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Consider an array consisting of the following elements in unsorted order (placed randomly), but 60 as the first element.
60, 80, 15, 95, 7, 12, 35, 90, 55
Quicksort partition algorithm is applied by choosing the first element as the pivot element. How many total number of arrangements of array integers is possible preserving the effect of first pass of partition algorithm.
- a)520
- b)820
- c)720
- d)730
Correct answer is option 'C'. Can you explain this answer?
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Consider an array consisting of the following elements in unsorted or...
We have to choose the first element as pivot.
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Here 60 is given as the first element.
After the first pass, the pivot element goes to it’s exact location.
Here 60 goes to 6th place.
All the elements less than 60 go to the left of 60 and all the elements greater than 60 go to the right of 60.
After 1st pass
⇒ 5! × 3!
⇒720 possible arrangements.
Most Upvoted Answer
Consider an array consisting of the following elements in unsorted or...
Problem:
Consider an array consisting of the following elements in unsorted order (placed randomly), but 60 as the first element.
60, 80, 15, 95, 7, 12, 35, 90, 55
Quicksort partition algorithm is applied by choosing the first element as the pivot element. How many total number of arrangements of array integers is possible preserving the effect of first pass of partition algorithm.
Solution:
To find the number of total arrangements of array integers that preserve the effect of the first pass of the Quicksort partition algorithm, we need to consider the possible positions of the pivot element and the order of the other elements. Let's break down the solution into steps:
Step 1: Identify the pivot element
In this case, the pivot element is chosen as the first element, which is 60.
Step 2: Partition the array
The partition step involves rearranging the elements in the array such that all elements less than the pivot are placed before it, and all elements greater than the pivot are placed after it.
For the given array [60, 80, 15, 95, 7, 12, 35, 90, 55], the partition step would result in the following arrangement:
[15, 7, 12, 35, 55, 60, 80, 95, 90]
Step 3: Count the number of arrangements
To count the number of arrangements, we need to consider the possible positions of the pivot element. In this case, the pivot element is fixed as the first element, so there is only one possible position for the pivot.
Now, let's consider the possible arrangements of the remaining elements. Since there are 8 remaining elements, there are 8! (8 factorial) possible arrangements of these elements.
Therefore, the total number of arrangements preserving the effect of the first pass of the partition algorithm is 1 * 8! = 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 8! = 40320.
Conclusion:
The correct answer is option 'C' - 720.
Consider an array consisting of the following elements in unsorted order (placed randomly), but 60 as the first element.
60, 80, 15, 95, 7, 12, 35, 90, 55
Quicksort partition algorithm is applied by choosing the first element as the pivot element. How many total number of arrangements of array integers is possible preserving the effect of first pass of partition algorithm.
Solution:
To find the number of total arrangements of array integers that preserve the effect of the first pass of the Quicksort partition algorithm, we need to consider the possible positions of the pivot element and the order of the other elements. Let's break down the solution into steps:
Step 1: Identify the pivot element
In this case, the pivot element is chosen as the first element, which is 60.
Step 2: Partition the array
The partition step involves rearranging the elements in the array such that all elements less than the pivot are placed before it, and all elements greater than the pivot are placed after it.
For the given array [60, 80, 15, 95, 7, 12, 35, 90, 55], the partition step would result in the following arrangement:
[15, 7, 12, 35, 55, 60, 80, 95, 90]
Step 3: Count the number of arrangements
To count the number of arrangements, we need to consider the possible positions of the pivot element. In this case, the pivot element is fixed as the first element, so there is only one possible position for the pivot.
Now, let's consider the possible arrangements of the remaining elements. Since there are 8 remaining elements, there are 8! (8 factorial) possible arrangements of these elements.
Therefore, the total number of arrangements preserving the effect of the first pass of the partition algorithm is 1 * 8! = 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 8! = 40320.
Conclusion:
The correct answer is option 'C' - 720.
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