Path Finding Visualization vs Polynomial Solver Step by Step

Want to see various pathfinding algorithms in action? With Path Finding Visualization, you can visualize, in action, six different algorithms. This app allows you to select your own starting and ending points, select the algorithm you want to use, and add walls in order to create boundaries. This app includes the following algorithms: Dijkstra's - Works by expanding outwards until it reaches the target node. Guaranteed to find the shortest path as long as there are not any negative weights. Bidirectional Dijkstra's - Dijkstra's algorithm from both sides. A* - Like Dijkstra's in that it favors nodes close to the starting point, but also favors nodes close to the ending point (heuristic). It does not guarantee the shortest path. A tie-breaker that prefers straight lines was included in order to prevent multiple nodes from having the same F values. Bidirectional A* - The A* algorithm from both sides. Breadth-First Search - Traverses through a graph one level at a time until it finds the target node. Since there are no weights, this algorithm does guarantee the shortest path. Depth-First Search - Traverses through a graph by going as deep as possible and then backtracking until it finds the target node. It does not guarantee the shortest path. Learning about or want to visualize any of the above algorithms in action? Download Path Finding Visualization today and have a better understanding of how each algorithm works.

Polynomial Solver Step by Step is a calculator, and, more importantly, a teaching tool. It is designed to help students of both basic and advanced levels. Basic Algebra functions: 1. Polynomial multiplication. 2. Polynomial long division with step by step explanation. 3. Algorithm for finding rational roots consisting of the following: a. Finding all possible rational roots. b. Eliminating the roots outside bounds. c. Performing polynomial long division for each of the roots. d. Adjusting bounds based on long division results if appropriate. Iterative polynomial solving algorithms for advanced-level students: 1. Durand-Kerner method. 2. Aberth method. 3. Newton method with both real and complex starting points. 4. Global (also known as "damped") Newton method with both real and complex starting points. 5. Laguerre method with both real and complex starting points. 6. Bairstow method. 7. Muller method. 8. Eigenvalues of ‘companion matrix’ (demonstration of QR algorithm for eigenvalue calculation is available in our “Matrix Solver Step by Step" app). Interactive graphs are available for: 1. Polynomial functions and their derivatives. 2. Aberth and Durand-Kerner method points on complex plane. 3. Newton, global Newton, Laguerre, and Muller algorithm steps. 4. Newton and global Newton method fractals / convergence images on complex plane 5. Laguerre method convergence images on complex plane 6 Bairstow method convergence images depending on initial approximation values. 7 Muller method convergence images depending on initial approximation values. (Images 4-7 have adjustable settings for area, resolution and shading). Links to online references are included. Please write to us if you like to have new features / chapters added! Developers welcome any feedback, please write to us at graphmath@aol.com.