Question

in old movies from the last century, criminals blackmail their victims by writing anonymous letters. to do that, they would cut out char- acters from some magazine or newspapers, and paste the characters onto the letter so their handwriting will not be revealed. we use a string to represent a letter. we also represent a magazine by a string. design an algorithm that takes an anonymous letter (a string) and a magazine (a string) as inputs, and returns a boolean value indicating if it is possible to construct the anonymous letter using characters from the magazine. analyze the running time of your algorithm. hint: do remember that we now live in the era of globaliza- tion: you cannot assume that there are only 26 characters. for example, java characters are encoded in the unicode standard, which is capable of representing cjk characters (chi- nese/japanese/korean). in short, the universe of characters is vast.

Answer 1

The task involves creating an algorithm to determine if an anonymous letter can be formed from characters in a given magazine, accounting for the vast character universe beyond just 26 English letters. The algorithm involves counting character frequencies in both the letter and the magazine and comparing them with a running time of O(n + m).

Step-by-step explanation:

In old movies from the last century, criminals often used a technique where they cut out characters from magazines or newspapers to compose anonymous letters, thereby avoiding handwriting recognition. To replicate this scenario in a modern practical problem, we can devise an algorithm that checks if it is possible to form an anonymous letter given the characters in a magazine. This involves iterating through each character in the letter and verifying if there is a sufficient number of the same characters in the magazine.

Algorithm:

1. Count the frequency of each character in the anonymous letter.
2. Count the frequency of each character in the magazine.
3. For each character in the anonymous letter, check if the magazine contains enough instances of that character.
4. If at any point, the magazine lacks enough characters to match the anonymous letter's needs, return false.
5. If all characters in the letter are accounted for using the magazine's characters, return true.

The running time of this algorithm would be O(n + m), where n is the length of the anonymous letter and m is the length of the magazine. This arises because we must go through each string completely to count the character frequencies.

The implementation details involve a more complex data structure that can accommodate the extensive Unicode character set, which includes not only ASCII characters but also CJK (Chinese, Japanese, Korean) characters and other possible symbols. This makes the traditional assumption of a limited character set, such as 26 letters in the English alphabet, obsolete in our globalized world, adding to the algorithm's complexity.