Frontend Developer

Implement and Apply Edit Distance Algorithms

Question Statement:
Develop two string comparison functions: one that calculates the standard Levenshtein distance and another that calculates a cost-constrained version of the Levenshtein distance, both optimized for correctness and efficiency (O(n × m) time complexity, where n and m are the lengths of the strings). Write these functions in a programming language of your choice.

For the standard function levenshtein_distance(str1, str2), test it using the following input-output pairs and include snapshots of your results:

• Input: "kitten", "sitting" → Expected Output: 3
• Input: "flaw", "lawn" → Expected Output: 2
• Input: "algorithm", "logarithm" → Expected Output: 3

Based on the levenshtein_distance function, build a basic spell checker. Given a dictionary of words, the program should suggest the closest match for a user-provided input. For example, with the dictionary ["cat", "bat", "rat", "drat", "dart"] and the input "dat", your program should return "bat" or another word with the smallest edit distance.

Calculates the minimum cost to convert one string into another based on user-defined costs for insertion (Ci), deletion (Cd), and substitution (Cs). Test your function using the following input and submit snapshots of your output:

Input: "kitten", "sitting" with Ci = 1, Cd = 2, Cs = 3 → Expected Output: 7

Ninja has a 'GRID' of size 'R' X 'C'. Each cell of the grid contains some chocolates. Ninja has two friends Alice and Bob, and he wants to collect as many chocolates as possible with the help of his friends.

Initially, Alice is in the top-left position i.e. (0, 0), and Bob is in the top-right place i.e. (0, ‘C’ - 1) in the grid. Each of them can move from their current cell to the cells just below them. When anyone passes from any cell, he will pick all chocolates in it, and then the number of chocolates in that cell will become zero. If both stay in the same cell, only one of them will pick the chocolates in it.

If Alice or Bob is at (i, j) then they can move to (i + 1, j), (i + 1, j - 1) or (i + 1, j + 1). They will always stay inside the ‘GRID’.

Your task is to find the maximum number of chocolates Ninja can collect with the help of his friends by following the above rules.

Example:

Input: ‘R’ = 3, ‘C’ = 4
       ‘GRID’ = [[2, 3, 1, 2], [3, 4, 2, 2], [5, 6, 3, 5]]
Output: 21

Initially Alice is at the position (0,0) he can follow the path (0,0) -> (1,1) -> (2,1) and will collect 2 + 4 + 6 = 12 chocolates.

Initially Bob is at the position (0, 3) and he can follow the path (0, 3) -> (1,3) -> (2, 3) and will colllect 2 + 2 + 5 = 9 chocolates.

Hence the total number of chocolates collected will be 12 + 9 = 21. there is no other possible way to collect a greater number of chocolates than 21.

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