1. Flowgorithm Array
2. Flowgorithm Online
3. Flowgorithm Examples
4. Flowgorithm Call

• Flowgorithm is a free beginner's programming language that is based on simple graphical flowcharts. Typically, when a student first learns to program, they often use one of the text-based programming languages.
• EXPLORE: Flowgorithm's Code Viewer Did your flowchart match the pseudocode? Well, Flowgorithm has the ability to convert your flowchart to traditional text-based programs. Select the 'Source Code Viewer' from the Tools menu. A new window will open. It will show, at first, your program in Java – which is a very popular language.

Only one dimensional arrays are supported in the Flowgorithm and
limited to the integer, real (floats), boolean and string types.
However, two dimensional arrays are natively required in many algorithms.
Vectors and matrices are indexed from '1' not from '0' .
This page describes, how two dimensional matrices can be defined, used and printed.
It is recommended to understand how the Flowgorithm source files ( *.fprg files) can be modified directly for additional libraries inclusion.
Please, see EDITING Flowgorithm Files
(unfortunately, a library handling is not available in the current Flowgorithm version, perhaps a specialized tool for *.fprg files will be available)

Apr 13, 2021 Flowgorithm 13 Aprile 2021 Marco D'Isanto Flowgorithm, Programmazione 0 Scriviamo un algoritmo che, dato in ingresso un numero num, restituisca il numero di divisori pari di num.

The Flowgorithm uses indexing from ZERO, i.e. the A[0], ... , A[N-1], which might cause some problems in mathematical formula use.
The following functionality is available (indexing [1..N] is to be used consistently).
In mathematics, usually the first index is ONE, i.e. A[1] in the vector case, resp. A[1,1] in the case of matrices

Flowgorithm Array

Declaration (N, M can be integer constants or variables)

• one dimensional arrays: A[1:N] - declare A[N] - generates actually a vector
• two dimensional arrays: A[1:N,1:M] - declare A[N*M] - generates actually vector for a matrix storing.

Indexing
As the Flowgorithm supports one dimensional arrays indexed from ZERO, each element of two dimensional array has to be re-indexed independently with checking the bounds of a vector or a matrix,
e.g. a mathematical formula k = A[i,j] is to be rewritten as k = A[ Index ( i, j, N, M )] in the case of matrix with integer elements.
All indexing starts from ONE, i.e. [1..N].

Vector and matrix support (indexing from '1')

The following re-indexing functions can be used for matrices; in the case of a vector,
elements can be accessed directly by decreasing index by '1', but without bounds detailed control.
(a vector A has N elements, a matrix A - has N rows, M columns):

The vector case (indexing from '1')

• Index1 ( i, N ) - returns integer value of the physical index for the integer vector element A[i] (matrix type independent)

The matrix case [2D arrays] (indexing from '1')

• Index ( i, j, N, M ) - returns the integer value of the physical index for the matrix element A[i,j] of the size NxM (matrix type independent)
• Index2 ( i, j, N ) - returns the integer value of the physical index for the matrix element A[i,j] of the size NxN (square matrix; matrix type independent)

Printing vectors and matrices with formatting (indexing from '1', resp. '1,1')
The Flowgorithm supports only 'non-formatted' output of one value only. However, formatted output is required in many cases.
Also for matrix output formatting is needed to see columns.
Unfortunately, output natively uses proportional font type on the screen.
However if output is stored, a non-proportional font type, e.g. Consolas in the Notepad, can be used.
For formatted print the following calls can be used:

Print of a value (it is expected, that d <= length of characters printed)

• PrintI ( i, d ) - prints integer value on the d positions
• PrintR ( r, d1, d2 ) - prints integer value on the d1 positions with d2 decimal points
• PrintS ( s, d ) - prints integer value on the d positions
• PrintB ( b, d ) - prints integer value on the d positions

