Basic of programming

The recurrent formula

Example

To do: Calculate an addition of the sequence from 1 to n (n is entered).

expected output:

N=5
1+2+3+4+5=15
result:

function sum(n: integer): integer;
begin
if n=1 then result:=1;
if n>1 then result:=n+sum(n-1);
end;

begin
var n:=readinteger('input n to make a sequence [1..n]');
print(sum(n))
end.

Example

To do: 

Output the binary code of the number

result:

Example

To do: Calculating the sum of the digits of a number

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• The recurrent formula (ratio) determines the value of the current member of the sequence through one or more preceding ones. 
• One or more initial members of the sequence must be defined.

Recursion – pros and cons

with each new call, stack memory is consumed (stack overflow is possible), the cost of performing service operations during a recursive call

{0.5} Task 1:

To do: Write a recursive real-valued function Fact(N) that returns the value of N-factorial: N! = 1·2·…·N, where N (> 0) is an integer parameter. Using this function, output factorials of five given integers.

Expected output:

Please enter the distance in centimeters
>>> 245
The distance in meters is  2 

[Program name: Recur1.pas]

{0.5} Task 2:

To do: Recur2. Write a recursive real-valued function Fact2(N) that returns the value of double factorial of N: N!! = N·(N−2)·(N−4)·…, where N (> 0) is an integer parameter; the last factor of the product equals 2 if N is an even number, and 1 otherwise. Using this function, output double factorials of five given integers.

Please enter the distance in centimeters
>>> 245
The distance in meters is  2 

[Program name: Recur2.pas]