## Introduction

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

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

### To Lower

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

--  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

```  --  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

### Fibonacci numbers

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

#### Simple Implementation

```...
```

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

```...
```

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 :=
```

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;
elsif 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

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

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