Easy2Siksha.com
   2022
/  
 
(    , ++    )
 : 3   :75
:     ,            
          
-
1.   ?   -     ?       
 ?          
2.         ?       ?
            ?
               

-
3.              ?  
          ? 
4. (A)        
(B)     ?      
Easy2Siksha.com
-
5.    ?            
      
6.    ?       ?   
              
   
-
7.   ?    ?         
C    
8. (A)       ?     

(B)   ?        ?      
  C++        ,      
           ?
Easy2Siksha.com
   2022
/  
 
(    , ++    )
 : 3   :75
:     ,            
          
-
1.   ?   -     ?       
 ?          
:󷈷󷈸󷈹󷈺󷈻󷈼  ?
                   
    :
  10      , 10 -    ,
       
     -   
    ( )        
  ,   5      :
[0] [1] [2] [3] [4]
   0     , 1  
  :
 1,  2,  3,  4,  5
Easy2Siksha.com
    :
[5]
, -  !
󺬣󺬡󺬢󺬤    
          , ,
          
󷄧󷄫 
     -   :      
󷄧󷄬
                    
     ,           - 
        
󷄧󷄭
            ,    
       
󷄧󷄮
                 :
   (-   )
  (           )
󷄰󷄯 
Easy2Siksha.com
         :      
 
󽆤  
         :
󷷷󷷸1.   
               

󷷷󷷸2.   ( )
    ,           
           
󷷷󷷸3.  
              ,     
  
󷷷󷷸4.    (-    )
 -      ,          

󽆱  
          ,         
󷷹󷷺1.  
         ,         
  ,     !         ,
   
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󷷹󷷺2.     
          ,      
  
󷷹󷷺3.    
         ( ,  , )     
  
󼩏󼩐󼩑      
       ,            

          5   ,     
            
   
     
󽆤:      
 :
A  
n   
pos         
       
:
󷄧󷄫
󷄧󷄬                  
󷄧󷄭i = n – 1  
󷄧󷄮  i >= pos    
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 A[i] A[i + 1]   
i 1  
󷄰󷄯 pos    A[pos] = 
󷄧󷄱n 1   (        )
󷄧󷄲
  !         
󷘹󷘴󷘵󷘶󷘷󷘸   
                 :
       
              
2.         ?       ?
            ?
               

:󷈷󷈸󷈹󷈺󷈻󷈼
            , ,  
  -           , 
               ,
           ,     

󷷑󷷒󷷓󷷔               
              ,
                 
  (  )            
      
󷈷󷈸󷈹󷈺󷈻󷈼  ?
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:      ,        
   
:  ( 25, 100),  (" "), ,  ,      
                 

󷷑󷷒󷷓󷷔    ""   , ,           
     
󷈷󷈸󷈹󷈺󷈻󷈼   ?
:            
        
              
   
󷷑󷷒󷷓󷷔:       ( ,  )   
( ,    )             , 
  -   ,            
󷈷󷈸󷈹󷈺󷈻󷈼   
         :
1.   
         
: ,  , , 
    ,         
2. -  
              :
a)   
   ,       
:
o :     
o  :   ,  
o : LIFO ( ,  )    
o : FIFO ( ,  )    
󷷑󷷒󷷓󷷔               
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b) -  
        ;      
:
o :  (  )
o : (    )      
󷷑󷷒󷷓󷷔-                
c) - 
            
:       
󷷑󷷒󷷓󷷔              
󷈷󷈸󷈹󷈺󷈻󷈼       ?
            ,    :  
      ?
       -         ,
              
             
  :
1.  :         
2.  :       
󷷑󷷒󷷓󷷔:         
    -   ,      (  )
    (  )     ,     
            
󷈷󷈸󷈹󷈺󷈻󷈼        ?
1.     :
o         (, )    
2.   (n):
o           
o : n       
3.  ,     :
o   :     (  , 
        )
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o  :  (  ,      )
o  :     
󷷑󷷒󷷓󷷔                

