DESCRIBING ALGORITHMS

1.

Informal English description

2.

Formal English description

3.

Pseudo-Code

4.

Code in programming lanuage (e.g., C++)

 


SORTING EXAMPLE for Array 1..n
 
I. Informal Description

• Find the smallest number and put it in the first position
• Find the second smallest number and put it in the second position
• Continue as above until the array is sorted

II. Formal Description

1.

Set i := 1

2.

Find the smallest number between positions i and n

3.

Swap the number at i with the smallest number

4.

Set i := i+1

5.

if  i  < n  go back to 2, otherwise quit

 


Pseudo-Code

procedure sort(intArray A[1..n])  
   for   $i \in [1..n-1] ~~\rightarrow$  
      pos  :=  i 
   for   $j \in [i+1..n] ~~ \rightarrow$  
      if   $A[j] ~<~ A[pos] ~~ \rightarrow$  
         pos  :=  j
      fi  
   rof
      swap(A[i], A[pos])  
   rof
end sort 

EXPONENTIATION

INCREMENTAL

function exp(int a, int p) returns int  
   if  $p ~ \leq ~0~~\rightarrow$   return  1 
   |  $p ~\gt ~0~ ~\rightarrow$  
      val  :=  a 
      for $i \in [1..p-1] ~~ \rightarrow$  
         val  :=  val*a  
      rof  
   fi 
   return val  
end exp 

EXPONENTIATION

DIVIDE-AND-CONQUER

function exp(int a, int p) returns int  
   if  $p ~ \leq ~0~~\rightarrow$   return  1 
   |  $p ~\gt ~0~ ~\rightarrow$  
      val  :=  exp(a, p/2) 
      if p is even     $\rightarrow$  
         return  val*val  
      |  p is odd     $\rightarrow$  
         return  val*val*a  
      fi 
   fi 
end exp