closing the loop.
Step 2: Calculating the Shortest Distance Between Two Servers
For any two servers, say A and B, in this circular arrangement, there are exactly two paths to go from A to B:
- Clockwise path: Moving forward from A to B along the circle.
- Counterclockwise path: Moving backward from A to B along the opposite direction.
Since the servers form a circle, moving from A to B clockwise might have a different total transition time than moving counterclockwise. The minimum of these two times is the shortest path.
To calculate these:
- Sum up the transition times along the clockwise path from A to B.
- Sum up the transition times along the counterclockwise path from A to B.
- Compare the two sums and pick the minimum.
This can be computationally expensive if you do this naively for each pair of requested servers and each query.
Step 3: Preprocessing for Fast Queries
To handle multiple queries efficiently, you can preprocess the transition times to allow quick calculation of sums along any path:
- Compute a prefix sum array over the transitionTime array to get cumulative sums of transition times along the circle.
- Use the prefix sums to quickly calculate the total transition time between any two servers in the clockwise direction by subtracting appropriate prefix sums.
- The counterclockwise path time can then be computed as total sum of all transition times minus the clockwise path time.
For example, if prefixSum[i] is the sum of transition times from server 1 up to server i, then the clockwise distance from server A to server B (assuming A ≤ B) is prefixSum[B-1] - prefixSum[A-1]. For cases where A > B, wrap around the circle accordingly using total sum and prefix sums.
Step 4: Iterating Through Requested Servers
The pointer starts at server 1, and you have to visit servers in the order given by requestedServers array. For each requested server in sequence:
- If the requested server is the same as the current server, no time is added.
- Otherwise, calculate the minimum transition time to move from the current server to the requested server using the preprocessed prefix sums and total sums as explained.
- Accumulate this time into the total time counter.
- Update the current server pointer to the requested server.
Step 5: Edge Cases and Constraints
- If the requested server list contains repeated consecutive servers, moving time is zero for those transitions.
- If m = 1, then all servers are the same and no transitions are needed.
- Transition times can be large, so use appropriate data types (like long) to store accumulated times.
- Validate inputs and handle 1-based indexing carefully in the calculations.
- Since m ≤ 1000, preprocessing with prefix sums and answering queries in O(1) per requested server is efficient.
Step 6: Final Result
After processing all requested servers in sequence, the accumulated total time is the minimum time required to process all requests in order starting from server 1.
Summary:
- Model the servers as a circle with weighted edges representing transition times.
- Precompute prefix sums for transition times to quickly calculate shortest path times between any two servers in either direction.
- For each requested server, calculate and accumulate the minimum transition time from the current server position.
- Update the pointer to the newly visited server and continue until all requests are processed.
- Return the total accumulated minimum time as the answer.
By leveraging prefix sums and the circular property, you avoid repeated summation and expensive pathfinding, making the solution efficient and scalable within the problem constraints.
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