󷈷󷈸󷈹󷈺󷈻󷈼         
    ,            
                 
1.   (O)
   (  )  
:      O(n).
:        
󷷑󷷒󷷓󷷔 "  "     
2.   (Ω)
   ( )  
:             Ω(1).
󷷑󷷒󷷓󷷔  "          "
3.   (Θ)
   ( )  
:    Θ(log n).
󷷑󷷒󷷓󷷔  "          "
󹶓󹶔󹶕󹶖󹶗󹶘  
       :
     -     ,  O(n) 
        3    ,  Ω(1)—
           ,  Θ(n/2)—
                 
         
󹵍󹵉󹵎󹵏󹵐 
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



   
 , , 
 
      

, , 
 
 
, 
 
/
, 


 
  
 ()
  
     O(n)
 (Ω)
 
    Ω(1)
 (Θ)
 
    
Θ(log n)
󷇮󷇭 
                
            ;      
                
 
 ,          ,      
,                  
 
-
3.              ?   
           ? 
:󷄧󼿒   ?
                
 :
FIFO –  ,  
   ,         :
       =       
      =    
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  :
   ()   
     
    :
        
       
󷄧󼿒  
      :
󷄧󷄫 (    )
                ?
󷷑󷷒󷷓󷷔   
         :
10, 20, 30
:
 → 10
 → 30
  40  ,  30     :
10, 20, 30, 40
   40  
                ,   
 ,      :
󽆱 
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󷄧󷄬 ( )
              ?
󷷑󷷒󷷓󷷔    
 :
10, 20, 30, 40
      :
10   
   20  
 :
20, 30, 40
               :
󽆱   
󷄧󼿒  



        

      

   ;     
 
  ;    
󷄧󼿒      ?
     ;         :󷄧󷄫󷄧󷄬

      
󽇐     
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                  , 5
         5  
: 0 1 2 3 4
: - - - - -
   :
   
    
:
 = -1
 = -1
󷷑󷷒󷷓󷷔    ()
:
1.         
2.     
3.      
4.      
5.       , = 0  
: 10 
 = 0
 = 0
: 10 - - - -
20 
 = 0
 = 1
: 10 20 - - -
30 
 = 0
 = 2
: 10 20 30 - -
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󷷑󷷒󷷓󷷔     ()
:
1.       
2.   
3.     
4.  
:
10 20 30
 = 0
 = 2
 10   
 = 1
 = 2
: - 20 30 - -
󽁔󽁕󽁖    
10    ,               
     ,    ,      
     ,         ,     
,  :
   
      
  
󽇐      
                   :

  
       :
Easy2Siksha.com
          
         
  :
    
    
   
󷷑󷷒󷷓󷷔    
:
1.     
2.   
3.     
4.         
5.    ,        
: 10 
→ 10 → 
 → 10
20 
→ 10 → 20 → 
 → 20
30 
→ 10 → 20 → 30 → 
 → 30
󷷑󷷒󷷓󷷔    
:
1.       
2.      
3.      
4.    
Easy2Siksha.com
10 :
: 10 → 20 → 30
 : 20 → 30
 → 20
       :
NULL  
  
  
󷄧󼿒        

 





   


  

󷘹󷘴󷘵󷘶󷘷󷘸           ?
           
:
󽆤,  ,     
󽆤 
󽆤  
󽆤    
󽆤  
󽆤  
󽆤     
         
󽇐 
Easy2Siksha.com
    
 FIFO (   )    
       
     
 :   
        :
 (    )
  (  )
4. (A)        
(B)     ?      
:󷈷󷈸󷈹󷈺󷈻󷈼
           
      ,      
             
      
                    ,
               
  ,           
󷈷󷈸󷈹󷈺󷈻󷈼 :   
1.    ?
   --             
         ""     ,     
  ,           
󷷑󷷒󷷓󷷔          :   
      (),    
    
