The minimum edit distance algorithm is a dynamic programming algorithm commonly used in evaluating the similarity between strings. Given two strings, the source string $X$ of length $n$, and target string $Y$ of length $m$, we define D[i, j] as the edit distance between X[1..i] and Y[1..j]. Initialization begins with the distance from the empty string (e.g., $D[0,0] = 0$). The remaining cells are computed using a recurrence relation that determines the minimum cost among insertion, deletion, and substitution operations.