Find the optimal binary search tree based on probabilities of the search keys

To view matrix multiplication ordering as an optimal triangulation problem, label the sides of the regular polygon (except the top) with the matrix names, and the vertices of the polygon with the matrix dimensions. Label each diagonal of a triangulation with the product of the two labels on the triangle below it (below meaning opposite from the top edge).

The top edge will end up labeled with a formula for multiplying all the matrices together. Conversely, from any such formula we can determine a triangulation. To count the number of operations for matrix multiplication, we should simply let @=sum and q(T) be the product of the three numbers written at the corners of each triangle T.

https://www.ics.uci.edu/~eppstein/260/011023/

https://github.com/zizzo/optimal-bst
guys i know that you got the NumBy download for the calculation of binaries ( the lengh is key of 3072 bits for a security of 280 binary operations)

JavaPrograms/MatrixChainMultiplication.java

AND FINALLY MEMORY

Messiah code (scanning the polygon pointers )

Plot Digitizer

Revisions SourceForge Project Downloads Forums Joe's Java Library

Description Plot Digitizer is a Java program used to digitize scanned plots of functional data. Often data is found presented in reports and references as functional X-Y type scatter or line plots. In order to use this data, it must somehow be digitized. This program will allow you to take a scanned image of a plot (in GIF, JPEG, or PNG format) and quickly digitize values off the plot just by clicking the mouse on each data point. The numbers can then be saved to a text file and used where ever you need them. Plot Digitizer works with both linear and logarithmic axis scales. Besides digitizing points off of data plots, this program can be used to digitize other types of scanned data (such as scaled drawings or orthographic photos). To make the digitizing task easier, this program includes many handy features. For example: You can recalibrate the Y axis without having to recalibrate the X axis (multiple sets of data are commonly plotted with the same X axis). You can insert points between two already digitized points by right clicking and choosing "Insert" from the pop-up menu. You can delete points by right-clicking on the points and choosing "Delete". You can move points by clicking and dragging them. You can compute the length of a digitized curve and you can compute the area of a digitized polygon. You can zoom images in and out. You can save calibrations for an image for later use, and finally, there is unlimited undo/redo. http://plotdigitizer.sourceforge.net/

Slope-intercept equation from graph (messiah decrypter part I)

https://www.khanacademy.org/math/algebra-home/alg-linear-eq-func/alg-writing-slope-intercept-equations/e/slope-intercept-equation-from-graph

Slope-intercept equation from graph

Problem

Find the equation of the line.
Use exact numbers.

$y=$y, equals 

$x+$x, plus 

$\small{1}$$\small{2}$$\small{3}$$\small{4}$$\small{5}$$\small{6}$$\small{7}$$\small{8}$$\small{9}$$\small{\llap{-}2}$$\small{\llap{-}3}$$\small{\llap{-}4}$$\small{\llap{-}5}$$\small{\llap{-}6}$$\small{\llap{-}7}$$\small{\llap{-}8}$$\small{\llap{-}9}$$\small{1}$$\small{2}$$\small{3}$$\small{4}$$\small{5}$$\small{6}$$\small{7}$$\small{8}$$\small{9}$$\small{\llap{-}2}$$\small{\llap{-}3}$$\small{\llap{-}4}$$\small{\llap{-}5}$$\small{\llap{-}6}$$\small{\llap{-}7}$$\small{\llap{-}8}$$\small{\llap{-}9}$$y$$x$

Stuck?