SDE - 1

Step 1: I first analyzed the problem and recognized that it is a variation of the "minimum cost path" problem with a constraint on how far you can jump (a maximum of K indices). The brute force approach would involve exploring all possible paths, but this would be inefficient.

Step 2: I implemented a dynamic programming (DP) approach. I created a DP array dp[] where each entry dp[i] represents the minimum cost to reach index i. The key observation was that, for each index i, the minimum cost to reach i would depend on the minimum cost to reach any of the previous indices within the jump limit K (i.e., indices i-1, i-2, ..., i-K).

Step 3: The recurrence relation is:

dp[i] = A[i] + min(dp[j] for j in range(i-K, i) if j >= 0)
This step ensures that the cost to reach index i is the minimum cost from any of the previous K indices plus the cost at index i.

Step 4: I initialized the base case, dp[0] = A[0], as the starting point has no previous cost. Then, I iterated over the array to fill the dp[] array based on the recurrence relation.

Step 5: Finally, I returned the value at dp[N-1], which gives the minimum cost to reach the last index.

Tip 1: Read Galvin for OS thoroughly: It provides in-depth explanations and examples for key concepts like semaphores, memory management, and other OS fundamentals. This textbook is essential for grasping operating system theory.
Tip 2: Understand how semaphores work in different scenarios: Practice using semaphores in multi-threading and inter-process communication problems. Focus on different use cases like producer-consumer, reader-writer problems, and resource allocation.
Tip 3: Practice OS concepts with real-world problems: Solve problems related to deadlocks, resource allocation, memory management, and process synchronization. This will improve your ability to apply theoretical knowledge in practical scenarios and interviews.

Tip 1: IPC allows processes to exchange data and synchronize their execution, using OS-provided primitives like semaphores and mutexes to ensure controlled access to shared resources.
Tip 2: Scheduling determines which process or thread gets to use the CPU at any given time, using algorithms like Round Robin, FCFS, and Priority Scheduling.
Tip 3:Memory management involves allocating and managing the computer’s memory resources, utilizing techniques like paging, segmentation, and virtual memory.

.Step 1:
I first looked at the problem's requirements, which involved generating a random permutation in-place without using additional space. I realized the Fisher-Yates (or Knuth) shuffle algorithm was a perfect fit. This algorithm guarantees a uniform distribution of permutations.

Step 2:
The Fisher-Yates algorithm works by iterating through the array from the last element to the second element. At each step, it selects a random index between 0 and the current index and swaps the two elements. This ensures that every element has an equal chance of being placed in any position.

Step 3:
I implemented the Fisher-Yates algorithm:

I started by iterating from the last index to the second index.
For each element, I generated a random index between 0 and the current index.
Then I swapped the current element with the randomly chosen element.
This process is repeated until the entire array has been shuffled.

Step 4:
Finally, I tested the solution by running it multiple times to ensure the array is shuffled randomly and uniformly without using any extra space.