  ,
                   
 
2.    
1.   :     (  ,     )
Easy2Siksha.com
2. :             

      

3. :   -      
4.  : -        ,       
3.    
    : [35, 12, 43, 8, 51]
 1:    , 51      
 2: 
51     → [35, 12, 43, 8]
 → 51
51    → []
    : [35, 12, 43, 8] | 51 | []
 3: 
        [35, 12, 43, 8]
 = 8
8    → []
8   → [35, 12, 43]
: [] | 8 | [35, 12, 43]
 4:  [35, 12, 43]
 = 43
43    → [35, 12]
43   → []
: [35, 12] | 43 | []
 5:  [35, 12]
 = 12
12    → []
12   → [35]
: [] | 12 | [35]
4.   
  : [8, 12, 35, 43, 51]
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󷷑󷷒󷷓󷷔        -     
  
5.    
     
  : O(n log n).
-  (           )
6. 
     : O(n²) (    )
            
󷈷󷈸󷈹󷈺󷈻󷈼 :   
1.    ?
  ,        ,     
   ,     
󷷑󷷒󷷓󷷔:     3 + 4     + 3 4 
                 
    
2.    
1.    ():   
o : + 3 4 →  3 + 4.
2.   ( ):   
o : 3 4 + →    3 + 4.
  ,        ,         
   
3.     
: (5 + 6) * 7
 ()  : (5 + 6) * 7
   : * + 5 6 7
󷷑󷷒󷷓󷷔:
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 , + 5 6    5 + 6 = 11.
, * 11 7    11 * 7 = 77.
  77
4.    
: (5 + 6) * 7
  : 5 6 + 7 *
󷷑󷷒󷷓󷷔:
 , 5 6 + → 11.
, 11 7 * → 77.
 ,  77
5.    
          
          
       
󹶓󹶔󹶕󹶖󹶗󹶘  
              (5 + 6) * 7,   
    : "       ?"       
  
   * + 5 6 7  ,            :
1. 5  6  
2.  7   
󷷑󷷒󷷓󷷔            
󹵍󹵉󹵎󹵏󹵐 



 
- - 
 
[35, 12, 43, 8, 51] → [8, 12, 35,
43, 51]
  
   
* + 5 6 7
 
   
5 6 + 7 *
   
, 
O(n log n) 
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   

     
   
󷇮󷇭 
          ,        
               , 
              
-
5.    ?            
      
:   ? ( )
               ,
                    ? 
   ,     ,    ,    , 
     ,    ,          
      
           
  ,         (   ) 
- ,              -,  
   
,    :
         
      (   )
      :
25, 10, 55, 30, 5
        
1:
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       5
5   (25)  
     :
5, 10, 55, 30, 25
 5   
 :
            :
10, 55, 30, 25
    10 ,      
   :
5, 10, 55, 30, 25
 3:
 :
55, 30, 25
   25 
55  25  - :
5, 10, 25, 30, 55
 4:
:
30, 55
    30 ,    
 ,  55          
 ,     :
Easy2Siksha.com
5, 10, 25, 30, 55
             -    
   
              ,
   
 ():
1.      
2.           
3.                
4.        ,        
5.    
6.          
   :
i = 0  n-2 
  = i
j = i+1  n-1 
 [j] < [minIndex]
  = j
[i] [minIndex]  

      :
  
    
  
 
 
  -!
    
       : 
Easy2Siksha.com
    :
          (  )  ?
  :
   ,      (n − 1)    
   ,    (n − 2)    
  ,  (n − 3)    ,      
    :
(n − 1) + (n − 2) + (n − 3) + ... + 1
   :
n(n − 1) / 2
       :
O(n²)
        :
  = O(n²)
  = O(n²)
   = O(n²)
                  
     
 
                
   
     :
(1)
          
    
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1.     
2.        
3.       
4.        ,    
5.     (    )
   
                   ,
           -       
  ,  ?

               :
     
   
        
 ,      ,        
    O(n²)           
 ,                  
        ,         
   
6.    ?       ?   
              
