The pseudocode provided is an implementation of Bubble Sort. Let’s analyze the number of swap operations in the case where the array is initially sorted in descending order:
Step 1: Understanding the Loop Execution
The outer loop runs from \( i = 0 \) to \( n-2 \), where \( n = 30 \). Therefore, the outer loop executes \( 29 \) times.
The inner loop runs from \( j = 0 \) to \( n-i-2 \), meaning the number of iterations decreases as \( i \) increases.
Step 2: Calculating Total Comparisons
The number of comparisons for each value of \( i \) is:
- For \( i = 0 \), the inner loop runs \( n-1 \) times.
- For \( i = 1 \), the inner loop runs \( n-2 \) times.
- For \( i = 2 \), the inner loop runs \( n-3 \) times.
- …
- For \( i = n-2 \), the inner loop runs 1 time.
Thus, the total number of comparisons is the sum of the first \( n-1 \) integers:
\[ \text{Total comparisons} = (n-1) + (n-2) + \ldots + 1 = \frac{n(n-1)}{2} \] For \( n = 30 \):
\[ \text{Total comparisons} = \frac{30 \times 29}{2} = 435 \] Step 3: Number of Swaps
In Bubble Sort, a swap occurs every time a comparison finds that \( A[j] > A[j+1] \). Since the array is initially sorted in descending order, every comparison will result in a swap.
Thus, the number of swaps is equal to the total number of comparisons, which is 435.
Final Answer: The number of swap operations performed is 435.
Consider game trees Tree-1 and Tree-2 as shown. The first level is a MAX agent and the second level is a MIN agent. The value in the square node is the output of the utility function.
For what ranges of \( x \) and \( y \), the right child of node B and the right child of node E will be pruned by the alpha-beta pruning algorithm?
Bird : Nest :: Bee : __________
Select the correct option to complete the analogy.
In the diagram, the lines QR and ST are parallel to each other. The shortest distance between these two lines is half the shortest distance between the point P and the line QR. What is the ratio of the area of the triangle PST to the area of the trapezium SQRT?
Note: The figure shown is representative
Consider the relationships among P, Q, R, S, and T:
• P is the brother of Q.
• S is the daughter of Q.
• T is the sister of S.
• R is the mother of Q.
The following statements are made based on the relationships given above.
(1) R is the grandmother of S.
(2) P is the uncle of S and T.
(3) R has only one son.
(4) Q has only one daughter.
Which one of the following options is correct?
According to the map shown in the figure, which one of the following statements is correct?
Note: The figure shown is representative.