This is a source code for projects and applications of Algorithmic Thinking class on Coursera.

The goal of this Module is to get you started with simple, yet central, concepts in graph theory, simple principles of discrete probability, and a light version of hypothesis testing.

For your first project, you will write Python code that creates dictionaries corresponding to some simple examples of graphs. You will also implement two short functions that compute information about the distribution of the in-degrees for nodes in these graphs. You will then use these functions in the Application component of Module 1 where you will analyze the degree distribution of a citation graph for a collection of physics papers. This final portion of module will be peer assessed.

The goal of this Module is for you to learn about graph exploration, how to use it to compute the connected components of graphs, and how to use the latter structure to reason about the resilience of networks. The module emphasizes the efficiency of algorithms, asymptotics, and the significance of efficient implementations. You will be exposed again to random graphs, graph properties, and the use of data structures like queues.

For the Project component of Module 2, you will first write Python code that implements breadth-first search. Then, you will use this function to compute the set of connected components (CCs) of an undirected graph as well as determine the size of its largest connected component. Finally, you will write a function that computes the resilience of a graph (measured by the size of its largest connected component) as a sequence of nodes are deleted from the graph.

You will use these functions in the Application component of Module 2 where you will analyze the resilience of a computer network, modeled by a graph. As in Module 1, graphs will be represented using dictionaries.

The goal of this Module is for you to learn about the closest pair problem, how to solve it using the divide-and-conquer algorithmic strategy, and how to use the solution in algorithms for data clustering, which is a very powerful tool in the toolkit of any data scientist. You will also use the programs you write to cluster cancer data collected from many counties across the United States. The module emphasizes divide-and-conquer algorithms, their recursive implementations, and how to analyze the running times of such algorithms.

For the Project and Application portion of Module 3, we will implement and assess two methods for clustering data. For Project 3, you will implement two methods for computing closest pairs and two methods for clustering data. In Application 3, you will then compare these two clustering methods in terms of efficiency, automation, and quality.

The goal of this Module is for you to learn about the pairwise sequence alignment problem, how to solve two versions of it (local and global) using the dynamic programming (DP) algorithmic strategy, and how to use the solutions in two applications involving genomic data and spell checking. The module emphasizes dynamic programming algorithms and their implementation.

In Homework 4, we explored the use of dynamic programming in measuring the similarity between two sequences of characters. Given an alphabet Σ and a scoring matrix M defined over Σ∪{′−′}, the dynamic programming method computed a score that measured the similarity of two sequences X and Y based on the values of this scoring matrix. In particular, this method involved computing an alignment matrix S between X and Y whose entry Sij scored the similarity of the substrings X[0…i−1] and Y[0…j−1]. These notes provided an overview of the process.

In Project 4, we will implement four functions. The first pair of functions will return matrices that we will use in computing the alignment of two sequences. The second pair of functions will return global and local alignments of two input sequences based on a provided alignment matrix. You will then use these functions in Application 4 to analyze two problems involving comparison of similar sequences.