Microsoft OA can cover different types of coding problems, from array processing and prefix sums to dynamic programming. In this HackerRank experience, both questions required a clear understanding of the problem and an efficient approach to handling the input.
The first question focused on calculating travel costs between servers, while the second was a variation of the classic House Robber problem. Both could be solved efficiently by identifying the right structure before processing the queries or making selection decisions.
Question 1: Calculate the Cost Between Servers
Problem Overview
The first problem involved a collection of servers arranged in a sequence. Each server had a capacity, and moving between servers incurred a cost determined by the relationship between neighboring servers.
The goal was to answer multiple queries, each asking for the cost of traveling between a starting server and a destination server. Calculating the entire route separately for every query would be inefficient, so the key was to preprocess the information and make each query faster.
Approach
The solution starts by determining which neighboring server is closer to each server. The results are stored in an array called nb, indicating whether the preferred neighbor is on the left or right.
Next, two cumulative cost arrays, rs and ls, are built to handle movement in opposite directions. The rightward array tracks the cost of moving through the servers from left to right, while the leftward array handles movement from right to left.
When calculating the cost of moving to the next server, the algorithm checks whether the previous server's nearest neighbor is the current server. If it is, the movement cost is 1. Otherwise, the cost is based on the difference between the capacities of the two servers.
Once both cumulative arrays have been calculated, answering a query becomes straightforward. If the destination is to the right of the starting server, the algorithm uses rs to calculate the cost. If the destination is to the left, it uses ls instead. Subtracting the corresponding prefix values gives the total cost between the two positions.
This preprocessing approach avoids recalculating the route for every query.
Complexity Analysis
Let n be the number of servers and m the number of queries.
- Preprocessing: (O(n))
- Each query: (O(1))
- Total time complexity: (O(n+m))
The main optimization is moving the repeated work into preprocessing, allowing each query to be answered in constant time.
Question 2: Maximum Sum With No Consecutive Values
Problem Overview
The second question asked for the maximum possible sum under a restriction: two consecutive integer values could not both be selected.
Multiple elements could share the same value, so the first step was to calculate the total sum contributed by each distinct value. After grouping the elements this way, the problem became a variation of the classic House Robber problem.
For example, if several elements have the value 3, their contributions can be combined into a single total for 3. The algorithm then decides whether to take that total or skip it, depending on the neighboring values.
Approach
First, calculate the total contribution of every distinct value and sort the distinct values in ascending order.
The algorithm then processes these values using dynamic programming. Two states, p and q, maintain the best results from the previous positions. Here, p represents the optimal sum before the previous value, while q represents the best sum calculated up to the previous value.
For each new value, there are two possible cases.
Case 1: The current value is consecutive to the previous value.
If the difference between the current value and the previous value is 1, they cannot both be selected. The algorithm compares two options:
- Skip the current value and keep the existing best result.
- Take the current value's total contribution and add it to
p.
The larger result becomes the new optimal state.
Case 2: The current value is not consecutive to the previous value.
If the difference is greater than 1, selecting the current value does not conflict with the previous value. Its total contribution can therefore be added to the existing optimal sum.
After processing each distinct value, the two DP states are updated for the next iteration. Once all values have been considered, q contains the maximum achievable sum.
Complexity Analysis
Let n be the number of input elements and k the number of distinct values.
- Grouping values: (O(n))
- Sorting distinct values: (O(k\log k))
- Dynamic programming: (O(k))
- Total time complexity: (O(n+k\log k))
The dynamic programming step uses only two rolling states, so it requires (O(1)) additional space after the distinct values have been sorted and stored.
Key Takeaways From This Microsoft OA
These two HackerRank questions tested different problem-solving skills.
The first question rewarded preprocessing. By building directional cumulative cost arrays, the solution reduced repeated route calculations to constant-time queries.
The second question tested whether a familiar dynamic programming pattern could be recognized in a different setting. Grouping equal values and sorting them transformed the original problem into a House Robber-style selection problem.
For Microsoft OA preparation, it is worth practicing prefix sums, array preprocessing, sorting, and dynamic programming. Understanding why an optimization works is more useful than memorizing a specific solution, especially when a question introduces slightly different constraints.
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