ποΈ Pattern 8: String DP (LCS/Edit Distance)
The Alignment Pattern: Compare two sequences character by character. State is dpi = answer for first i chars of string1 and first j chars of string2.
ποΈ π§¬ Sequence Alignment Overview
The DNA Matching Pattern: Find optimal alignment between two sequences using dynamic programming with insertions, deletions, and substitutions. Classic application in computational genomics.
ποΈ βοΈ Edit Distance (Levenshtein)
The Edit Distance problem, also known as Levenshtein Distance, is a fundamental string algorithm that measures the minimum number of single-character edits needed to transform one string into another. This problem perfectly demonstrates Pattern 4: String DP, where we build solutions by considering characters from both strings systematically.
ποΈ π Longest Common Subsequence (LCS)
The Longest Common Subsequence (LCS) is one of the most fundamental problems in dynamic programming, with applications ranging from DNA sequence analysis to version control systems. Understanding LCS deeply provides the foundation for solving many string-based optimization problems.
ποΈ π Needleman-Wunsch (Global Alignment)
The Needleman-Wunsch Algorithm represents a landmark achievement in computational biologyβthe first application of dynamic programming to biological sequence analysis. Developed by Saul B. Needleman and Christian D. Wunsch in 1970, this algorithm revolutionized how scientists compare DNA and protein sequences, enabling systematic analysis of evolutionary relationships and molecular structure-function connections.
ποΈ π― Smith-Waterman (Local Alignment)
The Smith-Waterman algorithm finds the best matching region between two sequences, even if the overall sequences are quite different. Unlike global alignment (Needleman-Wunsch), which aligns entire sequences, local alignment identifies conserved regions or motifs.