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Applied Python Algorithms:

WE USED PYTHON TO DO:

• Start of Course Python Tricks for famous problems: Iteration, Cube Roots, Binary to Decimal, Bisection Search, Newton Raphson Method, Square Roots, Iterative Power, X to the Power N, Understanding Root Finding, Area and Circumference of a Circle, Recursive verses Iterative Algorithms, Fibonacci, Factorial, Palindrome, Multiply, Towesr of Hanoi, Functions as Parameters, Common Divisors, Duplicate Removal Lists, Lists of Lists, List Reversal, Is It a Palimdrome?, String to Int, Hash string, Dictionary with Int Keys


• Financial Calculations in Python Example : Financial calculations demonstrating various speeds of paying off debt


• Algorithms for guessing, root finding, and using Python to write hang man and scrabble games : Successive Approximation Method, Newton Raphson Method of Finding Roots of Polynomial Functions, and the Hang Man and Word Find Games in PythonHang Man and Word Find Games programmed in Python.


• Caesar Cipher Encryption and Decryption Code and Secret Messages, along with Code to detect specific strings in other strings using only indexing, slicing, concatenation with a recursive function and no loops, and also, code to emulate and old fashioned type writer : Exercises in Python.


• Parsing web pages such as Yahoo and Google to create triggers when certain phrases were found within the web pages : We built a Python program to monitor and filter news feeds over the internet.


• Used a graphic of a tiled floor and various types of Python made robots to demonstrate how best and efficiently it could be cleaned by these : Exercises In Python.


• Stochastic Simulation of Patient Virus Population Dynamics And Treatment Regimens: cases where you have a number of diseased cells, antibiotics, resistances to antibiotics, and a percentage you need to achieve to remove the illness, and calculation to compare using and not using a drug for it : Exercises In Python.


• Stochastic Simulation of Patient Virus Population Dynamics: Effect of Delaying Drug Treatment on Patient Disease, Using 2 Drugs, and Patient non-Compliance : Exercises In Python.


• Brute Force Search, a variation of the Depth First Search, on a map of the MIT campus minimizing time outdoors : Exercises In Python.


• Breadth First Search Search, Depth First Search, Puzzles, Max Clique Subgraphs, Tree and Graph Algorithms, and Power Sets : Exercises in tree data search efficiency and optmization in Python. We explored graphs to find paths that represent physical networks. They are used for communication networks, circuits, genes, social networks, disease populations, etc.
  


• Optimization Problems and Dynamic Programming : fitting data to linear and quadratic curves, normal distributions, measuring goodness of fit of data to a curve, uniform distributions, estimating Pi, Monty Hall Problems, number of samples needed for a coin flip experiment, variance and standard deviation, plotted histograms, causal and predictive nondeterminism, stochastic processes, monte carlo simulations, hash tables, random walks and simulation models, examined different algorithms for searching and sorting and their Big O Notation performances. This lecture example Python code demonstrated code optimization. You start with an objective function and a set of constraints the solution must satisfy. Examples were the n-queens problem, where you place n-queens on an NxN board so that no 2 queens attack each other (no 2 queens share the same row, column or diagonal). Other examples were bin packing, cutting stock and min cut networks and the traveling salesmen problem. The challenge shown was that these problems are "hard" to solve. Often finding optimal solutions requires examining all possible combinations of items. The time to examine all combinations grows exponentially with the number of items. "Real World" problems have a large number of items. Dynamic Programming : The dynamic programming using optimal substructure and overlapping subproblems. In the Fibonacci example the memoize function was used to demonstrate using function arguments as a sequence, which works for immutable / hashable arguments. The memoize function remembers previously computed answers, much like a cache does in hardware.