# Top Ten Dynamic Programming Algorithms created in Grasshopper for Rhino3D

# Dynamic_Programming_Algorithms

Top Ten Dynamic Programming Algorithms created in Grasshopper for Rhino3D

Dynamic Programming (DP) is a method for solving complex problems by breaking them down into simpler subproblems and storing the results of subproblems to avoid redundant computations. Here are ten popular algorithms that use dynamic programming:

**Fibonacci Sequence**

**Description:**Computes the nth Fibonacci number. The sequence starts with 0 and 1, and each subsequent number is the sum of the previous two.**Applications:**Mathematical computations, optimization problems.

**Knapsack Problem**

**Description:**Given a set of items, each with a weight and a value, determine the number of each item to include in a collection so that the total weight is less than or equal to a given limit, and the total value is as large as possible.**Applications:**Resource allocation, budget management.

**Longest Common Subsequence (LCS)**

**Description:**Finds the longest subsequence common to two sequences. A subsequence is a sequence derived by deleting some or no elements without changing the order of the remaining elements.**Applications:**Bioinformatics (DNA sequence analysis), text comparison.

**Longest Increasing Subsequence (LIS)**

**Description:**Finds the longest subsequence in a given sequence such that all elements of the subsequence are sorted in increasing order.**Applications:**Stock market analysis, string processing.

**Edit Distance (Levenshtein Distance)**

**Description:**Measures the minimum number of single-character edits (insertions, deletions, or substitutions) required to change one word into another.**Applications:**Spell checking, DNA sequence alignment, natural language processing.

**0/1 Knapsack Problem**

**Description:**A variation of the knapsack problem where each item can either be taken or not taken (i.e., binary choice).**Applications:**Resource allocation, decision making.

**Coin Change Problem**

**Description:**Given an unlimited supply of coins of given denominations, find the fewest number of coins that add up to a given amount.**Applications:**Monetary systems, making change in vending machines.

**Matrix Chain Multiplication**

**Description:**Determines the most efficient way to multiply a given sequence of matrices.**Applications:**Computer graphics, scientific computing.

**Partition Problem**

**Description:**Determines if a given set can be partitioned into two subsets such that the sum of elements in both subsets is the same.**Applications:**Fair division, load balancing.

**Rod Cutting Problem**

**Description:**Given a rod of length n and a list of prices that contains prices of all pieces of size smaller than n, determine the maximum value obtainable by cutting up the rod and selling the pieces.**Applications:**Manufacturing, resource optimization.

- 01 Knapsack Problem.gh
- Coin Change Problem.gh
- Edit Distance (Levenshtein Distance).gh
- Fibonacci Sequence.gh
- Knapsack Problem.gh
- Longest Common Subsequence (LCS).gh
- Longest Increasing Subsequence (LIS).gh
- Matrix Chain Multiplication.gh
- Partition Problem.gh
- Rod Cutting Problem.gh