Print of a vector

• PrintVectorI (A, N, d ) - prints integer vector elements on d positions (N rows, M columns)
• PrintVectorR (A, N, d1, d2 ) - prints real vector elements on d1 positions with d2 decimals (N rows, M columns)
• PrintVectorS (A, N, d ) - prints string vector elements on d positions (N rows, M columns)
• PrintVectorB (A, N, d ) - prints boolean vector elements on d positions (N rows, M columns)

Print of a matrix

• PrintMatrixI (A, N, M, d ) - prints integer matrix A elements on d positions (N rows, M columns)
• PrintMatrixR (A, N, M, d1, d2 ) - prints real matrix A elements on d1 positions with d2 decimals (N rows, M columns)
• PrintMatrixS (A, N, M, d ) - prints string matrixA elements on d positions (N rows, M columns)
• PrintMatrixB (A, N, M, d ) - prints boolean matrix A elements on d positions (N rows, M columns)

Operations with vectors and matrices

• CopyVector (A, B, N) - copy a vector A to vector B of the size N
• CopyMatrix (A, B, N, M) - copy a matrix A to matrix B of the size N rows, M columns
• Transpose (A, B, N, M) - transpose a matrix A (size N rows, M columns) to a matrix B (size M rows, N columns)
• DotProduct (A, B, N) - result is a real value
• CrossPruduct (A, B, C, N) - result is a vector C (actually the outer product in the case N>3)
• GeometricProduct (A, B, C, D, N) - result is a bi-vector C and a scalar value D

Solution of a linear equations

• SolveGaussSeidel (A, x, b, N) - solution of a system of linear equations Ax = b, size of the matrix A is N by N, x is vector of unknowns, b is the right side
  (the Gauss elimination method is used)
• Solve (A, x, b, N) - solution of a system of linear equations Ax = b, size of the matrix A is N by N, x is vector of unknowns, b is the right side
  (the iterative method is used, matrix A must be strictly positive definitive)

Making a decision based on a single value (if statements)

When the computer needs to “decide” which branch of a flowchart (or algorithm to follow) it evaluates a variable against some condition that we place on it. These decisions are frequently documented in a condition/action table.For instance for the decision below: if age >= 18 we could document it like this:

The diamond shape is used to designate a decision. The “if” is not listed, just the condition.

• Declare a variable for age
• Output the instruction to the user and store the result in age
• Add an IF shape, then double-click the shape to add the condition

• Back on the flowchart, click on each branch of the if statement and add an action that the program will take (i.e. the message that is output to the user)

Flowgorithm Online

Making a decision based on multiple values (if statements with Boolean operators)

In the case of multiple conditions that need to be met, we would use Boolean operators to chain two or more conditions together. Boolean operators:

• AND – all conditions must be true in order to execute the code
• OR – only one of the conditions must be true in order to execute the code
• ! - NOT means that the code will only execute if the condition is not true

For instance for the decision below: if age >= 18 AND enrolled = true we could document it like this:

Making decisions using multiple values with != (if statements checking for a negative condition)

Many times we need to force the user to enter a certain value that we are looking for. This is especially true when we need to validate the users input before continuing on with the program.

The != operator (not equal) is very useful for this task.The flowchart below asks the user to enter a specific character from the menu. If the condition is met (the user didn’t enter an A, B or C) the true path is chosen. If the condition is not met (user entered an A, B or C) the false path is taken.

Note: We use AND rather than OR here because all conditions need to evaluate to true. For example, they didn’t enter any of the valid inputs (A, B and C).

Nested If (a condition within a condition)

Flowgorithm Examples

At times we may need to test for a certain condition, and then run a further test on another condition. However, if we want the program to be able to keep track of these individual evaluations we will need a nested conditional statement.

Flowgorithm Call

Think of this as an if statement inside another if statement.

In a previous section we were evaluating if a person was old enough to vote AND was enrolled to vote. The condition action table looked like the following:

In this case we can only respond to the two conditions:

• Either the user is old enough to vote and is enrolled
• Resulting in message: “Go vote”
• Or one of the conditions is false
• Resulting in the message: “Sorry, not yet”

If we want to be able target each individual condition, we will need a nested structure.