# Ada Programming/Algorithms

Welcome to the Ada implementations of the Algorithms Wikibook. For those who are new to Ada Programming a few notes:

- All examples are fully functional with all the needed input and output operations. However, only the code needed to outline the algorithms at hand is copied into the text - the full samples are available via the download links. (Note: It can take up to 48 hours until the cvs is updated).
- We seldom use predefined types in the sample code but define special types suitable for the algorithms at hand.
- Ada allows for default function parameters; however, we always fill in and name all parameters, so the reader can see which options are available.
- We seldom use shortcuts - like using the attributes Image or Value for String <=> Integer conversions.

All these rules make the code more elaborate than perhaps needed. However, we also hope it makes the code easier to understand

## Chapter 1: Introduction[edit]

The following subprograms are implementations of the *Inventing an Algorithm* examples.

### To Lower[edit]

The Ada example code does not append to the array as the algorithms. Instead we create an empty array of the desired length and then replace the characters inside.

`function`

To_Lower (C : Character)`return`

Character`renames`

Ada.Characters.Handling.To_Lower; -- tolower - translates all alphabetic, uppercase characters—in str to lowercase`function`

To_Lower (Str : String)`return`

String`is`

Result : String (Str'Range);`begin`

`for`

C`in`

Str'Range`loop`

Result (C) := To_Lower (Str (C));`end`

`loop`

;`return`

Result;`end`

To_Lower;

Would the append approach be impossible with Ada? No, but it would be significantly more complex and slower.

### Equal Ignore Case[edit]

—equal-ignore-case—returns true if s or t are equal,

-- ignoring case`function`

Equal_Ignore_Case (S : String; T : String)`return`

Boolean`is`

O :`constant`

Integer := S'First - T'First;`begin`

`if`

T'Length /= S'Length`then`

`return`

False; -- if they aren't the same length, they—aren't equal`else`

`for`

I`in`

S'Range`loop`

`if`

To_Lower (S (I)) /= To_Lower (T (I + O))`then`

`return`

False;`end`

`if`

;`end`

`loop`

;`end`

`if`

;`return`

True;`end`

Equal_Ignore_Case;

## Chapter 6: Dynamic Programming[edit]

### Fibonacci numbers[edit]

The following codes are implementations of the Fibonacci-Numbers examples.

#### Simple Implementation[edit]

...

To calculate Fibonacci numbers negative values are not needed so we define an integer type which starts at 0. With the integer type defined you can calculate up until `Fib (87)`

. `Fib (88)`

will result in an `Constraint_Error`

.

`type`

Integer_Type`is`

`range`

0 .. 999_999_999_999_999_999;

You might notice that there is not equivalence for the `assert (n >= 0)`

from the original example. Ada will test the correctness of the parameter *before* the function is called.

`function`

Fib (n : Integer_Type)`return`

Integer_Type`is`

`begin`

`if`

n = 0`then`

`return`

0;`elsif`

n = 1`then`

`return`

1;`else`

`return`

Fib (n - 1) + Fib (n - 2);`end`

`if`

;`end`

Fib; ...

#### Cached Implementation[edit]

...

For this implementation we need a special cache type can also store a -1 as "not calculated" marker

`type`

Cache_Type`is`

`range`

-1 .. 999_999_999_999_999_999;

The actual type for calculating the fibonacci numbers continues to start at 0. As it is a `subtype`

of the cache type Ada will automatically convert between the two. (the conversion is - of course - checked for validity)

`subtype`

Integer_Type`is`

Cache_Type`range`

0 .. Cache_Type'Last;

In order to know how large the cache need to be we first read the actual value from the command line.

` Value : ``constant`

Integer_Type :=
Integer_Type'Value (Ada.Command_Line.Argument (1));

The Cache array starts with element 2 since Fib (0) and Fib (1) are constants and ends with the value we want to calculate.

`type`

Cache_Array`is`

`array`

(Integer_Type`range`

2 .. Value)`of`

Cache_Type;

The Cache is initialized to the first valid value of the cache type — this is `-1`

.

` F : Cache_Array := (``others`

=> Cache_Type'First);

What follows is the actual algorithm.

`function`

Fib (N : Integer_Type)`return`

Integer_Type`is`

`begin`

`if`

N = 0`or`

`else`

N = 1`then`

`return`

N;`elsif`

F (N) /= Cache_Type'First`then`

`return`

F (N);`else`

F (N) := Fib (N - 1) + Fib (N - 2);`return`

F (N);`end`

`if`

;`end`

Fib; ...

This implementation is faithful to the original from the Algorithms book. However, in Ada you would normally do it a little different:

when you use a slightly larger array which also stores the elements 0 and 1 and initializes them to the correct values

`type`

Cache_Array`is`

`array`

(Integer_Type`range`

0 .. Value)`of`

Cache_Type; F : Cache_Array := (0 => 0, 1 => 1,`others`

=> Cache_Type'First);

and then you can remove the first `if`

path.

`if`

N = 0`or`

`else`

N = 1`then`

`return`

N; els`if`

F (N) /= Cache_Type'First`then`

This will save about 45% of the execution-time (measured on Linux i686) while needing only two more elements in the cache array.

#### Memory Optimized Implementation[edit]

This version looks just like the original in WikiCode.

`type`

Integer_Type`is`

`range`

0 .. 999_999_999_999_999_999;`function`

Fib (N : Integer_Type)`return`

Integer_Type`is`

U : Integer_Type := 0; V : Integer_Type := 1;`begin`

`for`

I`in`

2 .. N`loop`

Calculate_Next :`declare`

T :`constant`

Integer_Type := U + V;`begin`

U := V; V := T;`end`

Calculate_Next;`end`

`loop`

;`return`

V;`end`

Fib;

#### No 64 bit integers[edit]

Your Ada compiler does not support 64 bit integer numbers? Then you could try to use decimal numbers instead. Using decimal numbers results in a slower program (takes about three times as long) but the result will be the same.

The following example shows you how to define a suitable decimal type. Do experiment with the `digits`

and `range`

parameters until you get the optimum out of your Ada compiler.

`type`

Integer_Type`is`

`delta`

1.0`digits`

18`range`

0.0 .. 999_999_999_999_999_999.0;

You should know that floating point numbers are unsuitable for the calculation of fibonacci numbers. They will not report an error condition when the number calculated becomes too large — instead they will lose in precision which makes the result meaningless.