   
:󷈷󷈸󷈹󷈺󷈻󷈼
                     -
     ,        ,      
      ,              
           
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          ,   ,    
          - -     
󷷑󷷒󷷓󷷔    :          ,  
             
󷈷󷈸󷈹󷈺󷈻󷈼   ?
:                
        
            
       ,       ,    
    
󷷑󷷒󷷓󷷔 :   (    )      ,  
     
󷈷󷈸󷈹󷈺󷈻󷈼     ?
      :
1.     :
o     
o        
2.    :
o       ,   
3.    :
o          
4.    :
o         
5.     :
o        ,     

󷈷󷈸󷈹󷈺󷈻󷈼   
       : [5, 12, 23, 34, 45, 56, 67, 78, 89]
 45      
1:  = 34 ( 3)
 45 > 34. ,      
 : - = [45, 56, 67, 78, 89].
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  = 67.
 45 < 67. ,      
 3: - = [45, 56].
  = 56.
 45 < 56. ,      
 4: - = [45].
  = 45.
  4   
󷷑󷷒󷷓󷷔:       45  
󷈷󷈸󷈹󷈺󷈻󷈼    (-  )

int binarySearch(int arr[], int n, int target) {
int  = 0;
int high = n - 1;
 ( <= ) {
int mid = (low + high) / 2;
 (arr[mid] == )
 ; //   
  (arr[mid] < )
 =  + 1; //     

 =  - 1; //      
}
-1  ; //   
}
󷷑󷷒󷷓󷷔         
󷈷󷈸󷈹󷈺󷈻󷈼    
          :
:  
1.    :  = 0   = n - 1.
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2.              : a.    :  =
(  +  ) / 2. b.  arr[ ] ==  ,    c. 
arr[ ] <  ,     + 1    d.  arr[ ] >
 ,     - 1   
3.     , -1 
󷈷󷈸󷈹󷈺󷈻󷈼    
    78  : [5, 12, 23, 34, 45, 56, 67, 78, 89]
 1:
o  = 0,  = 8,  = 4.
o arr[mid] = 45.  78 > 45.
o  :  = 5,  = 8.
 2:
o  = (5 + 8) / 2 = 6.
o arr[mid] = 67.  78 > 67.
o  :  = 7,  = 8.
 3:
o  = (7 + 8) / 2 = 7.
o arr[mid] = 78.   .
󷷑󷷒󷷓󷷔:  78  7   
󷈷󷈸󷈹󷈺󷈻󷈼    
 :
o  : O(1) (    )
o   : O(log n) (         )
o  : O( n).
 :
o  : O(1).
o  : O(log n) (    )
󷷑󷷒󷷓󷷔 ,   (O(n))     
󹶓󹶔󹶕󹶖󹶗󹶘  
   1  100             
 ,               
 ,           50   ,
 75 ,  62 ,        7      
 
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󷷑󷷒󷷓󷷔               
       
󹵍󹵉󹵎󹵏󹵐 



1
   
   
2
 
  
3
  
      
4
 
      
5
 
     
󷇮󷇭 
                
        ,       
        ,         -
     
-
7.   ?    ?         
C    
:󹲉󹲊󹲋󹲌󹲍  ?
       ,   -   -  
      , ""      
   
     
   
  ,         -      
  
       :
= 
= 
,     "       "
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  ,    ,        -
           ,       
           -  
 ,            
󼪍󼪎󼪏󼪐󼪑󼪒󼪓  
 ,       :
󷄧󷄫-  ( )
             ,
              :
  
  
, C  C++              
   C      -   
 C++       
󷄧󷄬-  (  )
,         ,         
  C++  OOP            
  , C          , C    , 
              
      C     "  "     
,   C  -   
󼩼󼩽󼩾󼪀󼩿 C      ?
 C  C++      ,        :

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 
 -   ,            
         
    ,       :     -
    :


