動的計画法

Finds the optimal way to parenthesize a chain of matrices to minimize the number of scalar multiplications. Classic dynamic programming problem from CLRS Chapter 15.

動的計画法を使用して冗長な計算を避けながらフィボナッチ数を効率的に計算します。メモ化の力を示し、指数時間の再帰的解を線形時間アルゴリズムに変換します。動的計画法の概念への古典的な入門です。

2つの列に同じ順序で存在する最長の部分列を見つけます。動的計画法を使用して解テーブルを構築します。DNA配列アライメント、ファイル差分ツール（diff）、盗作検出などの応用があります。

Dynamic programming algorithm that calculates the minimum number of single-character edits (insertions, deletions, substitutions) required to transform one string into another. Fundamental in spell checking, DNA sequence alignment, and natural language processing.

Classic dynamic programming problem where you must select items with given weights and values to maximize total value while staying within a weight capacity. Each item can only be taken once (0/1). Applications include resource allocation, portfolio optimization, and cargo loading.

Find the longest subsequence where all elements are in increasing order. Classic DP problem.

Elegant dynamic programming algorithm that finds the contiguous subarray with maximum sum in O(n) time. Combines greedy and DP principles by deciding at each step whether to extend the current subarray or start a new one. Essential for stock profit optimization, signal processing, and understanding DP optimization techniques.

Classic dynamic programming problem that finds the minimum number of coins needed to make a target amount. Demonstrates optimal substructure where the solution depends on solutions to smaller amounts. Widely applied in financial systems, vending machines, and resource allocation optimization.

Dynamic programming problem that finds the minimum number of cuts needed to partition a string into palindromic substrings. Uses DP to precompute which substrings are palindromes, then finds optimal cuts. Applications include text segmentation, DNA sequence analysis, and string optimization problems.