Following and writing algorithms：練習問題

A linear search algorithm is used to find the value 25 in the following list: [10, 5, 25, 40, 15].
Assuming the algorithm stops as soon as the item is found, how many comparisons are made?

Which of the following statements accurately compares the worst-case time efficiency of Binary Search and Linear Search on a very large, sorted list containing \(n\) elements?

Hand-trace the following algorithm and determine the final value of B:

A = 6
B = 1
REPEAT
    A = A - 2
    B = B * 3
UNTIL B > A

What is the defining characteristic of an algorithm according to the standard definition in computer science?

Consider the list [8, 3, 6, 1]. After the first complete pass of the bubble sort algorithm (starting from the left and comparing adjacent elements), what is the state of the list?

What is the fundamental characteristic of an algorithm, as defined in computer science?

Explain the primary purpose of hand-tracing an algorithm using a set of test data.

Explain the importance of using erroneous test data when hand-tracing an algorithm intended for a production environment.

Consider the following algorithm expressed in pseudocode:

START
X = 15
Y = 7
Z = 0
IF X > Y THEN
    Z = X MOD Y
    X = X DIV Y
ELSE
    Z = Y - X
    X = Y * 2
END IF
Y = Y + Z
OUTPUT X
OUTPUT Y
OUTPUT Z
END

Trace the execution of this algorithm, assuming standard integer arithmetic (DIV is integer division and MOD is the remainder), and state the final output values of X, Y, and Z.

The following pseudocode processes an array Items of integers. Assume Items = [10, 4, 1, 9, 6] and the array indices run from 1 to 5 ( =5).

FUNCTION ProcessList(Items, n)
1. Total = 0
2. FOR I = 1 TO n DO
3.     Current = Items[I]
4.     IF Current < 5 AND Current MOD 2 == 0 THEN
5.         Total = Total + 1
6.     ELSE IF Current >= 10 OR Current MOD 3 == 0 THEN
7.         Total = Total + 2
8.     ELSE
9.         Total = Total + 0
10.     END IF
11. END FOR
12. RETURN Total

Hand-trace the execution of ProcessList(Items, 5) and state the final value returned by the function.