Path Finding Visualization vs Least Squares Curve Fit

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.

“Least Squares Curve Fit” is a user friendly, free of charge and free of ads app. User inputs point sets and chooses function types. Utilizing the Least Squares Linear Regression Method, the app calculates best fit curves, reports equations and draws graphs. Point sets can be stored in a table and are available after app is closed. Currently available function types are: 2D: 1. Line. 2. Parabola. 3. Polynomial up to 8th degree. 4. Circle. 5. Conic section (Ellipse or Hyperbola). 6. Trigonometric function as C + A1*cos(ω*x) + B1*sin(ω*x) + … + An*cos(n*ω*x) + Bn*sin(n*ω*x), where user can select n between 1 and 8 and enter any ω. 7. Exponential Function. 8. Bell Curve. 3D: 1. Plane. 2. Sphere. Also, there is an option to choose the Best Fit: the app goes through all the possible shapes and lists them in order from best to worst fit based on residuals. In some cases, when the standard Least Squares method with orthogonal projection does not work, best fit for Line, Parabola, Polynomial and Trigonometric functions can be calculated with SVD. Links to four other free apps by same developers are included in the app: 1. “Matrix Solver Step by Step” Linear Algebra Visual Guide. 2. “Polynomials and Linear Systems” Equation Solver. 3. “GraphMath” Graphing Calculator. 4. “Vectors and Planes” (and Spheres and Ellipsoids) 3D Geometry Guide. Developers hope to get feedback from users at graphmath@aol.com.