    "   ",   -       :
draw(),         
   C    
󷄧󼿒     
                 
 :
#include <stdio.h>
//     
 () {
printf("  \n");
}
//     
drawRectangle() {
printf("    \n");
}
//     
  {
 (* )(); //  
};
 () {
//   
  1;
  2;
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//    
 1. =   ;
2. =   ;
//        - 
printf("  1: ");
 1. ();
printf("  2: ");
2. ();
0  ;
}
󹴞󹴟󹴠󹴡󹶮󹶯󹶰󹶱󹶲   (  )
        :
󷄧󷄫 ,  stdio.h          printf 
  
󷄧󷄬  :
drawCircle() → “     
drawRectangle() →      
    -    
󷄧󷄭        :
(* )();
    :
      
                
 
    draw
          -     -
   
󷄧󷄮main() :    
:
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  1;
  2;
󷄰󷄯    :
 1. =   ;
2. =   ;
:
 shape1     
shape2       
󷄧󷄱 ,    :
 1. ();
2. ();
  draw()          ,    -

   -  !    - 
     :
  1:   
  2:  
󷘹󷘴󷘵󷘶󷘷󷘸   ?
      :
󽆤    
󽆤    :     
󽆤    
󽆤              
󽆤    
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8. (A)       ?     

(B)   ?        ?      
  C++        ,      
           ?
:󷈷󷈸󷈹󷈺󷈻󷈼
C++       -   (OOP)   
OOP         / 
    -         ( +, -, *)
       ,    OOP       
         
󷷑󷷒󷷓󷷔    :            ,
          
󷈷󷈸󷈹󷈺󷈻󷈼 :    
1.    ?
   C++       -   
        
 , +  -     (,  )      
                
󷷑󷷒󷷓󷷔:       ,  c1 + c2    
       +      
2.       ?
       
c1.add(c2)   ,   c1 + c2  
          
3.    

#include <iostream>
     ;
  {
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, ;
:
 ( r = 0, i = 0) {
 = r;
 = i;
}
// +    
  + (  &obj) {
 ;
. =  + .;
. =  + .;
  ;
}
 () {
cout << real << " + " << image << "i" << endl;
}
};
 () {
 c1(3, 4), c2(1, 2);
Complex c3 = c1 + c2; //   +     
c3.display(); // : 4 + 6i
0  ;
}
4.   
         
       +    
  c1 + c2  ,       ,  
  
 4 + 6i      
󷷑󷷒󷷓󷷔             

󷈷󷈸󷈹󷈺󷈻󷈼 B:   
1.   ?
          
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  (  )   ( )   
:     ,     ()  ()  
 
󷷑󷷒󷷓󷷔     ,         
      
2.   ?
      
             

:  Car   , myCar     =    =
120 / 
3.      
     ;      
          ,   

         ,       -
 
󷷑󷷒󷷓󷷔:  =   = , ,    ,     
-
4. ++   

#include <iostream>
     ;
//    
 {
 ;
;
:
//       
 ( ,  ) {
 = ;
 = ;
}
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//       
 () {
cout << ": " <<  << ", : " <<  << endl;
}
};
 () {
//    
 s1, s2;
//    
s1.setData("", 20);
s2.setData("", 19);
//    
s1.display(); // : : , : 20
s2.display(); // : : , : 19
0  ;
}
5.   
            
 s1  s2   
      ,        
   -  ,         
  
󷷑󷷒󷷓󷷔         ,      
 
󷈷󷈸󷈹󷈺󷈻󷈼      




/
   

,     
,    


 ,  

   
 
     
 
󹶓󹶔󹶕󹶖󹶗󹶘  
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             ,  
  ,           ,   
     ,       
󷷑󷷒󷷓󷷔 ,   ,    
󷈷󷈸󷈹󷈺󷈻󷈼 
   -     
     ,         
  OOP   ,        
     
    C++ ,        
󷷑󷷒󷷓󷷔 :          ,   
       
             
       ,       