«Favorites dynamic programming problems»

A module for Python in C that solves some dynamic programming problems.

Table of content

1. Algorithms
2. Module
3. Contributors
4. License

Algorithms

The selected tasks are the following tasks.

1. 0–1 Knapsack problem

Short description

In the 0–1 Knapsack problem, we are given a set of items, each with a weight and a value, and we need to 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.

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2. Rod Cutting Problem

Short description

Given a rod of length n and a list of prices of rods of length i, where 1 <= i <= n, find the optimal way to cut the rod into smaller rods to maximize profit.

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3. Coin Change Problem

Short description

Given an unlimited supply of coins of given denominations, find the total number of distinct ways to get the desired change.

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4. Coin Change-Making Problem

Short description

Given an unlimited supply of coins of given denominations, find the minimum number of coins required to get the desired change. That is, you need to find the minimum number of coins to exchange and withdraw this set.

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5. The Levenshtein Distance Problem

Short description

Edit distance is a way of quantifying how different two strings are from one another by counting the minimum number of operations required to transform one string into the other.

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6. Matrix Chain Multiplication Problem

Short description

Matrix chain multiplication is an optimization problem concerning the most efficient way to multiply a given sequence of matrices. The problem is not actually to perform the multiplications, but merely to decide the sequence of the matrix multiplications involved.

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7. Minimum Cost to Reach Last Cell of Matrix From Its First Cell Problem

Short description

Given an M × N matrix where each cell has a cost associated with it, find the minimum cost to reach the last cell (M-1, N-1) of the matrix from its first cell (0, 0). We can only move one unit right or one unit down from any cell, i.e., from cell (i, j), we can move to (i, j+1) or (i+1, j).

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8. Const Cost to Reach Last Cell of Matrix From Its First Cell Problem

Short description

Find the number of paths of a given cost from the upper left to the lower right element of the matrices.

9. Minimum Sum Partition Problem

Short description

Given a set of positive integers S, partition set S into two subsets, S1 and S2, such that the difference between the sum of elements in S1 and the sum of elements in S2 is minimized.

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10. Find All N-digit Binary Strings Without Any Consecutive 1's Problem

Short description

Given a positive integer n, count all n–digit binary strings without any consecutive 1's.

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Module

The task is decomposed into three modules:

1. Change-Making Problem
2. Knapsack Problem
3. FDPP (other problems)

Install

$ ./run

And also you can instant test installed packages

Usage

import fdpp
import knapsack
import change_making

Contributors

	Egor Bronnikov
	Roman Postolnik

License

dynamic-programming provided under the terms of the GPL-3.0 license. See the LICENSE files for details.

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_{👨‍💻 endygamedev}