Dynamic Programming Questions
The Edit Distance problem is a measure of similarity between two strings. It calculates the minimum number of operations required to transform one string into another, where the operations can be insertion, deletion, or substitution of a single character.
Dynamic Programming can be used to solve the Edit Distance problem efficiently. The problem can be broken down into smaller subproblems, where the edit distance between two substrings is calculated. By solving these subproblems and storing their results in a table, we can build up the solution for larger subproblems until we reach the final solution.
The dynamic programming approach involves creating a matrix of size (m+1) x (n+1), where m and n are the lengths of the two strings. Each cell in the matrix represents the edit distance between the corresponding substrings. The first row and column of the matrix are initialized with values representing the edit distance between an empty string and the corresponding substring.
Then, we iterate through the matrix, filling in each cell based on the values of its neighboring cells. The edit distance between two substrings can be calculated by considering three possible operations: insertion, deletion, or substitution. The value in each cell is determined by taking the minimum of the values from the neighboring cells, plus 1 if a substitution is required.
Finally, the value in the bottom-right cell of the matrix represents the minimum edit distance between the two strings. This value can be returned as the solution to the Edit Distance problem.
Overall, Dynamic Programming allows us to solve the Edit Distance problem efficiently by breaking it down into smaller subproblems and using a table to store and reuse the results of these subproblems.