I'm struggling to grasp a specific point in a Quicksort exercise. I have this 0-indexed array: [74, 55, 92, 80, 81, 95, 88, 19, 52, 38, 71, 4]. The task is to sort it in ascending order using the Quicksort algorithm, where the `partition()` function takes the rightmost element as the pivot. My main question is: what is the value of `k` that the `partition()` function returns after the third call? The solution suggests that it should be k = 1, but I'm unable to follow the steps or logic that leads to that conclusion. Can anyone help clarify?
2 Answers
To understand what `k` is, think of it as the index of the pivot after partitioning completes. You're right about the confusion regarding the third call. When we talk about partition calls in Quicksort, the order of calls isn't linear due to the recursive nature of the function.
1. In the first call, you use 4 as the pivot and it moves to index 0.
2. The second call uses 74 as the pivot from the right subarray.
3. Then you partition a smaller left subarray, leading to 4 being in the position of index 1.
So, they probably got k = 1 from that final step after sorting the left subarray. It's essential to track indices relative to the current partition, not just the original array.
Looking at the steps can help clarify this.
1. First call: pivot is 4, it returns k = 0 after swapping.
2. Then with the right subarray, you go through another partitioning, leading to k = 6 for pivot 74 in the next call.
3. Finally, you analyze a smaller section where the pivot's new position lands at index 1.
Keep in mind, the index is always relative to the ongoing partition, not the overall array. So, that’s why you end up with k = 1.
Exactly! The key is keeping track of the subarrays during recursion. When you partition, the indices shift based on the current context. It might take a few tries to get the hang of it, but once you do, it's much easier to visualize the process.