Question

Of the following pairs of strings, which comes first in lexicographic order? a. "Tom", "Jerry" b. "Ton", "Tonato" c. "church", "Churchin" d. "car manufacturer", "carburetor" e. "Harry". "hairy" f. "Pythen", "Car" 9\. "Ton", "Ton" h. "Car", "Carl" i. "car", "bar"

Short answer

Jerry, Ton, Churchin, carburetor, Harry, Car, Ton, Car, bar.

Step-by-step solution

Understand Lexicographical Order

Lexicographical order is similar to alphabetical order but applies to strings (series of characters). Each character is compared starting from the first character. The ordering is determined by the character's positions in the alphabet, with 'A' or 'a' being first, continuing through 'Z' or 'z'. In terms of ASCII, uppercase letters are valued lower than lowercase.

Compare 'Tom' and 'Jerry'

Compare the first letters, 'T' and 'J'. Since 'J' comes before 'T' in the alphabet, 'Jerry' comes first in lexicographical order.

Compare 'Ton' and 'Tonato'

Compare the first three letters 'Ton' with 'Ton'. Since they are identical, compare string lengths. 'Ton' is shorter than 'Tonato', thus 'Ton' comes first.

Compare 'church' and 'Churchin'

Compare the first letters 'c' and 'C'. Since lowercase 'c' has a higher ASCII value than uppercase 'C', 'Churchin' comes first.

Compare 'car manufacturer' and 'carburetor'

Compare the characters one-by-one: 'car' is the same in both strings, compare 'm' with 'b'. Since 'b' comes before 'm', 'carburetor' comes first.

Compare 'Harry' and 'hairy'

Compare the first letters 'H' and 'h'. Since uppercase 'H' comes before lowercase 'h', 'Harry' comes first.

Compare 'Pythen' and 'Car'

Compare the first letters 'P' and 'C'. Since 'C' comes before 'P', 'Car' comes first.

Compare 'Ton' and 'Ton'

Both strings are identical, hence order does not matter. 'Ton' comes first (or either can be considered first).

Compare 'Car' and 'Carl'

Compare the first three letters 'Car' with 'Car', then compare string lengths. 'Car' is shorter than 'Carl', thus 'Car' comes first.

Compare 'car' and 'bar'

Compare the first letters 'c' and 'b'. Since 'b' comes before 'c', 'bar' comes first.

Key concepts

String Comparison

When we talk about string comparison, it essentially means evaluating two strings to determine which one appears first in a specified order.
This order is usually lexicographic, similar to an alphabetical order, where the comparison begins with the first character. If the first characters are identical, the second characters are compared, and this process continues until a difference is found.
This is an essential concept often used in sorting algorithms and databases to organize and retrieve text data efficiently. In programming, string comparison is used frequently to accomplish tasks like sorting lists, verifying passwords, or filtering search results.

ASCII Value

When comparing strings, computers use ASCII (American Standard Code for Information Interchange) values. Each character is assigned a unique number from the ASCII table.
For example, the uppercase letter 'A' has an ASCII value of 65, while the lowercase 'a' is 97.
This explains why uppercase and lowercase letters are not considered equal; uppercase letters generally have smaller ASCII values than lowercase ones. When performing string comparisons programmatically, operations like using the '<', '>', and '==' operators allow comparisons based on ASCII values rather than the visible letter themselves.
Understanding ASCII values helps in knowing why certain characters precede others in lexicographic order.

Alphabetical Order

Alphabetical order is a familiar concept, usually used with words in a language to arrange them from A to Z.
Much like sorting books on a shelf, it helps in organizing lists in a readable and logical manner.
In the context of strings, alphabetical order refers to the arrangement of words based on the sequence of their characters. However, it gets a little more complex since computers use ASCII values to determine this order. For instance, 'Apple' would come after 'apple', owing to the differing case of the word's initial letters, which affects their ASCII values.
When dealing with both upper and lower case letters, the alphabetical order can differ from the expected arrangement if not properly accounted for.

Character Comparison

Character comparison is the action of checking individual characters from two strings against each other.
This process is key when determining the lexicographic order of strings. For each position, the character from one string is compared with the corresponding character from the other.
If the characters are the same, it moves on to the next position. However, as soon as a difference is observed, the decision is made based on the order of those differing characters. Character comparison relies on ASCII values for accuracy.
This technique is pivotal, especially when strings are similar in initial parts but diverge further along, making this an efficient method to determine precedence in lists.